API

The TMDybinidng package consists of several base lattices, objects to store the parameters for these lattices, functions to build the matrices associated to the hoppings of that model and classes that help user in defining new lattices with (rotational) symmetric aspects for orbitals of non-zero ml-quantum number.

Base lattices

Tight-binding lattices for TMDs for the Pybinding-package.

AbstractLattice

Bases: ABC

Abstract class for a tmd-lattice

Source code in tmdybinding/tmd_abstract_lattice.py

class AbstractLattice(ABC):
    """Abstract class for a tmd-lattice"""

    def __init__(self, orbital: LatticeOrbitals, params: ParametersList, soc: bool = False,
                 soc_eo_flip: bool = False, lat4: bool = False, single_orbital: bool = False, soc_sz_part: bool = True,
                 soc_polarized: bool = False, soc_sz: float = 1.,
                 n_v: int = 0, n_b: int = 0, lattice_name: str = "Abstract Lattice"):
        """Make an AbstractLattice object with the given parameters.

        Parameters:
            orbital (LatticeOrbitals): The orbitals for the lattice model.
            params (ParametersList): The parameters for the lattice model.
            soc (bool): If True, the spin-orbit coupling is considere.
            soc_eo_flip (bool): If True, the spin-flip term is included.
            lat4 (bool): If True, the lattice is a 4-atom lattice for use with the armchair direction.
            single_orbital (bool): If True, the lattice is a combination of suborbitals (slower as no matrices are used)
            soc_sz_part (bool): If False, the hamiltonian will not include the Sz part of the spin-orbit coupling.
            soc_polarized (bool): If True, the spin-orbit coupling is polarized (only spin-up part, given by `soc_sz`).
            soc_sz (float): The Sz part of the spin-orbit coupling.
            n_v (int): The index of the highest valence band (in the unitcell).
            n_b (int): The number of bands (in the unitcell).
            lattice_name (str): The name of the lattice. The name of the matrial is obtained from `params`.
        """
        self.lattice_params = VariableStorage()
        self.orbital: LatticeOrbitals = orbital
        self.__n_valence_band: int = n_v
        self.__n_bands: int = n_b
        self.__name: str = "MoS2"
        self.__x_name: str = "S"
        self.__x_type: str = "X"
        self.__m_name: str = "Mo"
        self.__m_type: str = "M"
        self.__params: ParametersList = ParametersList()
        self.__soc_eo_flip: bool = False
        self.__lattice_name: str = lattice_name
        self._lat4: bool = lat4
        self.single_orbital: bool = single_orbital
        self.soc: bool = soc
        self.soc_polarized: bool = soc_polarized
        self.soc_sz_part: bool = soc_sz_part
        self.sz: float = soc_sz
        self.params = params
        self.soc_eo_flip = soc_eo_flip

    @property
    def soc_eo_flip(self) -> bool:
        """If True, the spin-flip term is included.
        The structure is checked for the right shape and properties that it supports a spin-flip term.
        """
        return self.__soc_eo_flip

    @soc_eo_flip.setter
    def soc_eo_flip(self, pol_bool: bool):
        if pol_bool:
            if self.lattice_params.h_0_m is not None:
                assert len(self.orbital.l_number[self.orb_type(self.m_name)]) == 5, \
                    "the metal doesn't have the right shape for spin-flip term"
                assert sorted(self.orbital.l_number[self.orb_type(self.m_name)]) == sorted([0, 2, -2, 1, -1]), \
                    "the metal l is wrong for spin-flip"
            if self.lattice_params.h_0_c is not None:
                assert len(self.orbital.l_number[self.orb_type(self.x_name)]) == 6, \
                    "the chal. doesn't have the right shape for spin-flip term"
                assert sorted(self.orbital.l_number[self.orb_type(self.x_name)]) == sorted([1, -1, 0, 1, -1, 0]), \
                    "the chal. l is wrong for spin-flip"
        self.__soc_eo_flip = pol_bool

    @property
    def params(self) -> ParametersList:
        """The parameters for the lattice model."""
        return self.__params

    @params.setter
    def params(self, params: ParametersList):
        self.__params = params
        self.name = self.params["material"]

    @property
    def lattice_name(self) -> str:
        """The name of the lattice. This is not the name of the material."""
        return self.__lattice_name

    @lattice_name.setter
    def lattice_name(self, lattice_name: str):
        self.__lattice_name = lattice_name

    @property
    def name(self) -> str:
        """The name of the material."""
        return self.__name

    @property
    def m_name(self) -> str:
        """The name of the metal atom."""
        return self.__m_name

    def orb_type(self, z_name: str) -> Optional[str]:
        """Return the orbital type of the atom with the given name. Usefull for the case when `lat4` is True.
        Returns `"M"` for the metal atom and `"X"` for the chalcogen atom.
        """
        if z_name == self.m_name or (self.lat4 and z_name == self.m_name + "2"):
            return self.__m_type
        elif z_name == self.x_name or (self.lat4 and z_name == self.x_name + "2"):
            return self.__x_type
        else:
            return None

    def z_name(self, orb_type: str) -> Optional[str]:
        """Return the name of the atom with the given orbital type, for example, obtain `"S"` from `"X"` in the case
        the material is `"MoS2"`.
        """
        if orb_type == self.__m_type:
            return self.m_name
        elif orb_type == self.__x_type:
            return self.x_name
        else:
            return None

    @property
    def x_name(self) -> str:
        """The name of the chalcogen atom."""
        return self.__x_name

    @name.setter
    def name(self, name: str):
        self.__name = name
        self.__m_name, self.__x_name = re.findall("[A-Z][a-z]*", self.name)
        self._generate_matrices()

    @property
    def lat4(self) -> bool:
        """If True, the lattice is a 4-atom lattice for use with the armchair direction."""
        return self._lat4

    @lat4.setter
    def lat4(self, lat4: bool):
        self._lat4 = lat4
        self._generate_matrices()

    @property
    def a1(self) -> np.ndarray:
        """The first lattice vector. Corrected if `lat4` is True."""
        return np.array([1, 0]) * self.lattice_params.a

    @property
    def a2(self) -> np.ndarray:
        """The second lattice vector. Corrected if `lat4` is True."""
        return (np.array([0, np.sqrt(3)]) if self.lat4 else np.array([-1 / 2, np.sqrt(3) / 2])) * self.lattice_params.a

    @property
    def soc_doubled_ham(self) -> bool:
        """If True, the hamiltonian is doubled for the spin-orbit coupling."""
        return not self.soc_polarized if self.soc else False

    @property
    def soc_eo_flip_used(self) -> bool:
        """If True, the spin-flip term is used."""
        return self.soc and self.soc_eo_flip and not self.soc_polarized

    @property
    def n_valence_band(self) -> int:
        """The index of the highest valence band. Corrected for the SOC and `lat4`."""
        return (self.__n_valence_band + 1) * 2 - 1 if self.soc_doubled_ham else self.__n_valence_band

    @property
    def n_bands(self) -> int:
        """The total number of bands. Corrected for the SOC and `lat4`."""
        return self.__n_bands * (2 if self.soc_doubled_ham else 1)

    @property
    def _m_orbs(self) -> List[str]:
        m_orbs = [self.m_name + mi for mi in self.orbital.orbs[self.orb_type(self.m_name)]]
        if self.soc_doubled_ham:
            m_orbs = [mi + "u" for mi in m_orbs] + [mi + "d" for mi in m_orbs]
        return m_orbs

    @property
    def _m2_orbs(self) -> List[str]:
        m2_orbs = [self.m_name + "2" + mi for mi in self.orbital.orbs[self.orb_type(self.m_name)]]
        if self.soc_doubled_ham:
            m2_orbs = [mi + "u" for mi in m2_orbs] + [mi + "d" for mi in m2_orbs]
        return m2_orbs

    @property
    def _c_orbs(self) -> List[str]:
        c_orbs = [self.x_name + ci for ci in self.orbital.orbs[self.orb_type(self.x_name)]]
        if self.soc_doubled_ham:
            c_orbs = [ci + "u" for ci in c_orbs] + [ci + "d" for ci in c_orbs]
        return c_orbs

    @property
    def _c2_orbs(self) -> List[str]:
        c2_orbs = [self.x_name + "2" + ci for ci in self.orbital.orbs[self.orb_type(self.x_name)]]
        if self.soc_doubled_ham:
            c2_orbs = [ci + "u" for ci in c2_orbs] + [ci + "d" for ci in c2_orbs]
        return c2_orbs

    @staticmethod
    def _make_name(h_name: str, n_i: int, nfi: str, ntj: str) -> str:
        return h_name + "-" + str(n_i) + "-" + nfi + "-" + ntj

    @staticmethod
    def _separate_name(h_name_i) -> Tuple[str, int, str, str]:
        out = re.findall("[^-]+(?:[^-]*)*", h_name_i)
        assert len(out) == 4, "The given string isn't generated by the right function, the length isn't 4"
        out[1] = int(out[1])
        return str(out[0]), int(out[1]), str(out[2]), str(out[3])

    @abstractmethod
    def _generate_matrices(self):
        """Generate the matrices for the lattice model.
        This function should be implemented in the child class.
        """
        pass

    @staticmethod
    def _ham(h: np.ndarray, ur_l: np.ndarray, ur_r: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        return h, ur_l.dot(h.dot(ur_r.T)), ur_l.T.dot(h.dot(ur_r))

    @staticmethod
    def _reorder(matrix: np.ndarray, keys: Tuple[List[int], List[int]]) -> np.ndarray:
        return np.array([[matrix[xi, yi] for yi in keys[1]] for xi in keys[0]])

    def block_diag(self, *matrices) -> np.ndarray:
        """Make a block diagonal matrix from the given matrices."""
        if len(matrices) == 1:
            return matrices[0]
        else:
            matrix0 = matrices[0]
            matrix1 = self.block_diag(*matrices[1:])
            shape_0 = np.shape(matrix0)
            shape_1 = np.shape(matrix1)
            z_1 = [shape_0[-2], shape_1[-1]]
            z_2 = [shape_1[-2], shape_0[-1]]
            nd = len(shape_0)
            assert nd == len(shape_1), "The matrices don't have the right sizes in the additional dimensions"
            if nd > 2:
                for sh in shape_1[:-2]:
                    z_1.insert(0, sh)
                    z_2.insert(0, sh)
            return np.concatenate((np.concatenate((matrix0, np.zeros(z_1)), axis=nd - 1),
                                   np.concatenate((np.zeros(z_2), matrix1), axis=nd - 1)), axis=nd - 2)

    def _make_onsite(self, matrix, name, lamb):
        def ham_sz(sz):
            if self.soc_sz_part:
                s_part = sz * lamb * 1j * self.orbital.s_h[self.orb_type(name)]
                return matrix + s_part
            else:
                return np.array(matrix, dtype=complex)

        if self.soc:
            if self.soc_polarized:
                return ham_sz(self.sz)
            else:
                return self.block_diag(ham_sz(self.sz), ham_sz(-self.sz))
        else:
            return ham_sz(0.)

    def _make_h(self, matrix, from_name, to_name):
        (h_1, h_2, h_3) = self._ham(matrix,
                                    self.orbital.ur[self.orb_type(to_name)],
                                    self.orbital.ur[self.orb_type(from_name)])
        if self.soc_doubled_ham:
            h_1 = np.kron(np.eye(2), h_1)
            h_2 = np.kron(np.eye(2), h_2)
            h_3 = np.kron(np.eye(2), h_3)
        return h_1, h_2, h_3

    def _make_h_angle(self, matrix, from_name, to_name, angle):
        (h_1, h_2, h_3) = self._ham(matrix,
                                    self.orbital.ur_angle(angle)[self.orb_type(to_name)],
                                    self.orbital.ur_angle(angle)[self.orb_type(from_name)])
        return h_1, h_2, h_3

    def _add_hopping(self, lat, mat, f_n, t_n, cos, fnl, tnl, h_name):
        hn = self._make_h(mat, f_n, t_n)
        n_n_n = [0, 1, 2]
        if self.lat4:
            hn = [hn[int(ih / 2)] for ih in range(6)]
            n_n_n = [0, 0, 1, 1, 2, 2]
        # n_n = 6 if self.lat4 else 3
        if self.single_orbital:
            for f_i, nf_i in enumerate(fnl):
                for t_j, nt_j in enumerate(tnl):
                    h_names = [self._make_name(h_name, n_i, nfi, ntj) for n_i, nfi, ntj in zip(n_n_n, nf_i, nt_j)]
                    lat.register_hopping_energies(dict([(h_n_i, h.conj().T[f_i, t_j]) for h_n_i, h in zip(h_names, hn)]))
                    lat.add_hoppings(*[(co, nfi, ntj, h_n_i) for co, h_n_i, nfi, ntj in zip(cos, h_names, nf_i, nt_j)])
        else:
            h_names = [self._make_name(h_name, n_i, nfi, ntj) for n_i, nfi, ntj in zip(n_n_n, fnl, tnl)]
            lat.register_hopping_energies(dict([(h_n_i, h.conj().T) for h_n_i, h in zip(h_names, hn)]))
            lat.add_hoppings(*[(co, nfi, ntj, h_n_i) for co, h_n_i, nfi, ntj in zip(cos, h_names, fnl, tnl)])
        return lat

    def lattice(self) -> pb.Lattice:
        """Make the lattice model. It returns a `pybinding.Lattice` object."""
        lat = pb.Lattice(a1=self.a1, a2=self.a2)
        m_orbs, m2_orbs = 0, 0
        c_orbs, c2_orbs = 0, 0
        if self.lattice_params.h_0_m is not None:
            m_orbs = self._m_orbs
            m2_orbs = self._m2_orbs
            h_0_m = self._make_onsite(self.lattice_params.h_0_m, self.m_name, self.lattice_params.lamb_m)
            n_m, n_c = 0, 0
            if self.soc_eo_flip_used:
                soc_part_m = np.zeros((5, 5)) * 1j
                soc_part_m[3:, :3] = self.sz * self.lattice_params.lamb_m * np.array(
                    [[np.sqrt(3) / 2, -1 / 2, 1j / 2],
                     [-1j / 2 * np.sqrt(3), -1j / 2, -1 / 2]])
                soc_part_m[:3, 3:] = -soc_part_m[3:, :3].T
                reorder_keys = [np.abs(np.array([0, 2, -2, 1, -1]) - key).argmin()
                                for key in self.orbital.l_number[self.orb_type(self.m_name)]]
                soc_part_m = self._reorder(soc_part_m, (reorder_keys, reorder_keys))
                h_0_m[:5, 5:] = soc_part_m
                h_0_m[5:, :5] = soc_part_m.conj().T

            pos_m = np.array([0, 0])
            if self.single_orbital:
                n_m = len(m_orbs)
                for i_m in range(n_m):
                    lat.add_one_sublattice(m_orbs[i_m], pos_m, np.real(h_0_m[i_m, i_m]))
                for i_m in range(n_m):
                    for j_m in np.arange(i_m + 1, n_m):
                        h_name = self._make_name("h_0_m", 0, m_orbs[i_m], m_orbs[j_m])
                        lat.register_hopping_energies(dict([(h_name, h_0_m[i_m, j_m])]))
                        lat.add_one_hopping([0, 0], m_orbs[i_m], m_orbs[j_m], h_name)
            else:
                lat.add_one_sublattice(self.m_name, pos_m, h_0_m)
            if self.lat4:
                pos_m2 = np.array([self.lattice_params.a / 2, self.lattice_params.a * np.sqrt(3) / 2])
                if self.single_orbital:
                    for i_m in range(n_m):
                        lat.add_one_sublattice(m2_orbs[i_m], pos_m2, np.real(h_0_m[i_m, i_m]))
                    for i_m in range(n_m):
                        for j_m in np.arange(i_m + 1, n_m):
                            h_name = self._make_name("h_0_m", 0, m2_orbs[i_m], m2_orbs[j_m])
                            lat.register_hopping_energies(dict([(h_name, h_0_m[i_m, j_m])]))
                            lat.add_one_hopping([0, 0], m2_orbs[i_m], m2_orbs[j_m], h_name)
                else:
                    lat.add_one_sublattice(self.m_name + "2", pos_m2, h_0_m)

        if self.lattice_params.h_0_c is not None:
            h_0_c = self._make_onsite(self.lattice_params.h_0_c, self.x_name, self.lattice_params.lamb_c)
            c_orbs = self._c_orbs
            c2_orbs = self._c2_orbs
            n_c = len(c_orbs)
            if self.soc_eo_flip_used:
                soc_part_c = np.zeros((6, 6)) * 1j
                soc_part_c[:3, 3:] = self.sz * self.lattice_params.lamb_c * np.array(
                    [[0, 0, 1 / 2],
                     [0, 0, -1j / 2],
                     [-1 / 2, 1j / 2, 0]])
                soc_part_c[3:, :3] = -soc_part_c[:3, 3:].T
                reorder_keys1 = [np.abs(np.array([1, -1, 0]) - key).argmin()
                                 for key in self.orbital.l_number[self.orb_type(self.x_name)][:3]]
                reorder_keys2 = [3 + np.abs(np.array([1, -1, 0]) - key).argmin()
                                 for key in self.orbital.l_number[self.orb_type(self.x_name)][3:]]
                soc_part_c = self._reorder(soc_part_c, (reorder_keys1 + reorder_keys2, reorder_keys1 + reorder_keys2))
                h_0_c[:6, 6:] = soc_part_c
                h_0_c[6:, :6] = soc_part_c.conj().T
            pos_c = np.array([self.lattice_params.a / 2, self.lattice_params.a * np.sqrt(3) / 6])
            if self.single_orbital:
                for i_c in range(n_c):
                    lat.add_one_sublattice(c_orbs[i_c],pos_c, np.real(h_0_c[i_c, i_c]))
                for i_c in range(n_c):
                    for j_c in np.arange(i_c + 1, n_c):
                        h_name = self._make_name("h_0_c", 0, c_orbs[i_c], c_orbs[j_c])
                        lat.register_hopping_energies(dict([(h_name, h_0_c[i_c, j_c])]))
                        lat.add_one_hopping([0, 0], c_orbs[i_c], c_orbs[j_c], h_name)
            else:
                lat.add_one_sublattice(self.x_name, pos_c, h_0_c)

            if self.lat4:
                pos_c2 = np.array([0, self.lattice_params.a * 2 * np.sqrt(3) / 6])
                if self.single_orbital:
                    for i_c in range(n_c):
                        lat.add_one_sublattice(c2_orbs[i_c], pos_c2, np.real(h_0_c[i_c, i_c]))
                    for i_c in range(n_c):
                        for j_c in np.arange(i_c + 1, n_c):
                            h_name = self._make_name("h_0_c", 0, c2_orbs[i_c], c2_orbs[j_c])
                            lat.register_hopping_energies(dict([(h_name, h_0_c[i_c, j_c])]))
                            lat.add_one_hopping([0, 0], c2_orbs[i_c], c2_orbs[j_c], h_name)
                else:
                    lat.add_one_sublattice(self.x_name + "2", pos_c2, h_0_c)

        if self.lattice_params.h_1_m is not None:
            cos = [[-1, -1], [0, 0], [-1, 0]] if not self.lat4 else [[0, -1], [0, 0], [0, 0], [1, 0], [-1, 0], [0, 0]]
            fnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [mi * 3 for mi in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2"] * 3
                )
            )
            tnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [[c2, c1, c1, c2, c1, c2] for (c1, c2) in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name + "2", self.x_name, self.x_name, self.x_name + "2", self.x_name, self.x_name + "2"]
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_1_m,
                                    f_n=self.m_name,
                                    t_n=self.x_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_1_m")

        if self.lattice_params.h_2_m is not None:
            cos = [[1, 0], [0, 1], [-1, -1]] if not self.lat4 else [[1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [0, 0]]
            fnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [mi * 3 for mi in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2"] * 3
                )
            )
            tnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [[m1, m2, m2, m1, m2, m1] for (m1, m2) in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2", self.m_name + "2", self.m_name, self.m_name + "2", self.m_name]
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_2_m,
                                    f_n=self.m_name,
                                    t_n=self.m_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_2_m")

        if self.lattice_params.h_2_c is not None:
            cos = [[1, 0], [0, 1], [-1, -1]] if not self.lat4 else [[1, 0], [1, 0], [0, 0], [-1, 1], [0, -1], [-1, 0]]
            fnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [ci * 3 for ci in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2"] * 3
                )
            )
            tnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [[c1, c2, c2, c1, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2", self.x_name + "2", self.x_name, self.x_name + "2", self.x_name]
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_2_c,
                                    f_n=self.x_name,
                                    t_n=self.x_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_2_c")

        if self.lattice_params.h_3_m is not None:
            cos = [[0, 1], [-2, -1], [0, -1]] if not self.lat4 else [[0, 0], [0, 1], [-1, -1], [-1, 0], [1, -1], [1, 0]]
            fnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [mi * 3 for mi in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2"] * 3
                )
            )
            tnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [ci * 3 for ci in zip(c2_orbs, c_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name + "2", self.x_name] * 3
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_3_m,
                                    f_n=self.m_name,
                                    t_n=self.x_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_3_m")

        if self.lattice_params.h_4_m is not None:
            _, h_4_ma, h_4_mb = self._make_h_angle(
                self.lattice_params.h_4_m, self.m_name, self.x_name, np.arctan(np.sqrt(3) / 5)
            )
            cosa = [[-1, -2], [1, 1], [-2, 0]] \
                if not self.lat4 else [[0, -1], [1, -1], [1, 0], [1, 1], [-2, 0], [-1, 0]]
            cosb = [[-2, -2], [1, 0], [-1, 1]] \
                if not self.lat4 else [[-1, -1], [0, -1], [1, 0], [2, 0], [-1, 0], [-1, 1]]
            fnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [mi * 3 for mi in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2"] * 3
                )
            )
            tnla = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [[c1, c2, c2, c1, c1, c2] for (c1, c2) in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2", self.x_name + "2", self.x_name, self.x_name, self.x_name + "2"] * 3
                )
            )
            tnlb = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [[c1, c2, c1, c2, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2", self.x_name, self.x_name + "2", self.x_name + "2", self.x_name] * 3
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=h_4_ma,
                                    f_n=self.m_name,
                                    t_n=self.x_name,
                                    cos=cosa,
                                    fnl=fnl,
                                    tnl=tnla,
                                    h_name="h_4_ma")
            lat = self._add_hopping(lat=lat,
                                    mat=h_4_mb,
                                    f_n=self.m_name,
                                    t_n=self.x_name,
                                    cos=cosb,
                                    fnl=fnl,
                                    tnl=tnlb,
                                    h_name="h_4_mb")

        if self.lattice_params.h_5_m is not None:
            cos = [[1, 2], [-2, -1], [1, -1]] if not self.lat4 else [[0, 1], [0, 1], [-2, -1], [-1, 0], [1, -1], [2, 0]]
            fnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [mi * 3 for mi in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2"] * 3
                )
            )
            tnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [[m1, m2, m2, m1, m2, m1] for (m1, m2) in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2", self.m_name + "2", self.m_name, self.m_name + "2", self.m_name]
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_5_m,
                                    f_n=self.m_name,
                                    t_n=self.m_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_5_m")

        if self.lattice_params.h_5_c is not None:
            cos = [[1, 2], [-2, -1], [1, -1]] if not self.lat4 else [[0, 1], [0, 1], [-1, -1], [-2, 0], [2, -1], [1, 0]]
            fnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [ci * 3 for ci in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2"] * 3
                )
            )
            tnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [[c1, c2, c2, c1, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2", self.x_name + "2", self.x_name, self.x_name + "2", self.x_name]
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_5_c,
                                    f_n=self.x_name,
                                    t_n=self.x_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_5_c")

        if self.lattice_params.h_6_m is not None:
            cos = [[2, 0], [0, 2], [-2, -2]] \
                if not self.lat4 else [[2, 0], [2, 0], [-1, 1], [-1, 1], [-1, -1], [-1, -1]]
            fnl = (
                (
                    [[m_i] * 3 for m_i in m_orbs]
                    if not self.lat4 else
                    [mi * 3 for mi in zip(m_orbs, m2_orbs)]
                ) if self.single_orbital else (
                    [self.m_name] * 3
                    if not self.lat4 else
                    [self.m_name, self.m_name + "2"] * 3
                )
            )
            tnl = fnl
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_6_m,
                                    f_n=self.m_name,
                                    t_n=self.m_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_6_m")

        if self.lattice_params.h_6_c is not None:
            cos = [[2, 0], [0, 2], [-2, -2]] \
                if not self.lat4 else [[2, 0], [2, 0], [-1, 1], [-1, 1], [-1, -1], [-1, -1]]
            fnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [ci * 3 for ci in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2"] * 3
                )
            )
            tnl = (
                (
                    [[c_i] * 3 for c_i in c_orbs]
                    if not self.lat4 else
                    [[c1, c2, c2, c1, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
                ) if self.single_orbital else (
                    [self.x_name] * 3
                    if not self.lat4 else
                    [self.x_name, self.x_name + "2"] * 3
                )
            )
            lat = self._add_hopping(lat=lat,
                                    mat=self.lattice_params.h_6_c,
                                    f_n=self.x_name,
                                    t_n=self.x_name,
                                    cos=cos,
                                    fnl=fnl,
                                    tnl=tnl,
                                    h_name="h_6_c")
        return lat

a1: np.ndarray property

The first lattice vector. Corrected if lat4 is True.

a2: np.ndarray property

The second lattice vector. Corrected if lat4 is True.

lat4: bool property writable

If True, the lattice is a 4-atom lattice for use with the armchair direction.

lattice_name: str property writable

The name of the lattice. This is not the name of the material.

m_name: str property

The name of the metal atom.

n_bands: int property

The total number of bands. Corrected for the SOC and lat4.

n_valence_band: int property

The index of the highest valence band. Corrected for the SOC and lat4.

name: str property writable

The name of the material.

params: ParametersList property writable

The parameters for the lattice model.

soc_doubled_ham: bool property

If True, the hamiltonian is doubled for the spin-orbit coupling.

soc_eo_flip: bool property writable

If True, the spin-flip term is included. The structure is checked for the right shape and properties that it supports a spin-flip term.

soc_eo_flip_used: bool property

If True, the spin-flip term is used.

x_name: str property

The name of the chalcogen atom.

__init__(orbital, params, soc=False, soc_eo_flip=False, lat4=False, single_orbital=False, soc_sz_part=True, soc_polarized=False, soc_sz=1.0, n_v=0, n_b=0, lattice_name='Abstract Lattice')

Make an AbstractLattice object with the given parameters.

Parameters:

Name	Type	Description	Default
orbital	LatticeOrbitals	The orbitals for the lattice model.	required
params	ParametersList	The parameters for the lattice model.	required
soc	bool	If True, the spin-orbit coupling is considere.	False
soc_eo_flip	bool	If True, the spin-flip term is included.	False
lat4	bool	If True, the lattice is a 4-atom lattice for use with the armchair direction.	False
single_orbital	bool	If True, the lattice is a combination of suborbitals (slower as no matrices are used)	False
soc_sz_part	bool	If False, the hamiltonian will not include the Sz part of the spin-orbit coupling.	True
soc_polarized	bool	If True, the spin-orbit coupling is polarized (only spin-up part, given by soc_sz).	False
soc_sz	float	The Sz part of the spin-orbit coupling.	1.0
n_v	int	The index of the highest valence band (in the unitcell).	0
n_b	int	The number of bands (in the unitcell).	0
lattice_name	str	The name of the lattice. The name of the matrial is obtained from params.	'Abstract Lattice'

Source code in tmdybinding/tmd_abstract_lattice.py

def __init__(self, orbital: LatticeOrbitals, params: ParametersList, soc: bool = False,
             soc_eo_flip: bool = False, lat4: bool = False, single_orbital: bool = False, soc_sz_part: bool = True,
             soc_polarized: bool = False, soc_sz: float = 1.,
             n_v: int = 0, n_b: int = 0, lattice_name: str = "Abstract Lattice"):
    """Make an AbstractLattice object with the given parameters.

    Parameters:
        orbital (LatticeOrbitals): The orbitals for the lattice model.
        params (ParametersList): The parameters for the lattice model.
        soc (bool): If True, the spin-orbit coupling is considere.
        soc_eo_flip (bool): If True, the spin-flip term is included.
        lat4 (bool): If True, the lattice is a 4-atom lattice for use with the armchair direction.
        single_orbital (bool): If True, the lattice is a combination of suborbitals (slower as no matrices are used)
        soc_sz_part (bool): If False, the hamiltonian will not include the Sz part of the spin-orbit coupling.
        soc_polarized (bool): If True, the spin-orbit coupling is polarized (only spin-up part, given by `soc_sz`).
        soc_sz (float): The Sz part of the spin-orbit coupling.
        n_v (int): The index of the highest valence band (in the unitcell).
        n_b (int): The number of bands (in the unitcell).
        lattice_name (str): The name of the lattice. The name of the matrial is obtained from `params`.
    """
    self.lattice_params = VariableStorage()
    self.orbital: LatticeOrbitals = orbital
    self.__n_valence_band: int = n_v
    self.__n_bands: int = n_b
    self.__name: str = "MoS2"
    self.__x_name: str = "S"
    self.__x_type: str = "X"
    self.__m_name: str = "Mo"
    self.__m_type: str = "M"
    self.__params: ParametersList = ParametersList()
    self.__soc_eo_flip: bool = False
    self.__lattice_name: str = lattice_name
    self._lat4: bool = lat4
    self.single_orbital: bool = single_orbital
    self.soc: bool = soc
    self.soc_polarized: bool = soc_polarized
    self.soc_sz_part: bool = soc_sz_part
    self.sz: float = soc_sz
    self.params = params
    self.soc_eo_flip = soc_eo_flip

block_diag(*matrices)

Make a block diagonal matrix from the given matrices.

Source code in tmdybinding/tmd_abstract_lattice.py

def block_diag(self, *matrices) -> np.ndarray:
    """Make a block diagonal matrix from the given matrices."""
    if len(matrices) == 1:
        return matrices[0]
    else:
        matrix0 = matrices[0]
        matrix1 = self.block_diag(*matrices[1:])
        shape_0 = np.shape(matrix0)
        shape_1 = np.shape(matrix1)
        z_1 = [shape_0[-2], shape_1[-1]]
        z_2 = [shape_1[-2], shape_0[-1]]
        nd = len(shape_0)
        assert nd == len(shape_1), "The matrices don't have the right sizes in the additional dimensions"
        if nd > 2:
            for sh in shape_1[:-2]:
                z_1.insert(0, sh)
                z_2.insert(0, sh)
        return np.concatenate((np.concatenate((matrix0, np.zeros(z_1)), axis=nd - 1),
                               np.concatenate((np.zeros(z_2), matrix1), axis=nd - 1)), axis=nd - 2)

lattice()

Make the lattice model. It returns a pybinding.Lattice object.

Source code in tmdybinding/tmd_abstract_lattice.py

def lattice(self) -> pb.Lattice:
    """Make the lattice model. It returns a `pybinding.Lattice` object."""
    lat = pb.Lattice(a1=self.a1, a2=self.a2)
    m_orbs, m2_orbs = 0, 0
    c_orbs, c2_orbs = 0, 0
    if self.lattice_params.h_0_m is not None:
        m_orbs = self._m_orbs
        m2_orbs = self._m2_orbs
        h_0_m = self._make_onsite(self.lattice_params.h_0_m, self.m_name, self.lattice_params.lamb_m)
        n_m, n_c = 0, 0
        if self.soc_eo_flip_used:
            soc_part_m = np.zeros((5, 5)) * 1j
            soc_part_m[3:, :3] = self.sz * self.lattice_params.lamb_m * np.array(
                [[np.sqrt(3) / 2, -1 / 2, 1j / 2],
                 [-1j / 2 * np.sqrt(3), -1j / 2, -1 / 2]])
            soc_part_m[:3, 3:] = -soc_part_m[3:, :3].T
            reorder_keys = [np.abs(np.array([0, 2, -2, 1, -1]) - key).argmin()
                            for key in self.orbital.l_number[self.orb_type(self.m_name)]]
            soc_part_m = self._reorder(soc_part_m, (reorder_keys, reorder_keys))
            h_0_m[:5, 5:] = soc_part_m
            h_0_m[5:, :5] = soc_part_m.conj().T

        pos_m = np.array([0, 0])
        if self.single_orbital:
            n_m = len(m_orbs)
            for i_m in range(n_m):
                lat.add_one_sublattice(m_orbs[i_m], pos_m, np.real(h_0_m[i_m, i_m]))
            for i_m in range(n_m):
                for j_m in np.arange(i_m + 1, n_m):
                    h_name = self._make_name("h_0_m", 0, m_orbs[i_m], m_orbs[j_m])
                    lat.register_hopping_energies(dict([(h_name, h_0_m[i_m, j_m])]))
                    lat.add_one_hopping([0, 0], m_orbs[i_m], m_orbs[j_m], h_name)
        else:
            lat.add_one_sublattice(self.m_name, pos_m, h_0_m)
        if self.lat4:
            pos_m2 = np.array([self.lattice_params.a / 2, self.lattice_params.a * np.sqrt(3) / 2])
            if self.single_orbital:
                for i_m in range(n_m):
                    lat.add_one_sublattice(m2_orbs[i_m], pos_m2, np.real(h_0_m[i_m, i_m]))
                for i_m in range(n_m):
                    for j_m in np.arange(i_m + 1, n_m):
                        h_name = self._make_name("h_0_m", 0, m2_orbs[i_m], m2_orbs[j_m])
                        lat.register_hopping_energies(dict([(h_name, h_0_m[i_m, j_m])]))
                        lat.add_one_hopping([0, 0], m2_orbs[i_m], m2_orbs[j_m], h_name)
            else:
                lat.add_one_sublattice(self.m_name + "2", pos_m2, h_0_m)

    if self.lattice_params.h_0_c is not None:
        h_0_c = self._make_onsite(self.lattice_params.h_0_c, self.x_name, self.lattice_params.lamb_c)
        c_orbs = self._c_orbs
        c2_orbs = self._c2_orbs
        n_c = len(c_orbs)
        if self.soc_eo_flip_used:
            soc_part_c = np.zeros((6, 6)) * 1j
            soc_part_c[:3, 3:] = self.sz * self.lattice_params.lamb_c * np.array(
                [[0, 0, 1 / 2],
                 [0, 0, -1j / 2],
                 [-1 / 2, 1j / 2, 0]])
            soc_part_c[3:, :3] = -soc_part_c[:3, 3:].T
            reorder_keys1 = [np.abs(np.array([1, -1, 0]) - key).argmin()
                             for key in self.orbital.l_number[self.orb_type(self.x_name)][:3]]
            reorder_keys2 = [3 + np.abs(np.array([1, -1, 0]) - key).argmin()
                             for key in self.orbital.l_number[self.orb_type(self.x_name)][3:]]
            soc_part_c = self._reorder(soc_part_c, (reorder_keys1 + reorder_keys2, reorder_keys1 + reorder_keys2))
            h_0_c[:6, 6:] = soc_part_c
            h_0_c[6:, :6] = soc_part_c.conj().T
        pos_c = np.array([self.lattice_params.a / 2, self.lattice_params.a * np.sqrt(3) / 6])
        if self.single_orbital:
            for i_c in range(n_c):
                lat.add_one_sublattice(c_orbs[i_c],pos_c, np.real(h_0_c[i_c, i_c]))
            for i_c in range(n_c):
                for j_c in np.arange(i_c + 1, n_c):
                    h_name = self._make_name("h_0_c", 0, c_orbs[i_c], c_orbs[j_c])
                    lat.register_hopping_energies(dict([(h_name, h_0_c[i_c, j_c])]))
                    lat.add_one_hopping([0, 0], c_orbs[i_c], c_orbs[j_c], h_name)
        else:
            lat.add_one_sublattice(self.x_name, pos_c, h_0_c)

        if self.lat4:
            pos_c2 = np.array([0, self.lattice_params.a * 2 * np.sqrt(3) / 6])
            if self.single_orbital:
                for i_c in range(n_c):
                    lat.add_one_sublattice(c2_orbs[i_c], pos_c2, np.real(h_0_c[i_c, i_c]))
                for i_c in range(n_c):
                    for j_c in np.arange(i_c + 1, n_c):
                        h_name = self._make_name("h_0_c", 0, c2_orbs[i_c], c2_orbs[j_c])
                        lat.register_hopping_energies(dict([(h_name, h_0_c[i_c, j_c])]))
                        lat.add_one_hopping([0, 0], c2_orbs[i_c], c2_orbs[j_c], h_name)
            else:
                lat.add_one_sublattice(self.x_name + "2", pos_c2, h_0_c)

    if self.lattice_params.h_1_m is not None:
        cos = [[-1, -1], [0, 0], [-1, 0]] if not self.lat4 else [[0, -1], [0, 0], [0, 0], [1, 0], [-1, 0], [0, 0]]
        fnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [mi * 3 for mi in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2"] * 3
            )
        )
        tnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [[c2, c1, c1, c2, c1, c2] for (c1, c2) in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name + "2", self.x_name, self.x_name, self.x_name + "2", self.x_name, self.x_name + "2"]
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_1_m,
                                f_n=self.m_name,
                                t_n=self.x_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_1_m")

    if self.lattice_params.h_2_m is not None:
        cos = [[1, 0], [0, 1], [-1, -1]] if not self.lat4 else [[1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [0, 0]]
        fnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [mi * 3 for mi in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2"] * 3
            )
        )
        tnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [[m1, m2, m2, m1, m2, m1] for (m1, m2) in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2", self.m_name + "2", self.m_name, self.m_name + "2", self.m_name]
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_2_m,
                                f_n=self.m_name,
                                t_n=self.m_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_2_m")

    if self.lattice_params.h_2_c is not None:
        cos = [[1, 0], [0, 1], [-1, -1]] if not self.lat4 else [[1, 0], [1, 0], [0, 0], [-1, 1], [0, -1], [-1, 0]]
        fnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [ci * 3 for ci in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2"] * 3
            )
        )
        tnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [[c1, c2, c2, c1, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2", self.x_name + "2", self.x_name, self.x_name + "2", self.x_name]
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_2_c,
                                f_n=self.x_name,
                                t_n=self.x_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_2_c")

    if self.lattice_params.h_3_m is not None:
        cos = [[0, 1], [-2, -1], [0, -1]] if not self.lat4 else [[0, 0], [0, 1], [-1, -1], [-1, 0], [1, -1], [1, 0]]
        fnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [mi * 3 for mi in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2"] * 3
            )
        )
        tnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [ci * 3 for ci in zip(c2_orbs, c_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name + "2", self.x_name] * 3
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_3_m,
                                f_n=self.m_name,
                                t_n=self.x_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_3_m")

    if self.lattice_params.h_4_m is not None:
        _, h_4_ma, h_4_mb = self._make_h_angle(
            self.lattice_params.h_4_m, self.m_name, self.x_name, np.arctan(np.sqrt(3) / 5)
        )
        cosa = [[-1, -2], [1, 1], [-2, 0]] \
            if not self.lat4 else [[0, -1], [1, -1], [1, 0], [1, 1], [-2, 0], [-1, 0]]
        cosb = [[-2, -2], [1, 0], [-1, 1]] \
            if not self.lat4 else [[-1, -1], [0, -1], [1, 0], [2, 0], [-1, 0], [-1, 1]]
        fnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [mi * 3 for mi in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2"] * 3
            )
        )
        tnla = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [[c1, c2, c2, c1, c1, c2] for (c1, c2) in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2", self.x_name + "2", self.x_name, self.x_name, self.x_name + "2"] * 3
            )
        )
        tnlb = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [[c1, c2, c1, c2, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2", self.x_name, self.x_name + "2", self.x_name + "2", self.x_name] * 3
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=h_4_ma,
                                f_n=self.m_name,
                                t_n=self.x_name,
                                cos=cosa,
                                fnl=fnl,
                                tnl=tnla,
                                h_name="h_4_ma")
        lat = self._add_hopping(lat=lat,
                                mat=h_4_mb,
                                f_n=self.m_name,
                                t_n=self.x_name,
                                cos=cosb,
                                fnl=fnl,
                                tnl=tnlb,
                                h_name="h_4_mb")

    if self.lattice_params.h_5_m is not None:
        cos = [[1, 2], [-2, -1], [1, -1]] if not self.lat4 else [[0, 1], [0, 1], [-2, -1], [-1, 0], [1, -1], [2, 0]]
        fnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [mi * 3 for mi in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2"] * 3
            )
        )
        tnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [[m1, m2, m2, m1, m2, m1] for (m1, m2) in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2", self.m_name + "2", self.m_name, self.m_name + "2", self.m_name]
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_5_m,
                                f_n=self.m_name,
                                t_n=self.m_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_5_m")

    if self.lattice_params.h_5_c is not None:
        cos = [[1, 2], [-2, -1], [1, -1]] if not self.lat4 else [[0, 1], [0, 1], [-1, -1], [-2, 0], [2, -1], [1, 0]]
        fnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [ci * 3 for ci in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2"] * 3
            )
        )
        tnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [[c1, c2, c2, c1, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2", self.x_name + "2", self.x_name, self.x_name + "2", self.x_name]
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_5_c,
                                f_n=self.x_name,
                                t_n=self.x_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_5_c")

    if self.lattice_params.h_6_m is not None:
        cos = [[2, 0], [0, 2], [-2, -2]] \
            if not self.lat4 else [[2, 0], [2, 0], [-1, 1], [-1, 1], [-1, -1], [-1, -1]]
        fnl = (
            (
                [[m_i] * 3 for m_i in m_orbs]
                if not self.lat4 else
                [mi * 3 for mi in zip(m_orbs, m2_orbs)]
            ) if self.single_orbital else (
                [self.m_name] * 3
                if not self.lat4 else
                [self.m_name, self.m_name + "2"] * 3
            )
        )
        tnl = fnl
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_6_m,
                                f_n=self.m_name,
                                t_n=self.m_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_6_m")

    if self.lattice_params.h_6_c is not None:
        cos = [[2, 0], [0, 2], [-2, -2]] \
            if not self.lat4 else [[2, 0], [2, 0], [-1, 1], [-1, 1], [-1, -1], [-1, -1]]
        fnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [ci * 3 for ci in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2"] * 3
            )
        )
        tnl = (
            (
                [[c_i] * 3 for c_i in c_orbs]
                if not self.lat4 else
                [[c1, c2, c2, c1, c2, c1] for (c1, c2) in zip(c_orbs, c2_orbs)]
            ) if self.single_orbital else (
                [self.x_name] * 3
                if not self.lat4 else
                [self.x_name, self.x_name + "2"] * 3
            )
        )
        lat = self._add_hopping(lat=lat,
                                mat=self.lattice_params.h_6_c,
                                f_n=self.x_name,
                                t_n=self.x_name,
                                cos=cos,
                                fnl=fnl,
                                tnl=tnl,
                                h_name="h_6_c")
    return lat

orb_type(z_name)

Return the orbital type of the atom with the given name. Usefull for the case when lat4 is True. Returns "M" for the metal atom and "X" for the chalcogen atom.

Source code in tmdybinding/tmd_abstract_lattice.py

def orb_type(self, z_name: str) -> Optional[str]:
    """Return the orbital type of the atom with the given name. Usefull for the case when `lat4` is True.
    Returns `"M"` for the metal atom and `"X"` for the chalcogen atom.
    """
    if z_name == self.m_name or (self.lat4 and z_name == self.m_name + "2"):
        return self.__m_type
    elif z_name == self.x_name or (self.lat4 and z_name == self.x_name + "2"):
        return self.__x_type
    else:
        return None

z_name(orb_type)

Return the name of the atom with the given orbital type, for example, obtain "S" from "X" in the case the material is "MoS2".

Source code in tmdybinding/tmd_abstract_lattice.py

def z_name(self, orb_type: str) -> Optional[str]:
    """Return the name of the atom with the given orbital type, for example, obtain `"S"` from `"X"` in the case
    the material is `"MoS2"`.
    """
    if orb_type == self.__m_type:
        return self.m_name
    elif orb_type == self.__x_type:
        return self.x_name
    else:
        return None

FloatParameter dataclass

Bases: Parameter

Class to store one separate float parameter

Source code in tmdybinding/parameters/symmetry_group.py

@dataclass
class FloatParameter(Parameter):
    """Class to store one separate float parameter"""
    param: Optional[float] = None

LatticeOrbitals

Object for saving the l and s values of a lattice model.

Source code in tmdybinding/tmd_abstract_lattice.py

class LatticeOrbitals:
    """ Object for saving the l and s values of a lattice model."""

    def __init__(self, l_number: Dict[str, List[int]], orbs: Dict[str, List[str]],
                 group: Optional[Dict[str, List[int]]] = None, clockwise: bool = False):
        """Make a LatticeOrbitals object with the given combinations of l and orbs.
        The input for `l`, `orbs` and `group` must be in the format `"atom_name": variables`.


        Parameters:
            l_number (Dict[str, List[int]]): The l-values for the orbitals.
                The dictionary entries must be in the format `"atom_name": l_number`.
                The l-values must be integers.
                They must come in pairs of negative and positive values, except for zero.
                Example: `{"S": [0, 1, -1, 0, 1, -1]}
            orbs (Dict[str, List[str]]): The orbital names for the orbitals.
                The dictionary entries must be in the format `"atom_name": orbs`.
                The orbital names must be strings.
                Example: `{"S": ["pze", "pxe", pye", "pzo", "pxo", "pyo"]}`
            group (Optional[Dict[str, List[int]]): The group of orbitals with the same l-value.
                If multiple orbitals with the same `l` are present on one atom, you can group the similar orbitals.
                If all the `l`-values are unique, the group is not needed.
                The dictionary entries must be in the format `"atom_name": group`.
                Example: `{"S": [0, 1, 1, 2, 3, 3]}`
            clockwise (bool): If True, the rotation matrices are clockwise.
        """
        self.__l_number = None
        self.__orbs = None
        self.__names = None
        self.__group = None
        self.clockwise = clockwise
        self.set_params(l_number=l_number, orbs=orbs, group=group)

    def set_params(self, l_number: Optional[Dict[str, List[int]]] = None, orbs: Optional[Dict[str, List[str]]] = None,
                   group: Optional[Dict[str, List[int]]] = None):
        """Set the parameters for the lattice model.

        Parameters:
            l_number (Optional[Dict[str, List[int]]]): The l-values for the orbitals.
                The dictionary entries must be in the format `"atom_name": l_number`.
                The l-values must be integers.
                They must come in pairs of negative and positive values, except for zero.
                If None, the previous value is kept.
                Example: `{"S": [0, 1, -1, 0, 1, -1]}
            orbs (Optional[Dict[str, Dict[str]]]): The orbital names for the orbitals.
                The dictionary entries must be in the format `"atom_name": orbs`.
                The orbital names must be strings.
                If None, the previous value is kept.
                Example: `{"S": ["pze", "pxe", pye", "pzo", "pxo", "pyo"]}`
            group (Optional[Dict[str, List[int]]): The group of orbitals with the same l-value.
                If multiple orbitals with the same `l` are present on one atom, you can group the similar orbitals.
                If all the `l`-values are unique, the group is not needed.
                If None, the previous value is kept (if there).
                The dictionary entries must be in the format `"atom_name": group`.
                Example: `{"S": [0, 1, 1, 2, 3, 3]}`
        """
        l_pass = l_number or self.l_number
        orbs_pass = orbs or self.orbs
        group_pass = group or self.group
        self._check_names(l_pass, orbs_pass, group_pass)
        self._check_shape(l_pass, orbs_pass, group_pass)

    @staticmethod
    def _make_bools(l_number: Dict[str, List[int]], orbs: Dict[str, List[str]],
                    group: Optional[Dict[str, List[int]]]) -> Tuple[bool, bool, bool]:
        """Make the boolean values for the input.

        Parameters:
            l_number (Dict[str, List[int]]): The l-values for the orbitals.
            orbs (Dict[str, List[str]]): The orbital names for the orbitals.
            group (Optional[Dict[str, List[int]]): The group of orbitals with the same l-value.
        """
        l_bool = l_number is not None
        orbs_bool = orbs is not None
        group_bool = group is not None
        assert l_bool or orbs_bool, "not enough input given, at least l or orbs needed"
        return l_bool, orbs_bool, group_bool

    def _check_names(self, l_number: Dict[str, List[int]], orbs: Dict[str, List[str]],
                     group: Optional[Dict[str, List[int]]]):
        """Check if the names of the orbitals are the same."""
        (l_bool, orbs_bool, group_bool) = self._make_bools(l_number, orbs, group)
        names = None
        if l_bool:
            names_l = [str(name) for name in l_number.keys()]
            names = names_l
        if orbs_bool:
            names_orbs = [str(name) for name in orbs.keys()]
            if names is None:
                names = names_orbs
            else:
                assert names == names_orbs, f"the names of l_number and orbs are not the same, {names} != {names_orbs}"
        if group_bool:
            names_group = [str(name) for name in group.keys()]
            assert names == names_group, \
                f"the names of l_number/orbs  and group are not the same, {names} != {names_group}"
        self.__names = names

    def _check_shape(self, l_number: Dict[str, List[int]], orbs: Dict[str, List[str]],
                     group: Optional[Dict[str, List[int]]]):
        """Check if the shape of the orbitals is correct."""
        (l_bool, orbs_bool, group_bool) = self._make_bools(l_number, orbs, group)
        shape = None
        if l_bool:
            shape_l = [np.shape(l_number[name]) for name in self.names]
            shape = shape_l
        if orbs_bool:
            shape_orbs = [np.shape(orbs[name]) for name in self.names]
            if shape is None:
                shape = shape_orbs
            else:
                assert shape == shape_orbs, f"the shape of l_number and orbs are not the same, {shape} !m {shape_orbs}"
        if group_bool:
            shape_group = [np.shape(group[name]) for name in self.names]
            assert shape == shape_group, "the shape of group and l_number and/or orbs are not the same"

        # see if definition of group and l are correct. If no group is specified, but there is an l, the l is checked
        l_local = l_number if l_bool else dict([(name, np.zeros(shape[j])) for j, name in enumerate(self.names)])
        if not group_bool:
            for name in self.names:
                l_num = np.array(l_local[name])
                for lm in set(np.abs(l_num)):
                    l_b = np.abs(l_num) == lm
                    assert np.sum(l_b) < 3, \
                        f"the representation can only be given for max two parts, {np.sum(l_b)} given"
                    if np.sum(l_b) == 2:
                        assert l_num[l_b][0] == -l_num[l_b][1], \
                            f"can't have same l-number if group is not defined, for '{lm}'"
                    else:
                        assert lm == 0, \
                            f"can't have a sole l-number other than zero, '{lm}' given"
                    assert np.sum(l_b) == 1, \
                        f"can't have a sole l-number, only one '{lm}' given"
        group_local = group if group_bool else dict([(name, np.abs(l_local[name])) for name in self.names])

        # check l and group
        for name in self.names:
            group_l = np.array(group_local[name])
            l_num = np.array(l_local[name])
            for group_i in set(group_l):
                group_b = group_i == group_l
                assert np.sum(group_b) < 3, "the group for representation can only be given for max two parts"
                assert (np.sum(group_b) == 2 and l_num[group_b][0] == -l_num[group_b][1]) or np.sum(group_b) == 1, \
                    "can't have same l-number in same group"
        self.__l_number = l_local
        self.__orbs = orbs
        self.__group = group_local

    @staticmethod
    def rot_mat(phi: float = 0) -> np.ndarray:
        """Make a rotation matrix for the given angle.

        Parameters:
            phi (float): The angle of the rotation matrix.
        """
        return np.array([[np.cos(phi), -np.sin(phi)], [np.sin(phi), np.cos(phi)]])

    @property
    def l_number(self) -> Dict[str, List[int]]:
        """The l-values for the orbitals."""
        return self.__l_number

    @property
    def names(self) -> List[str]:
        """The names of the atoms."""
        return self.__names

    @property
    def orbs(self) -> Dict[str, List[str]]:
        """The orbital names for the orbitals."""
        return self.__orbs

    @property
    def group(self) -> Dict[str, List[int]]:
        """The group of orbitals with the same l-value."""
        return self.__group

    def _make_matrix(self, matrix_func, single) -> Dict[str, np.ndarray]:
        out_dict: Dict[str, np.ndarray] = {}
        for name in self.names:
            group_l = np.array(self.group[name])
            l_num = np.array(self.l_number[name])
            value = np.zeros((len(l_num), len(l_num)))
            for group_i in set(group_l):
                group_b = group_i == group_l
                lm = np.abs(l_num[group_b][0])
                sign = -1 if l_num[group_b][0] < 0 else 1
                if np.sum(group_b) == 2:
                    matrix = matrix_func(lm, sign)
                    for ik, k in enumerate(np.arange(len(l_num))[group_b]):
                        for ikk, kk in enumerate(np.arange(len(l_num))[group_b]):
                            value[k, kk] = matrix[ik, ikk]
                else:
                    value[np.arange(len(l_num))[group_b], np.arange(len(l_num))[group_b]] = single(lm, sign)
            out_dict[name] = value
        return out_dict

    @property
    def ur(self) -> Dict[str, np.ndarray]:
        """Rotation matrix for the orbitals over an angle of 2pi/3.
        Returns a dict of rotation matrices for the orbitals in the format `"atom_name": matrix`.
        """

        def matrix_func(lm, sign):
            ur_t = self.rot_mat(np.pi * 2 / 3 * lm)
            if sign == -1:
                ur_t = np.transpose(ur_t)
            if self.clockwise:
                ur_t = np.transpose(ur_t)
            return ur_t

        def single(lm, sign):
            return 1 + (lm * 0 + sign * 0)

        return self._make_matrix(matrix_func, single)

    @property
    def sr(self) -> Dict[str, np.ndarray]:
        """Mirror on yz-plane.
        Returns a dict of mirror matrices for the orbitals in the format `"atom_name": matrix`.
        """

        def matrix_func(lm, sign):
            return sign * np.diag([-1, 1]) * (1 if np.abs(lm) == 1 else -1)

        def single(lm, sign):
            return 1 + (lm * 0 + sign * 0)

        return self._make_matrix(matrix_func, single)

    def ur_angle(self, angle) -> Dict[str, np.ndarray]:
        """Rotation matrix for the orbitals over an angle of `angle`.
        Returns a dict of rotation matrices for the orbitals over an angle of `angle` in the
        format `"atom_name": matrix`.

        Parameters:
            angle (float): The angle of the rotation matrix.
        """

        def matrix_func(lm, sign):
            ur_t = self.rot_mat(angle * lm)
            if sign == -1:
                ur_t = np.transpose(ur_t)
            if self.clockwise:
                ur_t = np.transpose(ur_t)
            return ur_t

        def single(lm, sign):
            return 1 + (lm * 0 + sign * 0)

        return self._make_matrix(matrix_func, single)

    @property
    def s_h(self):
        """Spin factor for the orbitals.
        Returns a dict of spin matrices for the orbitals in the format `"atom_name": matrix`.
        """

        def matrix_func(lm, sign):
            ur_t = lm / 2 * np.array([[0, -1], [1, 0]])
            if sign == -1:
                ur_t = np.transpose(ur_t)
            return ur_t

        def single(lm, sign):
            return 0 + (lm * 0 + sign * 0)

        return self._make_matrix(matrix_func, single)

group: Dict[str, List[int]] property

The group of orbitals with the same l-value.

l_number: Dict[str, List[int]] property

The l-values for the orbitals.

names: List[str] property

The names of the atoms.

orbs: Dict[str, List[str]] property

The orbital names for the orbitals.

s_h property

Spin factor for the orbitals. Returns a dict of spin matrices for the orbitals in the format "atom_name": matrix.

sr: Dict[str, np.ndarray] property

Mirror on yz-plane. Returns a dict of mirror matrices for the orbitals in the format "atom_name": matrix.

ur: Dict[str, np.ndarray] property

Rotation matrix for the orbitals over an angle of 2pi/3. Returns a dict of rotation matrices for the orbitals in the format "atom_name": matrix.

__init__(l_number, orbs, group=None, clockwise=False)

Make a LatticeOrbitals object with the given combinations of l and orbs. The input for l, orbs and group must be in the format "atom_name": variables.

Parameters:

Name	Type	Description	Default
l_number	Dict[str, List[int]]	The l-values for the orbitals. The dictionary entries must be in the format "atom_name": l_number. The l-values must be integers. They must come in pairs of negative and positive values, except for zero. Example: `{"S": [0, 1, -1, 0, 1, -1]}	required
orbs	Dict[str, List[str]]	The orbital names for the orbitals. The dictionary entries must be in the format "atom_name": orbs. The orbital names must be strings. Example: {"S": ["pze", "pxe", pye", "pzo", "pxo", "pyo"]}	required
group	Optional[Dict[str, List[int]]	The group of orbitals with the same l-value. If multiple orbitals with the same l are present on one atom, you can group the similar orbitals. If all the l-values are unique, the group is not needed. The dictionary entries must be in the format "atom_name": group. Example: {"S": [0, 1, 1, 2, 3, 3]}	None
clockwise	bool	If True, the rotation matrices are clockwise.	False

Source code in tmdybinding/tmd_abstract_lattice.py

def __init__(self, l_number: Dict[str, List[int]], orbs: Dict[str, List[str]],
             group: Optional[Dict[str, List[int]]] = None, clockwise: bool = False):
    """Make a LatticeOrbitals object with the given combinations of l and orbs.
    The input for `l`, `orbs` and `group` must be in the format `"atom_name": variables`.


    Parameters:
        l_number (Dict[str, List[int]]): The l-values for the orbitals.
            The dictionary entries must be in the format `"atom_name": l_number`.
            The l-values must be integers.
            They must come in pairs of negative and positive values, except for zero.
            Example: `{"S": [0, 1, -1, 0, 1, -1]}
        orbs (Dict[str, List[str]]): The orbital names for the orbitals.
            The dictionary entries must be in the format `"atom_name": orbs`.
            The orbital names must be strings.
            Example: `{"S": ["pze", "pxe", pye", "pzo", "pxo", "pyo"]}`
        group (Optional[Dict[str, List[int]]): The group of orbitals with the same l-value.
            If multiple orbitals with the same `l` are present on one atom, you can group the similar orbitals.
            If all the `l`-values are unique, the group is not needed.
            The dictionary entries must be in the format `"atom_name": group`.
            Example: `{"S": [0, 1, 1, 2, 3, 3]}`
        clockwise (bool): If True, the rotation matrices are clockwise.
    """
    self.__l_number = None
    self.__orbs = None
    self.__names = None
    self.__group = None
    self.clockwise = clockwise
    self.set_params(l_number=l_number, orbs=orbs, group=group)

rot_mat(phi=0) staticmethod

Make a rotation matrix for the given angle.

Parameters:

Name	Type	Description	Default
phi	float	The angle of the rotation matrix.	0

Source code in tmdybinding/tmd_abstract_lattice.py

@staticmethod
def rot_mat(phi: float = 0) -> np.ndarray:
    """Make a rotation matrix for the given angle.

    Parameters:
        phi (float): The angle of the rotation matrix.
    """
    return np.array([[np.cos(phi), -np.sin(phi)], [np.sin(phi), np.cos(phi)]])

set_params(l_number=None, orbs=None, group=None)

Set the parameters for the lattice model.

Parameters:

Name	Type	Description	Default
l_number	Optional[Dict[str, List[int]]]	The l-values for the orbitals. The dictionary entries must be in the format "atom_name": l_number. The l-values must be integers. They must come in pairs of negative and positive values, except for zero. If None, the previous value is kept. Example: `{"S": [0, 1, -1, 0, 1, -1]}	None
orbs	Optional[Dict[str, Dict[str]]]	The orbital names for the orbitals. The dictionary entries must be in the format "atom_name": orbs. The orbital names must be strings. If None, the previous value is kept. Example: {"S": ["pze", "pxe", pye", "pzo", "pxo", "pyo"]}	None
group	Optional[Dict[str, List[int]]	The group of orbitals with the same l-value. If multiple orbitals with the same l are present on one atom, you can group the similar orbitals. If all the l-values are unique, the group is not needed. If None, the previous value is kept (if there). The dictionary entries must be in the format "atom_name": group. Example: {"S": [0, 1, 1, 2, 3, 3]}	None

Source code in tmdybinding/tmd_abstract_lattice.py

def set_params(self, l_number: Optional[Dict[str, List[int]]] = None, orbs: Optional[Dict[str, List[str]]] = None,
               group: Optional[Dict[str, List[int]]] = None):
    """Set the parameters for the lattice model.

    Parameters:
        l_number (Optional[Dict[str, List[int]]]): The l-values for the orbitals.
            The dictionary entries must be in the format `"atom_name": l_number`.
            The l-values must be integers.
            They must come in pairs of negative and positive values, except for zero.
            If None, the previous value is kept.
            Example: `{"S": [0, 1, -1, 0, 1, -1]}
        orbs (Optional[Dict[str, Dict[str]]]): The orbital names for the orbitals.
            The dictionary entries must be in the format `"atom_name": orbs`.
            The orbital names must be strings.
            If None, the previous value is kept.
            Example: `{"S": ["pze", "pxe", pye", "pzo", "pxo", "pyo"]}`
        group (Optional[Dict[str, List[int]]): The group of orbitals with the same l-value.
            If multiple orbitals with the same `l` are present on one atom, you can group the similar orbitals.
            If all the `l`-values are unique, the group is not needed.
            If None, the previous value is kept (if there).
            The dictionary entries must be in the format `"atom_name": group`.
            Example: `{"S": [0, 1, 1, 2, 3, 3]}`
    """
    l_pass = l_number or self.l_number
    orbs_pass = orbs or self.orbs
    group_pass = group or self.group
    self._check_names(l_pass, orbs_pass, group_pass)
    self._check_shape(l_pass, orbs_pass, group_pass)

ur_angle(angle)

Rotation matrix for the orbitals over an angle of angle. Returns a dict of rotation matrices for the orbitals over an angle of angle in the format "atom_name": matrix.

Parameters:

Name	Type	Description	Default
angle	float	The angle of the rotation matrix.	required

Source code in tmdybinding/tmd_abstract_lattice.py

def ur_angle(self, angle) -> Dict[str, np.ndarray]:
    """Rotation matrix for the orbitals over an angle of `angle`.
    Returns a dict of rotation matrices for the orbitals over an angle of `angle` in the
    format `"atom_name": matrix`.

    Parameters:
        angle (float): The angle of the rotation matrix.
    """

    def matrix_func(lm, sign):
        ur_t = self.rot_mat(angle * lm)
        if sign == -1:
            ur_t = np.transpose(ur_t)
        if self.clockwise:
            ur_t = np.transpose(ur_t)
        return ur_t

    def single(lm, sign):
        return 1 + (lm * 0 + sign * 0)

    return self._make_matrix(matrix_func, single)

Parameter dataclass

Class to store one separate parameter

Source code in tmdybinding/parameters/symmetry_group.py

@dataclass
class Parameter:
    """Class to store one separate parameter"""
    name: str = ""

ParametersList

Class to save the parameters

Source code in tmdybinding/parameters/symmetry_group.py

class ParametersList:
    """Class to save the parameters"""

    def __init__(self, input_dict: Optional[Dict[str, Union[float, str]]] = None):
        """Initialize the parameters for the TMD lattice.

        Parameters:
            input_dict (Optional[Dict[str, Union[float, str]]]): The parameters for the TMD lattice.
                The keys are the names of the parameters and the values are the values of the parameters.
                The keys are:
                `a`,            `lamb_m`,       `lamb_x`,       `material`,
                `eps_0_x_e`, `eps_1_x_e`, `eps_0_m_e`, `eps_1_m_e`,
                `u_1_0_m_e`, `u_1_1_m_e`, `u_1_2_m_e`, `u_1_3_m_e`, `u_1_4_m_e`,
                `u_2_0_m_e`, `u_2_1_m_e`, `u_2_2_m_e`, `u_2_3_m_e`, `u_2_4_m_e`, `u_2_5_m_e`,
                `u_2_0_x_e`, `u_2_1_x_e`, `u_2_2_x_e`, `u_2_3_x_e`, `u_2_4_x_e`, `u_2_5_x_e`,
                `u_3_0_m_e`, `u_3_1_m_e`, `u_3_2_m_e`, `u_3_3_m_e`, `u_3_4_m_e`,
                `u_4_0_m_e`, `u_4_1_m_e`, `u_4_2_m_e`, `u_4_3_m_e`, `u_4_4_m_e`,
                `u_5_0_m_e`, `u_5_1_m_e`, `u_5_3_m_e`, `u_5_5_m_e`, `u_5_6_m_e`,
                `u_5_0_x_e`, `u_5_2_x_e`, `u_5_3_x_e`, `u_5_5_x_e`, `u_5_6_x_e`,
                `u_6_0_m_e`, `u_6_1_m_e`, `u_6_2_m_e`, `u_6_3_m_e`, `u_6_4_m_e`, `u_6_5_m_e`,
                `u_6_0_x_e`, `u_6_1_x_e`, `u_6_2_x_e`, `u_6_3_x_e`, `u_6_4_x_e`, `u_6_5_x_e`,
                `eps_0_x_o`, `eps_1_x_o`, `eps_0_m_o`,
                `u_1_0_m_o`, `u_1_1_m_o`, `u_1_2_m_o`,
                `u_2_0_m_o`, `u_2_1_m_o`, `u_2_2_m_o`,
                `u_2_0_x_o`, `u_2_1_x_o`, `u_2_2_x_o`, `u_2_3_x_o`, `u_2_4_x_o`, `u_2_5_x_o`,
                `u_3_0_m_o`, `u_3_1_m_o`, `u_3_2_m_o`,
                `u_4_0_m_o`, `u_4_1_m_o`, `u_4_2_m_o`,
                `u_5_0_m_o`, `u_5_2_m_o`,
                `u_5_0_x_o`, `u_5_2_x_o`, `u_5_3_x_o`, `u_5_5_x_o`, `u_5_6_x_o`,
                `u_6_0_m_o`, `u_6_1_m_o`, `u_6_2_m_o`,
                `u_6_0_x_o`, `u_6_1_x_o`, `u_6_2_x_o`, `u_6_3_x_o`, `u_6_4_x_o` and `u_6_5_x_o`
        """
        energy_params = [
            *[f"eps_{i}_x_{r}" for i in range(2) for r in ("e", "o")],
            *[f"eps_{i}_m_{r}" for i in "0" for r in ("e", "o")],
            *[f"eps_{i}_m_{r}" for i in "1" for r in "e"],
            *[f"u_{u}_{i}_m_e" for u in ("1", "3", "4") for i in range(5)],
            *[f"u_{u}_{i}_m_o" for u in ("1", "3", "4") for i in range(3)],
            *[f"u_{u}_{i}_{m}_e" for u in ("2", "6") for i in range(6) for m in ("m", "x")],
            *[f"u_{u}_{i}_x_o" for u in ("2", "6") for i in range(6)],
            *[f"u_{u}_{i}_m_o" for u in ("2", "6") for i in range(3)],
            *[f"u_{u}_{i}_m_e" for u in "5" for i in ("0", "1", "3", "5", "6")],
            *[f"u_{u}_{i}_x_{r}" for u in "5" for i in ("0", "2", "3", "5", "6") for r in ("e", "o")],
            *[f"u_{u}_{i}_m_o" for u in "5" for i in ("0", "2")],
        ]

        energy_params_names = [
            *[rf"$\epsilon_{i}^{{X,{r}}}$" for i in range(2) for r in ("e", "o")],
            *[rf"$\epsilon_{i}^{{M,{r}}}$" for i in "0" for r in ("e", "o")],
            *[rf"$\epsilon_{i}^{{M,{r}}}$" for i in "1" for r in "e"],
            *[rf"$u_{u}^{{{i},e}}$" for u in ("1", "3", "4") for i in range(5)],
            *[rf"$u_{u}^{{{i},o}}$" for u in ("1", "3", "4") for i in range(3)],
            *[rf"$u_{u}^{{{i},{m}e}}$" for u in ("2", "6") for i in range(6) for m in ("M", "X")],
            *[rf"$u_{u}^{{{i},Xo}}$" for u in ("2", "6") for i in range(6)],
            *[rf"$u_{u}^{{{i},Mo}}$" for u in ("2", "6") for i in range(3)],
            *[rf"$u_{u}^{{{i},Me}}$" for u in "5" for i in ("0", "1", "3", "5", "6")],
            *[rf"$u_{u}^{{{i},X{r}}}$" for u in "5" for i in ("0", "2", "3", "5", "6") for r in ("e", "o")],
            *[rf"$u_{u}^{{{i},Mo}}$" for u in "5" for i in ("0", "2")],
        ]

        self._energy_params_dict: Dict[str, FloatParameter] = dict(zip(
            energy_params,
            [FloatParameter(name=p_name) for p_name in energy_params_names]
        ))

        self._general_params_dict: Dict[str, Union[FloatParameter, StringParameter]] = dict(zip(
            ["a", "lamb_m", "lamb_x", "material"],
            [
                FloatParameter(param=1., name=r"$a$"),
                FloatParameter(name=r"$\lambda_M$"),
                FloatParameter(name=r"$\lambda_X$"),
                StringParameter(name="material")
            ]
        ))
        if input_dict is not None:
            self.from_dict(input_dict)

    @property
    def _unique_params_dict(self) -> List[dict]:
        return [self._general_params_dict, self._energy_params_dict]

    @property
    def _protected_params_dict(self) -> Optional[List[dict]]:
        return None

    @property
    def _all_params_dict(self) -> List[dict]:
        return self._unique_params_dict + (self._protected_params_dict or [])

    @property
    def _allowed_params(self):
        return [param_key for param_dict in self._all_params_dict for param_key in param_dict.keys()]

    def _check_key(self, key) -> bool:
        if key not in self._allowed_params:
            warnings.warn(f"Variable {key} is not an expected variable, it is ignored", UserWarning, stacklevel=2)
        return True

    def __setitem__(self, key, value):
        if self._check_key(key):
            for param_dict in self._unique_params_dict:
                if key in param_dict.keys():
                    param_dict[key].param = value
                    return
            if self._protected_params_dict is not None:
                for param_dict in self._protected_params_dict:
                    if key in param_dict.keys():
                        param_dict[key].param = value
                        warnings.warn(f"The variable {key} is read-only, you should not change it.", UserWarning, stacklevel=2)
                        return
            warnings.warn(f"This should not happen, {key} should be a valid key.", UserWarning, stacklevel=2)

    def __getitem__(self, item) -> Union[float, str]:
        return self.get_param(item) or 0.0

    def t_m(self) -> dict:
        """Function to get the variables as a dict."""
        out_dict = {}
        for param_dict in self._unique_params_dict:
            for key, item in param_dict.items():
                if item.param is not None:
                    out_dict[key] = item.param
        return out_dict

    def get_param(self, key):
        """Function to get the specific variable"""
        if self._check_key(key):
            for param_dict in self._all_params_dict:
                if key in param_dict.keys():
                    return param_dict[key].param
            warnings.warn(f"This should not happen, {key} should be a valid key.", UserWarning, stacklevel=2)

    def get_name(self, key) -> str:
        """Function to get the name (in LaTeX) of the specific variable"""
        if self._check_key(key):
            for param_dict in self._all_params_dict:
                if key in param_dict.keys():
                    return param_dict[key].name
            warnings.warn(f"This should not happen, {key} should be a valid key.", UserWarning, stacklevel=2)

    def from_dict(self, input_dict: Dict[str, Union[float, str]]):
        """Function to set the variables with a dict.

        Parameters:
            input_dict (dict): The dictionary containing the parameters for the TMD lattice.
                The allowed keys are:
                `a`,            `lamb_m`,       `lamb_x`,       `material`,
                `eps_0_x_e`, `eps_1_x_e`, `eps_0_m_e`, `eps_1_m_e`,
                `u_1_0_m_e`, `u_1_1_m_e`, `u_1_2_m_e`, `u_1_3_m_e`, `u_1_4_m_e`,
                `u_2_0_m_e`, `u_2_1_m_e`, `u_2_2_m_e`, `u_2_3_m_e`, `u_2_4_m_e`, `u_2_5_m_e`,
                `u_2_0_x_e`, `u_2_1_x_e`, `u_2_2_x_e`, `u_2_3_x_e`, `u_2_4_x_e`, `u_2_5_x_e`,
                `u_3_0_m_e`, `u_3_1_m_e`, `u_3_2_m_e`, `u_3_3_m_e`, `u_3_4_m_e`,
                `u_4_0_m_e`, `u_4_1_m_e`, `u_4_2_m_e`, `u_4_3_m_e`, `u_4_4_m_e`,
                `u_5_0_m_e`, `u_5_1_m_e`, `u_5_3_m_e`, `u_5_5_m_e`, `u_5_6_m_e`,
                `u_5_0_x_e`, `u_5_2_x_e`, `u_5_3_x_e`, `u_5_5_x_e`, `u_5_6_x_e`,
                `u_6_0_m_e`, `u_6_1_m_e`, `u_6_2_m_e`, `u_6_3_m_e`, `u_6_4_m_e`, `u_6_5_m_e`,
                `u_6_0_x_e`, `u_6_1_x_e`, `u_6_2_x_e`, `u_6_3_x_e`, `u_6_4_x_e`, `u_6_5_x_e`,
                `eps_0_x_o`, `eps_1_x_o`, `eps_0_m_o`,
                `u_1_0_m_o`, `u_1_1_m_o`, `u_1_2_m_o`,
                `u_2_0_m_o`, `u_2_1_m_o`, `u_2_2_m_o`,
                `u_2_0_x_o`, `u_2_1_x_o`, `u_2_2_x_o`, `u_2_3_x_o`, `u_2_4_x_o`, `u_2_5_x_o`,
                `u_3_0_m_o`, `u_3_1_m_o`, `u_3_2_m_o`,
                `u_4_0_m_o`, `u_4_1_m_o`, `u_4_2_m_o`,
                `u_5_0_m_o`, `u_5_2_m_o`,
                `u_5_0_x_o`, `u_5_2_x_o`, `u_5_3_x_o`, `u_5_5_x_o`, `u_5_6_x_o`,
                `u_6_0_m_o`, `u_6_1_m_o`, `u_6_2_m_o`,
                `u_6_0_x_o`, `u_6_1_x_o`, `u_6_2_x_o`, `u_6_3_x_o`, `u_6_4_x_o` and `u_6_5_x_o`
        """
        for param_name, value in input_dict.items():
            self[param_name] = value

__init__(input_dict=None)

Initialize the parameters for the TMD lattice.

Parameters:

Name	Type	Description	Default
input_dict	Optional[Dict[str, Union[float, str]]]	The parameters for the TMD lattice. The keys are the names of the parameters and the values are the values of the parameters. The keys are: a, lamb_m, lamb_x, material, eps_0_x_e, eps_1_x_e, eps_0_m_e, eps_1_m_e, u_1_0_m_e, u_1_1_m_e, u_1_2_m_e, u_1_3_m_e, u_1_4_m_e, u_2_0_m_e, u_2_1_m_e, u_2_2_m_e, u_2_3_m_e, u_2_4_m_e, u_2_5_m_e, u_2_0_x_e, u_2_1_x_e, u_2_2_x_e, u_2_3_x_e, u_2_4_x_e, u_2_5_x_e, u_3_0_m_e, u_3_1_m_e, u_3_2_m_e, u_3_3_m_e, u_3_4_m_e, u_4_0_m_e, u_4_1_m_e, u_4_2_m_e, u_4_3_m_e, u_4_4_m_e, u_5_0_m_e, u_5_1_m_e, u_5_3_m_e, u_5_5_m_e, u_5_6_m_e, u_5_0_x_e, u_5_2_x_e, u_5_3_x_e, u_5_5_x_e, u_5_6_x_e, u_6_0_m_e, u_6_1_m_e, u_6_2_m_e, u_6_3_m_e, u_6_4_m_e, u_6_5_m_e, u_6_0_x_e, u_6_1_x_e, u_6_2_x_e, u_6_3_x_e, u_6_4_x_e, u_6_5_x_e, eps_0_x_o, eps_1_x_o, eps_0_m_o, u_1_0_m_o, u_1_1_m_o, u_1_2_m_o, u_2_0_m_o, u_2_1_m_o, u_2_2_m_o, u_2_0_x_o, u_2_1_x_o, u_2_2_x_o, u_2_3_x_o, u_2_4_x_o, u_2_5_x_o, u_3_0_m_o, u_3_1_m_o, u_3_2_m_o, u_4_0_m_o, u_4_1_m_o, u_4_2_m_o, u_5_0_m_o, u_5_2_m_o, u_5_0_x_o, u_5_2_x_o, u_5_3_x_o, u_5_5_x_o, u_5_6_x_o, u_6_0_m_o, u_6_1_m_o, u_6_2_m_o, u_6_0_x_o, u_6_1_x_o, u_6_2_x_o, u_6_3_x_o, u_6_4_x_o and u_6_5_x_o	None

Source code in tmdybinding/parameters/symmetry_group.py

def __init__(self, input_dict: Optional[Dict[str, Union[float, str]]] = None):
    """Initialize the parameters for the TMD lattice.

    Parameters:
        input_dict (Optional[Dict[str, Union[float, str]]]): The parameters for the TMD lattice.
            The keys are the names of the parameters and the values are the values of the parameters.
            The keys are:
            `a`,            `lamb_m`,       `lamb_x`,       `material`,
            `eps_0_x_e`, `eps_1_x_e`, `eps_0_m_e`, `eps_1_m_e`,
            `u_1_0_m_e`, `u_1_1_m_e`, `u_1_2_m_e`, `u_1_3_m_e`, `u_1_4_m_e`,
            `u_2_0_m_e`, `u_2_1_m_e`, `u_2_2_m_e`, `u_2_3_m_e`, `u_2_4_m_e`, `u_2_5_m_e`,
            `u_2_0_x_e`, `u_2_1_x_e`, `u_2_2_x_e`, `u_2_3_x_e`, `u_2_4_x_e`, `u_2_5_x_e`,
            `u_3_0_m_e`, `u_3_1_m_e`, `u_3_2_m_e`, `u_3_3_m_e`, `u_3_4_m_e`,
            `u_4_0_m_e`, `u_4_1_m_e`, `u_4_2_m_e`, `u_4_3_m_e`, `u_4_4_m_e`,
            `u_5_0_m_e`, `u_5_1_m_e`, `u_5_3_m_e`, `u_5_5_m_e`, `u_5_6_m_e`,
            `u_5_0_x_e`, `u_5_2_x_e`, `u_5_3_x_e`, `u_5_5_x_e`, `u_5_6_x_e`,
            `u_6_0_m_e`, `u_6_1_m_e`, `u_6_2_m_e`, `u_6_3_m_e`, `u_6_4_m_e`, `u_6_5_m_e`,
            `u_6_0_x_e`, `u_6_1_x_e`, `u_6_2_x_e`, `u_6_3_x_e`, `u_6_4_x_e`, `u_6_5_x_e`,
            `eps_0_x_o`, `eps_1_x_o`, `eps_0_m_o`,
            `u_1_0_m_o`, `u_1_1_m_o`, `u_1_2_m_o`,
            `u_2_0_m_o`, `u_2_1_m_o`, `u_2_2_m_o`,
            `u_2_0_x_o`, `u_2_1_x_o`, `u_2_2_x_o`, `u_2_3_x_o`, `u_2_4_x_o`, `u_2_5_x_o`,
            `u_3_0_m_o`, `u_3_1_m_o`, `u_3_2_m_o`,
            `u_4_0_m_o`, `u_4_1_m_o`, `u_4_2_m_o`,
            `u_5_0_m_o`, `u_5_2_m_o`,
            `u_5_0_x_o`, `u_5_2_x_o`, `u_5_3_x_o`, `u_5_5_x_o`, `u_5_6_x_o`,
            `u_6_0_m_o`, `u_6_1_m_o`, `u_6_2_m_o`,
            `u_6_0_x_o`, `u_6_1_x_o`, `u_6_2_x_o`, `u_6_3_x_o`, `u_6_4_x_o` and `u_6_5_x_o`
    """
    energy_params = [
        *[f"eps_{i}_x_{r}" for i in range(2) for r in ("e", "o")],
        *[f"eps_{i}_m_{r}" for i in "0" for r in ("e", "o")],
        *[f"eps_{i}_m_{r}" for i in "1" for r in "e"],
        *[f"u_{u}_{i}_m_e" for u in ("1", "3", "4") for i in range(5)],
        *[f"u_{u}_{i}_m_o" for u in ("1", "3", "4") for i in range(3)],
        *[f"u_{u}_{i}_{m}_e" for u in ("2", "6") for i in range(6) for m in ("m", "x")],
        *[f"u_{u}_{i}_x_o" for u in ("2", "6") for i in range(6)],
        *[f"u_{u}_{i}_m_o" for u in ("2", "6") for i in range(3)],
        *[f"u_{u}_{i}_m_e" for u in "5" for i in ("0", "1", "3", "5", "6")],
        *[f"u_{u}_{i}_x_{r}" for u in "5" for i in ("0", "2", "3", "5", "6") for r in ("e", "o")],
        *[f"u_{u}_{i}_m_o" for u in "5" for i in ("0", "2")],
    ]

    energy_params_names = [
        *[rf"$\epsilon_{i}^{{X,{r}}}$" for i in range(2) for r in ("e", "o")],
        *[rf"$\epsilon_{i}^{{M,{r}}}$" for i in "0" for r in ("e", "o")],
        *[rf"$\epsilon_{i}^{{M,{r}}}$" for i in "1" for r in "e"],
        *[rf"$u_{u}^{{{i},e}}$" for u in ("1", "3", "4") for i in range(5)],
        *[rf"$u_{u}^{{{i},o}}$" for u in ("1", "3", "4") for i in range(3)],
        *[rf"$u_{u}^{{{i},{m}e}}$" for u in ("2", "6") for i in range(6) for m in ("M", "X")],
        *[rf"$u_{u}^{{{i},Xo}}$" for u in ("2", "6") for i in range(6)],
        *[rf"$u_{u}^{{{i},Mo}}$" for u in ("2", "6") for i in range(3)],
        *[rf"$u_{u}^{{{i},Me}}$" for u in "5" for i in ("0", "1", "3", "5", "6")],
        *[rf"$u_{u}^{{{i},X{r}}}$" for u in "5" for i in ("0", "2", "3", "5", "6") for r in ("e", "o")],
        *[rf"$u_{u}^{{{i},Mo}}$" for u in "5" for i in ("0", "2")],
    ]

    self._energy_params_dict: Dict[str, FloatParameter] = dict(zip(
        energy_params,
        [FloatParameter(name=p_name) for p_name in energy_params_names]
    ))

    self._general_params_dict: Dict[str, Union[FloatParameter, StringParameter]] = dict(zip(
        ["a", "lamb_m", "lamb_x", "material"],
        [
            FloatParameter(param=1., name=r"$a$"),
            FloatParameter(name=r"$\lambda_M$"),
            FloatParameter(name=r"$\lambda_X$"),
            StringParameter(name="material")
        ]
    ))
    if input_dict is not None:
        self.from_dict(input_dict)

from_dict(input_dict)

Function to set the variables with a dict.

Parameters:

Name	Type	Description	Default
input_dict	dict	The dictionary containing the parameters for the TMD lattice. The allowed keys are: a, lamb_m, lamb_x, material, eps_0_x_e, eps_1_x_e, eps_0_m_e, eps_1_m_e, u_1_0_m_e, u_1_1_m_e, u_1_2_m_e, u_1_3_m_e, u_1_4_m_e, u_2_0_m_e, u_2_1_m_e, u_2_2_m_e, u_2_3_m_e, u_2_4_m_e, u_2_5_m_e, u_2_0_x_e, u_2_1_x_e, u_2_2_x_e, u_2_3_x_e, u_2_4_x_e, u_2_5_x_e, u_3_0_m_e, u_3_1_m_e, u_3_2_m_e, u_3_3_m_e, u_3_4_m_e, u_4_0_m_e, u_4_1_m_e, u_4_2_m_e, u_4_3_m_e, u_4_4_m_e, u_5_0_m_e, u_5_1_m_e, u_5_3_m_e, u_5_5_m_e, u_5_6_m_e, u_5_0_x_e, u_5_2_x_e, u_5_3_x_e, u_5_5_x_e, u_5_6_x_e, u_6_0_m_e, u_6_1_m_e, u_6_2_m_e, u_6_3_m_e, u_6_4_m_e, u_6_5_m_e, u_6_0_x_e, u_6_1_x_e, u_6_2_x_e, u_6_3_x_e, u_6_4_x_e, u_6_5_x_e, eps_0_x_o, eps_1_x_o, eps_0_m_o, u_1_0_m_o, u_1_1_m_o, u_1_2_m_o, u_2_0_m_o, u_2_1_m_o, u_2_2_m_o, u_2_0_x_o, u_2_1_x_o, u_2_2_x_o, u_2_3_x_o, u_2_4_x_o, u_2_5_x_o, u_3_0_m_o, u_3_1_m_o, u_3_2_m_o, u_4_0_m_o, u_4_1_m_o, u_4_2_m_o, u_5_0_m_o, u_5_2_m_o, u_5_0_x_o, u_5_2_x_o, u_5_3_x_o, u_5_5_x_o, u_5_6_x_o, u_6_0_m_o, u_6_1_m_o, u_6_2_m_o, u_6_0_x_o, u_6_1_x_o, u_6_2_x_o, u_6_3_x_o, u_6_4_x_o and u_6_5_x_o	required

Source code in tmdybinding/parameters/symmetry_group.py

def from_dict(self, input_dict: Dict[str, Union[float, str]]):
    """Function to set the variables with a dict.

    Parameters:
        input_dict (dict): The dictionary containing the parameters for the TMD lattice.
            The allowed keys are:
            `a`,            `lamb_m`,       `lamb_x`,       `material`,
            `eps_0_x_e`, `eps_1_x_e`, `eps_0_m_e`, `eps_1_m_e`,
            `u_1_0_m_e`, `u_1_1_m_e`, `u_1_2_m_e`, `u_1_3_m_e`, `u_1_4_m_e`,
            `u_2_0_m_e`, `u_2_1_m_e`, `u_2_2_m_e`, `u_2_3_m_e`, `u_2_4_m_e`, `u_2_5_m_e`,
            `u_2_0_x_e`, `u_2_1_x_e`, `u_2_2_x_e`, `u_2_3_x_e`, `u_2_4_x_e`, `u_2_5_x_e`,
            `u_3_0_m_e`, `u_3_1_m_e`, `u_3_2_m_e`, `u_3_3_m_e`, `u_3_4_m_e`,
            `u_4_0_m_e`, `u_4_1_m_e`, `u_4_2_m_e`, `u_4_3_m_e`, `u_4_4_m_e`,
            `u_5_0_m_e`, `u_5_1_m_e`, `u_5_3_m_e`, `u_5_5_m_e`, `u_5_6_m_e`,
            `u_5_0_x_e`, `u_5_2_x_e`, `u_5_3_x_e`, `u_5_5_x_e`, `u_5_6_x_e`,
            `u_6_0_m_e`, `u_6_1_m_e`, `u_6_2_m_e`, `u_6_3_m_e`, `u_6_4_m_e`, `u_6_5_m_e`,
            `u_6_0_x_e`, `u_6_1_x_e`, `u_6_2_x_e`, `u_6_3_x_e`, `u_6_4_x_e`, `u_6_5_x_e`,
            `eps_0_x_o`, `eps_1_x_o`, `eps_0_m_o`,
            `u_1_0_m_o`, `u_1_1_m_o`, `u_1_2_m_o`,
            `u_2_0_m_o`, `u_2_1_m_o`, `u_2_2_m_o`,
            `u_2_0_x_o`, `u_2_1_x_o`, `u_2_2_x_o`, `u_2_3_x_o`, `u_2_4_x_o`, `u_2_5_x_o`,
            `u_3_0_m_o`, `u_3_1_m_o`, `u_3_2_m_o`,
            `u_4_0_m_o`, `u_4_1_m_o`, `u_4_2_m_o`,
            `u_5_0_m_o`, `u_5_2_m_o`,
            `u_5_0_x_o`, `u_5_2_x_o`, `u_5_3_x_o`, `u_5_5_x_o`, `u_5_6_x_o`,
            `u_6_0_m_o`, `u_6_1_m_o`, `u_6_2_m_o`,
            `u_6_0_x_o`, `u_6_1_x_o`, `u_6_2_x_o`, `u_6_3_x_o`, `u_6_4_x_o` and `u_6_5_x_o`
    """
    for param_name, value in input_dict.items():
        self[param_name] = value

get_name(key)

Function to get the name (in LaTeX) of the specific variable

Source code in tmdybinding/parameters/symmetry_group.py

def get_name(self, key) -> str:
    """Function to get the name (in LaTeX) of the specific variable"""
    if self._check_key(key):
        for param_dict in self._all_params_dict:
            if key in param_dict.keys():
                return param_dict[key].name
        warnings.warn(f"This should not happen, {key} should be a valid key.", UserWarning, stacklevel=2)

get_param(key)

Function to get the specific variable

Source code in tmdybinding/parameters/symmetry_group.py

def get_param(self, key):
    """Function to get the specific variable"""
    if self._check_key(key):
        for param_dict in self._all_params_dict:
            if key in param_dict.keys():
                return param_dict[key].param
        warnings.warn(f"This should not happen, {key} should be a valid key.", UserWarning, stacklevel=2)

t_m()

Function to get the variables as a dict.

Source code in tmdybinding/parameters/symmetry_group.py

def t_m(self) -> dict:
    """Function to get the variables as a dict."""
    out_dict = {}
    for param_dict in self._unique_params_dict:
        for key, item in param_dict.items():
            if item.param is not None:
                out_dict[key] = item.param
    return out_dict

SKParametersList

Bases: ParametersList

Class to store the parameters for SK e/o model

Source code in tmdybinding/parameters/slater_koster.py

class SKParametersList(ParametersList):
    """Class to store the parameters for SK e/o model"""

    def __init__(self, input_dict: Optional[Dict[str, Union[str, Optional[float]]]] = None):
        """Initialize the SK parameters

        Parameters:
            input_dict (dict): The dictionary containing the SK parameters. The keys are the parameter names and the
                values are the parameter values. The keys are:
                `a`, `lamb_x`, `lamb_m`, `material`, `theta`,
                `delta_p`, `delta_z`, `delta_0`, `delta_1`, `delta_2`,
                `v_0_pps`, `v_0_ppp`,
                `v_1_e_pds`, `v_1_e_pdp`, `v_1_o_pds`, `v_1_o_pdp`,
                `v_2_e_pps`, `v_2_e_ppp`, `v_2_e_pps_tb`, `v_2_e_ppp_tb`,
                `v_2_o_pps`, `v_2_o_ppp`, `v_2_o_pps_tb`, `v_2_o_ppp_tb`,
                `v_2_e_dds`, `v_2_e_ddp`, `v_2_e_ddd`,
                `v_2_o_ddp`, `v_2_o_ddd`,
                `v_3_e_pds`, `v_3_e_pdp`, `v_3_o_pds`, `v_3_o_pdp`,
                `v_4_e_pds`, `v_4_e_pdp`, `v_4_o_pds`, `v_4_o_pdp`,
                `v_5_e_pps`, `v_5_e_ppp`, `v_5_e_pps_tb`, `v_5_e_ppp_tb`,
                `v_5_o_pps`, `v_5_o_ppp`, `v_5_o_pps_tb`, `v_5_o_ppp_tb`,
                `v_5_e_dds`, `v_5_e_ddp`, `v_5_e_ddd`,
                `v_5_o_ddp`, `v_5_o_ddd`,
                `v_6_e_pps`, `v_6_e_ppp`, `v_6_e_pps_tb`, `v_6_e_ppp_tb`,
                `v_6_o_pps`, `v_6_o_ppp`, `v_6_o_pps_tb`, `v_6_o_ppp_tb`,
                `v_6_e_dds`, `v_6_e_ddp`, `v_6_e_ddd`,
                `v_6_o_ddp` and `v_6_o_ddd`"""
        super().__init__(None)
        self._recalculate_params_bool: bool = True
        self._tan_theta: Optional[float] = None

        onsite_sk_params = [
            "theta",
            *[f"delta_{r}" for r in ("p", "z", "0", "1", "2")],
            *[f"v_0_pp{r}" for r in ("s", "p")]
        ]
        onsite_sk_params_names = [
            r"$\theta$",
            *[rf"$\delta_{r}$" for r in ("p", "z", "0", "1", "2")],
            *[rf"$V^0_{{pp{r}}}$" for r in (r"\sigma", r"\pi")],
        ]

        self._onsite_sk_params_dict: dict = dict(zip(
            onsite_sk_params,
            [FloatParameter(name=p_name) for p_name in onsite_sk_params_names]
        ))

        sk_params = [
            *[f"v_{n}_{r}_pd{i}" for n in ("1", "3", "4") for r in ("e", "o") for i in ("s", "p")],
            *[f"v_{n}_{r}_pp{i}{t}" for n in ("2", "5", "6")
              for r in ("e", "o") for i in ("s", "p") for t in ("", "_tb")],
            *[f"v_{n}_e_dds" for n in ("2", "5", "6")],
            *[f"v_{n}_{r}_dd{i}" for n in ("2", "5", "6") for r in ("e", "o") for i in ("p", "d")]
        ]

        sk_params_names = [
            *[rf"$V^{{{n}_{r}}}_{{pd{i}}}$" for n in ("1", "3", "4") for r in ("e", "o") for i in (r"\sigma", r"\pi")],
            *[rf"$V^{{{n}_{r}}}_{{pp{i}{t}}}$" for n in ("2", "5", "6")
              for r in ("e", "o") for i in (r"\sigma", r"\pi") for t in ("", ",tb")],
            *[rf"$V^{{{n}_e}}_{{dd\sigmas}}$" for n in ("2", "5", "6")],
            *[rf"$V^{{{n}_{r}}}_{{dd{i}}}$" for n in ("2", "5", "6") for r in ("e", "o") for i in (r"\pi", r"\delta")]
        ]
        self._sk_params_dict: dict = dict(zip(
            sk_params,
            [FloatParameter(name=p_name) for p_name in sk_params_names]
        ))

        if input_dict is not None:
            self.from_dict(input_dict)

    @property
    def _unique_params_dict(self) -> List[dict]:
        return [self._general_params_dict, self._onsite_sk_params_dict, self._sk_params_dict]

    @property
    def _protected_params_dict(self) -> Optional[List[dict]]:
        return [self._energy_params_dict]

    def __setitem__(self, key, value):
        """Set the value of a parameter and recalculate the parameters."""
        super().__setitem__(key, value)
        self._recalculate_params()

    def from_dict(self, input_dict: Dict[str, Union[float, str]]):
        """Set the parameters from a dictionary and recalculate the parameters.

        Parameters:
            input_dict (dict): The dictionary containing the SK parameters. The keys are the parameter names and the
                values are the parameter values. The keys are:
                `a`, `lamb_x`, `lamb_m`, `material`, `theta`,
                `delta_p`, `delta_z`, `delta_0`, `delta_1`, `delta_2`,
                `v_0_pps`, `v_0_ppp`,
                `v_1_e_pds`, `v_1_e_pdp`, `v_1_o_pds`, `v_1_o_pdp`,
                `v_2_e_pps`, `v_2_e_ppp`, `v_2_e_pps_tb`, `v_2_e_ppp_tb`,
                `v_2_o_pps`, `v_2_o_ppp`, `v_2_o_pps_tb`, `v_2_o_ppp_tb`,
                `v_2_e_dds`, `v_2_e_ddp`, `v_2_e_ddd`,
                `v_2_o_ddp`, `v_2_o_ddd`,
                `v_3_e_pds`, `v_3_e_pdp`, `v_3_o_pds`, `v_3_o_pdp`,
                `v_4_e_pds`, `v_4_e_pdp`, `v_4_o_pds`, `v_4_o_pdp`,
                `v_5_e_pps`, `v_5_e_ppp`, `v_5_e_pps_tb`, `v_5_e_ppp_tb`,
                `v_5_o_pps`, `v_5_o_ppp`, `v_5_o_pps_tb`, `v_5_o_ppp_tb`,
                `v_5_e_dds`, `v_5_e_ddp`, `v_5_e_ddd`,
                `v_5_o_ddp`, `v_5_o_ddd`,
                `v_6_e_pps`, `v_6_e_ppp`, `v_6_e_pps_tb`, `v_6_e_ppp_tb`,
                `v_6_o_pps`, `v_6_o_ppp`, `v_6_o_pps_tb`, `v_6_o_ppp_tb`,
                `v_6_e_dds`, `v_6_e_ddp`, `v_6_e_ddd`,
                `v_6_o_ddp` and `v_6_o_ddd`"""
        self._recalculate_params_bool = False
        super().from_dict(input_dict)
        self._recalculate_params_bool = True
        self._recalculate_params()

    def _recalculate_params(self):
        if self._recalculate_params_bool:
            self._tan_theta = np.tan(self["theta"]) if self["theta"] is not None else np.sqrt(3 / 4)
            # Onsite elements
            # X
            self._energy_params_dict["eps_0_x_e"].param = self._comb_nonefloat([self["delta_p"], self["v_0_ppp"]])
            self._energy_params_dict["eps_1_x_e"].param = self._subtract_param(self["delta_z"], self["v_0_pps"])
            self._energy_params_dict["eps_0_x_o"].param = self._subtract_param(self["delta_p"], self["v_0_ppp"])
            self._energy_params_dict["eps_1_x_o"].param = self._comb_nonefloat([self["delta_z"], self["v_0_pps"]])
            # M
            self._energy_params_dict["eps_0_m_e"].param = self["delta_0"]
            self._energy_params_dict["eps_1_m_e"].param = self["delta_2"]
            self._energy_params_dict["eps_0_m_o"].param = self["delta_1"]
            # h1
            [
                self._energy_params_dict["u_1_0_m_e"].param,
                self._energy_params_dict["u_1_1_m_e"].param,
                self._energy_params_dict["u_1_2_m_e"].param,
                self._energy_params_dict["u_1_3_m_e"].param,
                self._energy_params_dict["u_1_4_m_e"].param
            ] = self._h_mx_e(r=-1, vpds=self["v_1_e_pds"], vpdp=self["v_1_e_pdp"])
            [
                self._energy_params_dict["u_1_0_m_o"].param,
                self._energy_params_dict["u_1_1_m_o"].param,
                self._energy_params_dict["u_1_2_m_o"].param
            ] = self._h_mx_o(r=-1, vpds=self["v_1_o_pds"], vpdp=self["v_1_o_pdp"])
            # h2
            [
                self._energy_params_dict["u_2_0_m_e"].param,
                self._energy_params_dict["u_2_1_m_e"].param,
                self._energy_params_dict["u_2_2_m_e"].param,
                self._energy_params_dict["u_2_3_m_e"].param,
                self._energy_params_dict["u_2_4_m_e"].param,
                self._energy_params_dict["u_2_5_m_e"].param
            ] = self._h_mm_x_e(vdds=self["v_2_e_dds"], vddp=self["v_2_e_ddp"], vddd=self["v_2_e_ddd"])
            [
                self._energy_params_dict["u_2_0_m_o"].param,
                self._energy_params_dict["u_2_1_m_o"].param,
                self._energy_params_dict["u_2_2_m_o"].param
            ] = self._h_mm_x_o(vddp=self["v_2_o_ddp"], vddd=self["v_2_o_ddd"])
            [
                self._energy_params_dict["u_2_0_x_e"].param,
                self._energy_params_dict["u_2_1_x_e"].param,
                self._energy_params_dict["u_2_2_x_e"].param,
                self._energy_params_dict["u_2_3_x_e"].param,
                self._energy_params_dict["u_2_4_x_e"].param,
                self._energy_params_dict["u_2_5_x_e"].param
            ] = self._h_xx_x_e(r=np.sqrt(3), vpps=self["v_2_e_pps"], vppp=self["v_2_e_ppp"],
                               vppstb=self["v_2_e_pps_tb"], vppptb=self["v_2_e_ppp_tb"])
            [
                self._energy_params_dict["u_2_0_x_o"].param,
                self._energy_params_dict["u_2_1_x_o"].param,
                self._energy_params_dict["u_2_2_x_o"].param,
                self._energy_params_dict["u_2_3_x_o"].param,
                self._energy_params_dict["u_2_4_x_o"].param,
                self._energy_params_dict["u_2_5_x_o"].param
            ] = self._h_xx_x_o(r=np.sqrt(3), vpps=self["v_2_o_pps"], vppp=self["v_2_o_ppp"],
                               vppstb=self["v_2_o_pps_tb"], vppptb=self["v_2_o_ppp_tb"])
            # h3
            [
                self._energy_params_dict["u_3_0_m_e"].param,
                self._energy_params_dict["u_3_1_m_e"].param,
                self._energy_params_dict["u_3_2_m_e"].param,
                self._energy_params_dict["u_3_3_m_e"].param,
                self._energy_params_dict["u_3_4_m_e"].param
            ] = self._h_mx_e(r=2, vpds=self["v_3_e_pds"], vpdp=self["v_3_e_pdp"])
            [
                self._energy_params_dict["u_3_0_m_o"].param,
                self._energy_params_dict["u_3_1_m_o"].param,
                self._energy_params_dict["u_3_2_m_o"].param
            ] = self._h_mx_o(r=2, vpds=self["v_3_o_pds"], vpdp=self["v_3_o_pdp"])
            # h4
            [
                self._energy_params_dict["u_4_0_m_e"].param,
                self._energy_params_dict["u_4_1_m_e"].param,
                self._energy_params_dict["u_4_2_m_e"].param,
                self._energy_params_dict["u_4_3_m_e"].param,
                self._energy_params_dict["u_4_4_m_e"].param
            ] = self._h_mx_e(r=-np.sqrt(7), vpds=self["v_4_e_pds"], vpdp=self["v_4_e_pdp"])
            [
                self._energy_params_dict["u_4_0_m_o"].param,
                self._energy_params_dict["u_4_1_m_o"].param,
                self._energy_params_dict["u_4_2_m_o"].param
            ] = self._h_mx_o(r=-np.sqrt(7), vpds=self["v_4_o_pds"], vpdp=self["v_4_o_pdp"])
            # h5
            [
                self._energy_params_dict["u_5_0_m_e"].param,
                self._energy_params_dict["u_5_1_m_e"].param,
                self._energy_params_dict["u_5_3_m_e"].param,
                self._energy_params_dict["u_5_5_m_e"].param,
                self._energy_params_dict["u_5_6_m_e"].param
            ] = self._h_mm_y_e(vdds=self["v_5_e_dds"], vddp=self["v_5_e_ddp"], vddd=self["v_5_e_ddd"])
            [
                self._energy_params_dict["u_5_0_m_o"].param,
                self._energy_params_dict["u_5_2_m_o"].param
            ] = self._h_mm_y_o(vddp=self["v_5_o_ddp"], vddd=self["v_5_o_ddd"])
            [
                self._energy_params_dict["u_5_0_x_e"].param,
                self._energy_params_dict["u_5_2_x_e"].param,
                self._energy_params_dict["u_5_3_x_e"].param,
                self._energy_params_dict["u_5_5_x_e"].param,
                self._energy_params_dict["u_5_6_x_e"].param
            ] = self._h_xx_y_e(r=3, vpps=self["v_5_e_pps"], vppp=self["v_5_e_ppp"],
                               vppstb=self["v_5_e_pps_tb"], vppptb=self["v_5_e_ppp_tb"])
            [
                self._energy_params_dict["u_5_0_x_o"].param,
                self._energy_params_dict["u_5_2_x_o"].param,
                self._energy_params_dict["u_5_3_x_o"].param,
                self._energy_params_dict["u_5_5_x_o"].param,
                self._energy_params_dict["u_5_6_x_o"].param
            ] = self._h_xx_y_o(r=3, vpps=self["v_5_o_pps"], vppp=self["v_5_o_ppp"],
                               vppstb=self["v_5_e_pps_tb"], vppptb=self["v_5_o_ppp_tb"])
            # h6
            [
                self._energy_params_dict["u_6_0_m_e"].param,
                self._energy_params_dict["u_6_1_m_e"].param,
                self._energy_params_dict["u_6_2_m_e"].param,
                self._energy_params_dict["u_6_3_m_e"].param,
                self._energy_params_dict["u_6_4_m_e"].param,
                self._energy_params_dict["u_6_5_m_e"].param
            ] = self._h_mm_x_e(vdds=self["v_6_e_dds"], vddp=self["v_6_e_ddp"], vddd=self["v_6_e_ddd"])
            [
                self._energy_params_dict["u_6_0_m_o"].param,
                self._energy_params_dict["u_6_1_m_o"].param,
                self._energy_params_dict["u_6_2_m_o"].param
            ] = self._h_mm_x_o(vddp=self["v_6_o_ddp"], vddd=self["v_6_o_ddd"])
            [
                self._energy_params_dict["u_6_0_x_e"].param,
                self._energy_params_dict["u_6_1_x_e"].param,
                self._energy_params_dict["u_6_2_x_e"].param,
                self._energy_params_dict["u_6_3_x_e"].param,
                self._energy_params_dict["u_6_4_x_e"].param,
                self._energy_params_dict["u_6_5_x_e"].param
            ] = self._h_xx_x_e(r=np.sqrt(3), vpps=self["v_6_e_pps"], vppp=self["v_6_e_ppp"],
                               vppstb=self["v_6_e_pps_tb"], vppptb=self["v_6_e_ppp_tb"])
            [
                self._energy_params_dict["u_6_0_x_o"].param,
                self._energy_params_dict["u_6_1_x_o"].param,
                self._energy_params_dict["u_6_2_x_o"].param,
                self._energy_params_dict["u_6_3_x_o"].param,
                self._energy_params_dict["u_6_4_x_o"].param,
                self._energy_params_dict["u_6_5_x_o"].param
            ] = self._h_xx_x_o(r=np.sqrt(3), vpps=self["v_6_o_pps"], vppp=self["v_6_o_ppp"],
                               vppstb=self["v_6_o_pps_tb"], vppptb=self["v_6_o_ppp_tb"])

    def _subtract_param(self, p1: Optional[float], p2: Optional[float]):
        return self._comb_nonefloat([p1, -p2 if p2 is not None else None])

    @staticmethod
    def _h_mm_x_e(vdds: Optional[float], vddp: Optional[float], vddd: Optional[float]) -> List[Optional[float]]:
        vddsd_bool = (vdds is not None) and (vddd is not None)
        vddp_bool = vddp is not None
        u_0: Optional[float] = 1 / 4 * (vdds + 3 * vddd) if vddsd_bool else None
        u_1: Optional[float] = np.sqrt(3) / 4 * (-vdds + vddd) if vddsd_bool else None
        u_2: Optional[float] = 0 if (vddsd_bool or vddp_bool) else None
        u_3: Optional[float] = 1 / 4 * (3 * vdds + vddd) if vddsd_bool else None
        u_4: Optional[float] = 0 if (vddsd_bool or vddp_bool) else None
        u_5: Optional[float] = vddp if vddp_bool else None
        return [u_0, u_1, u_2, u_3, u_4, u_5]

    @staticmethod
    def _h_mm_y_e(vdds: Optional[float], vddp: Optional[float], vddd: Optional[float]) -> List[Optional[float]]:
        vddsd_bool = (vdds is not None) and (vddd is not None)
        vddp_bool = vddp is not None
        u_0: Optional[float] = 1 / 4 * (vdds + 3 * vddd) if vddsd_bool else None
        u_1: Optional[float] = np.sqrt(3) / 4 * (-vdds + vddd) if vddsd_bool else None
        u_3: Optional[float] = 1 / 4 * (3 * vdds + vddd) if vddsd_bool else None
        u_5: Optional[float] = vddp if vddp_bool else None
        u_6: Optional[float] = np.sqrt(3) / 4 * (-vdds + vddd) if vddsd_bool else None
        return [u_0, u_1, u_3, u_5, u_6]

    @staticmethod
    def _h_mm_x_o(vddp: Optional[float], vddd: Optional[float]) -> List[Optional[float]]:
        vddd_bool = vddd is not None
        vddp_bool = vddp is not None
        u_0: Optional[float] = vddp if vddp_bool else None
        u_1: Optional[float] = 0 if (vddd_bool or vddp_bool) else None
        u_2: Optional[float] = vddd if vddd_bool else None
        return [u_0, u_1, u_2]

    @staticmethod
    def _h_mm_y_o(vddp: Optional[float], vddd: Optional[float]) -> List[Optional[float]]:
        vddd_bool = vddd is not None
        vddp_bool = vddp is not None
        u_0: Optional[float] = vddp if vddp_bool else None
        u_2: Optional[float] = vddd if vddd_bool else None
        return [u_0, u_2]

    @staticmethod
    def _comb_nonefloat(u_list: List[Optional[float]]) -> Optional[float]:
        bl = [ul is not None for ul in u_list]
        return None if np.all(np.logical_not(bl)) else np.sum([u_list[li] for li in np.arange(len(u_list))[bl]])

    def _h_xx_x_e(self, r: float, vpps: Optional[float], vppp: Optional[float],
                  vppstb: Optional[float] = None, vppptb: Optional[float] = None) -> List[Optional[float]]:
        vpps_bool = vpps is not None
        vppp_bool = vppp is not None
        vptb_bool = vppstb is not None
        vstb_bool = vppptb is not None
        u_0_0: Optional[float] = vpps if vpps_bool else None
        u_0_1: Optional[float] = vppptb if vptb_bool else None
        u_0_2: Optional[float] = -r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_0: Optional[float] = self._comb_nonefloat([u_0_0, u_0_1, u_0_2])
        u_1: Optional[float] = 0 if (vpps_bool or vppp_bool or vstb_bool or vptb_bool) else None
        u_2: Optional[float] = -2 * self._tan_theta * r * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_3_0: Optional[float] = vppp if vppp_bool else None
        u_3_1: Optional[float] = vppptb if vptb_bool else None
        u_3: Optional[float] = self._comb_nonefloat([u_3_0, u_3_1])
        u_4: Optional[float] = 0 if (vpps_bool or vppp_bool or vstb_bool or vptb_bool) else None
        u_5_0: Optional[float] = vppp if vppp_bool else None
        u_5_1: Optional[float] = -vppstb if vstb_bool else None
        u_5_2: Optional[float] = -r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_5: Optional[float] = self._comb_nonefloat([u_5_0, u_5_1, u_5_2])
        return [u_0, u_1, u_2, u_3, u_4, u_5]

    def _h_xx_y_e(self, r: float, vpps: Optional[float], vppp: Optional[float],
                  vppstb: Optional[float] = None, vppptb: Optional[float] = None) -> List[Optional[float]]:
        vpps_bool = vpps is not None
        vppp_bool = vppp is not None
        vptb_bool = vppstb is not None
        vstb_bool = vppptb is not None
        u_0_0: Optional[float] = vpps if vpps_bool else None
        u_0_1: Optional[float] = vppptb if vptb_bool else None
        u_0_2: Optional[float] = -r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_0: Optional[float] = self._comb_nonefloat([u_0_0, u_0_1, u_0_2])
        u_2: Optional[float] = -2 * self._tan_theta * r * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_3_0: Optional[float] = vppp if vppp_bool else None
        u_3_1: Optional[float] = vppptb if vptb_bool else None
        u_3: Optional[float] = self._comb_nonefloat([u_3_0, u_3_1])
        u_5_0: Optional[float] = vppp if vppp_bool else None
        u_5_1: Optional[float] = -vppstb if vstb_bool else None
        u_5_2: Optional[float] = -r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_5: Optional[float] = self._comb_nonefloat([u_5_0, u_5_1, u_5_2])
        u_6: Optional[float] = 2 * self._tan_theta * r * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        return [u_0, u_2, u_3, u_5, u_6]

    def _h_xx_x_o(self, r: float, vpps: Optional[float], vppp: Optional[float],
                  vppstb: Optional[float] = None, vppptb: Optional[float] = None) -> List[Optional[float]]:
        vpps_bool = vpps is not None
        vppp_bool = vppp is not None
        vptb_bool = vppstb is not None
        vstb_bool = vppptb is not None
        u_0_0: Optional[float] = vpps if vpps_bool else None
        u_0_1: Optional[float] = -vppptb if vptb_bool else None
        u_0_2: Optional[float] = r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_0: Optional[float] = self._comb_nonefloat([u_0_0, u_0_1, u_0_2])
        u_1: Optional[float] = 0 if (vpps_bool or vppp_bool or vstb_bool or vptb_bool) else None
        u_2: Optional[float] = -2 * self._tan_theta * r * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_3_0: Optional[float] = vppp if vppp_bool else None
        u_3_1: Optional[float] = -vppptb if vptb_bool else None
        u_3: Optional[float] = self._comb_nonefloat([u_3_0, u_3_1])
        u_4: Optional[float] = 0 if (vpps_bool or vppp_bool or vstb_bool or vptb_bool) else None
        u_5_0: Optional[float] = vppp if vppp_bool else None
        u_5_1: Optional[float] = vppstb if vstb_bool else None
        u_5_2: Optional[float] = r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_5: Optional[float] = self._comb_nonefloat([u_5_0, u_5_1, u_5_2])
        return [u_0, u_1, u_2, u_3, u_4, u_5]

    def _h_xx_y_o(self, r: float, vpps: Optional[float], vppp: Optional[float],
                  vppstb: Optional[float] = None, vppptb: Optional[float] = None) -> List[Optional[float]]:
        vpps_bool = vpps is not None
        vppp_bool = vppp is not None
        vptb_bool = vppstb is not None
        vstb_bool = vppptb is not None
        u_0_0: Optional[float] = vpps if vpps_bool else None
        u_0_1: Optional[float] = -vppptb if vptb_bool else None
        u_0_2: Optional[float] = r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_0: Optional[float] = self._comb_nonefloat([u_0_0, u_0_1, u_0_2])
        u_2: Optional[float] = 2 * self._tan_theta * r * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_3_0: Optional[float] = vppp if vppp_bool else None
        u_3_1: Optional[float] = -vppptb if vptb_bool else None
        u_3: Optional[float] = self._comb_nonefloat([u_3_0, u_3_1])
        u_5_0: Optional[float] = vppp if vppp_bool else None
        u_5_1: Optional[float] = vppstb if vstb_bool else None
        u_5_2: Optional[float] = r ** 2 * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        u_5: Optional[float] = self._comb_nonefloat([u_5_0, u_5_1, u_5_2])
        u_6: Optional[float] = -2 * self._tan_theta * r * (vppptb - vppstb) / (r ** 2 + 4 * self._tan_theta ** 2)\
            if vstb_bool and vptb_bool else None
        return [u_0, u_2, u_3, u_5, u_6]

    def _h_mx_e(self, r: float, vpds: Optional[float], vpdp: Optional[float]) -> List[Optional[float]]:
        if (vpds is not None) and (vpdp is not None):
            u_0 = np.sqrt(2) * r * vpdp / (np.sqrt(r ** 2 + self._tan_theta ** 2))
            u_1 = -r * (
                    2 * np.sqrt(3) * self._tan_theta ** 2 * vpdp + (r ** 2 - 2 * self._tan_theta ** 2) * vpds
            ) / (np.sqrt(2) * ((r ** 2 + self._tan_theta ** 2) ** (3 / 2)))
            u_2 = -r * (
                    2 * self._tan_theta ** 2 * vpdp + np.sqrt(3) * r ** 2 * vpds
            ) / (np.sqrt(2) * ((r ** 2 + self._tan_theta ** 2) ** (3 / 2)))
            u_3 = self._tan_theta * (
                    r ** 2 * 2 * np.sqrt(3) * vpdp + (2 * self._tan_theta ** 2 - r ** 2) * vpds
            ) / (np.sqrt(2) * ((r ** 2 + self._tan_theta ** 2) ** (3 / 2)))
            u_4 = r ** 2 * self._tan_theta * (
                    2 * vpdp - np.sqrt(3) * vpds
            ) / (np.sqrt(2) * ((r ** 2 + self._tan_theta ** 2) ** (3 / 2)))
            return [u_0, u_1, u_2, u_3, u_4]
        else:
            return [None, None, None, None, None]

    def _h_mx_o(self, r: float, vpds: Optional[float], vpdp: Optional[float]) -> List[Optional[float]]:
        if (vpds is not None) and (vpdp is not None):
            u_0 = np.sqrt(2) * self._tan_theta * vpdp / np.sqrt(r ** 2 + self._tan_theta ** 2)
            u_1 = np.sqrt(2) * self._tan_theta * (
                    (self._tan_theta ** 2 - r ** 2) * vpdp + r ** 2 * np.sqrt(3) * vpds
            ) / ((r ** 2 + self._tan_theta ** 2) ** (3 / 2))
            u_2 = np.sqrt(2) * r * (
                    (r ** 2 - self._tan_theta ** 2) * vpdp + self._tan_theta ** 2 * np.sqrt(3) * vpds
            ) / ((r ** 2 + self._tan_theta ** 2) ** (3 / 2))
            return [u_0, u_1, u_2]
        else:
            return [None, None, None]

__init__(input_dict=None)

Initialize the SK parameters

Parameters:

Name	Type	Description	Default
input_dict	dict	The dictionary containing the SK parameters. The keys are the parameter names and the values are the parameter values. The keys are: a, lamb_x, lamb_m, material, theta, delta_p, delta_z, delta_0, delta_1, delta_2, v_0_pps, v_0_ppp, v_1_e_pds, v_1_e_pdp, v_1_o_pds, v_1_o_pdp, v_2_e_pps, v_2_e_ppp, v_2_e_pps_tb, v_2_e_ppp_tb, v_2_o_pps, v_2_o_ppp, v_2_o_pps_tb, v_2_o_ppp_tb, v_2_e_dds, v_2_e_ddp, v_2_e_ddd, v_2_o_ddp, v_2_o_ddd, v_3_e_pds, v_3_e_pdp, v_3_o_pds, v_3_o_pdp, v_4_e_pds, v_4_e_pdp, v_4_o_pds, v_4_o_pdp, v_5_e_pps, v_5_e_ppp, v_5_e_pps_tb, v_5_e_ppp_tb, v_5_o_pps, v_5_o_ppp, v_5_o_pps_tb, v_5_o_ppp_tb, v_5_e_dds, v_5_e_ddp, v_5_e_ddd, v_5_o_ddp, v_5_o_ddd, v_6_e_pps, v_6_e_ppp, v_6_e_pps_tb, v_6_e_ppp_tb, v_6_o_pps, v_6_o_ppp, v_6_o_pps_tb, v_6_o_ppp_tb, v_6_e_dds, v_6_e_ddp, v_6_e_ddd, v_6_o_ddp and v_6_o_ddd	None

Source code in tmdybinding/parameters/slater_koster.py

def __init__(self, input_dict: Optional[Dict[str, Union[str, Optional[float]]]] = None):
    """Initialize the SK parameters

    Parameters:
        input_dict (dict): The dictionary containing the SK parameters. The keys are the parameter names and the
            values are the parameter values. The keys are:
            `a`, `lamb_x`, `lamb_m`, `material`, `theta`,
            `delta_p`, `delta_z`, `delta_0`, `delta_1`, `delta_2`,
            `v_0_pps`, `v_0_ppp`,
            `v_1_e_pds`, `v_1_e_pdp`, `v_1_o_pds`, `v_1_o_pdp`,
            `v_2_e_pps`, `v_2_e_ppp`, `v_2_e_pps_tb`, `v_2_e_ppp_tb`,
            `v_2_o_pps`, `v_2_o_ppp`, `v_2_o_pps_tb`, `v_2_o_ppp_tb`,
            `v_2_e_dds`, `v_2_e_ddp`, `v_2_e_ddd`,
            `v_2_o_ddp`, `v_2_o_ddd`,
            `v_3_e_pds`, `v_3_e_pdp`, `v_3_o_pds`, `v_3_o_pdp`,
            `v_4_e_pds`, `v_4_e_pdp`, `v_4_o_pds`, `v_4_o_pdp`,
            `v_5_e_pps`, `v_5_e_ppp`, `v_5_e_pps_tb`, `v_5_e_ppp_tb`,
            `v_5_o_pps`, `v_5_o_ppp`, `v_5_o_pps_tb`, `v_5_o_ppp_tb`,
            `v_5_e_dds`, `v_5_e_ddp`, `v_5_e_ddd`,
            `v_5_o_ddp`, `v_5_o_ddd`,
            `v_6_e_pps`, `v_6_e_ppp`, `v_6_e_pps_tb`, `v_6_e_ppp_tb`,
            `v_6_o_pps`, `v_6_o_ppp`, `v_6_o_pps_tb`, `v_6_o_ppp_tb`,
            `v_6_e_dds`, `v_6_e_ddp`, `v_6_e_ddd`,
            `v_6_o_ddp` and `v_6_o_ddd`"""
    super().__init__(None)
    self._recalculate_params_bool: bool = True
    self._tan_theta: Optional[float] = None

    onsite_sk_params = [
        "theta",
        *[f"delta_{r}" for r in ("p", "z", "0", "1", "2")],
        *[f"v_0_pp{r}" for r in ("s", "p")]
    ]
    onsite_sk_params_names = [
        r"$\theta$",
        *[rf"$\delta_{r}$" for r in ("p", "z", "0", "1", "2")],
        *[rf"$V^0_{{pp{r}}}$" for r in (r"\sigma", r"\pi")],
    ]

    self._onsite_sk_params_dict: dict = dict(zip(
        onsite_sk_params,
        [FloatParameter(name=p_name) for p_name in onsite_sk_params_names]
    ))

    sk_params = [
        *[f"v_{n}_{r}_pd{i}" for n in ("1", "3", "4") for r in ("e", "o") for i in ("s", "p")],
        *[f"v_{n}_{r}_pp{i}{t}" for n in ("2", "5", "6")
          for r in ("e", "o") for i in ("s", "p") for t in ("", "_tb")],
        *[f"v_{n}_e_dds" for n in ("2", "5", "6")],
        *[f"v_{n}_{r}_dd{i}" for n in ("2", "5", "6") for r in ("e", "o") for i in ("p", "d")]
    ]

    sk_params_names = [
        *[rf"$V^{{{n}_{r}}}_{{pd{i}}}$" for n in ("1", "3", "4") for r in ("e", "o") for i in (r"\sigma", r"\pi")],
        *[rf"$V^{{{n}_{r}}}_{{pp{i}{t}}}$" for n in ("2", "5", "6")
          for r in ("e", "o") for i in (r"\sigma", r"\pi") for t in ("", ",tb")],
        *[rf"$V^{{{n}_e}}_{{dd\sigmas}}$" for n in ("2", "5", "6")],
        *[rf"$V^{{{n}_{r}}}_{{dd{i}}}$" for n in ("2", "5", "6") for r in ("e", "o") for i in (r"\pi", r"\delta")]
    ]
    self._sk_params_dict: dict = dict(zip(
        sk_params,
        [FloatParameter(name=p_name) for p_name in sk_params_names]
    ))

    if input_dict is not None:
        self.from_dict(input_dict)

__setitem__(key, value)

Set the value of a parameter and recalculate the parameters.

Source code in tmdybinding/parameters/slater_koster.py

def __setitem__(self, key, value):
    """Set the value of a parameter and recalculate the parameters."""
    super().__setitem__(key, value)
    self._recalculate_params()

from_dict(input_dict)

Set the parameters from a dictionary and recalculate the parameters.

Parameters:

Name	Type	Description	Default
input_dict	dict	The dictionary containing the SK parameters. The keys are the parameter names and the values are the parameter values. The keys are: a, lamb_x, lamb_m, material, theta, delta_p, delta_z, delta_0, delta_1, delta_2, v_0_pps, v_0_ppp, v_1_e_pds, v_1_e_pdp, v_1_o_pds, v_1_o_pdp, v_2_e_pps, v_2_e_ppp, v_2_e_pps_tb, v_2_e_ppp_tb, v_2_o_pps, v_2_o_ppp, v_2_o_pps_tb, v_2_o_ppp_tb, v_2_e_dds, v_2_e_ddp, v_2_e_ddd, v_2_o_ddp, v_2_o_ddd, v_3_e_pds, v_3_e_pdp, v_3_o_pds, v_3_o_pdp, v_4_e_pds, v_4_e_pdp, v_4_o_pds, v_4_o_pdp, v_5_e_pps, v_5_e_ppp, v_5_e_pps_tb, v_5_e_ppp_tb, v_5_o_pps, v_5_o_ppp, v_5_o_pps_tb, v_5_o_ppp_tb, v_5_e_dds, v_5_e_ddp, v_5_e_ddd, v_5_o_ddp, v_5_o_ddd, v_6_e_pps, v_6_e_ppp, v_6_e_pps_tb, v_6_e_ppp_tb, v_6_o_pps, v_6_o_ppp, v_6_o_pps_tb, v_6_o_ppp_tb, v_6_e_dds, v_6_e_ddp, v_6_e_ddd, v_6_o_ddp and v_6_o_ddd	required

Source code in tmdybinding/parameters/slater_koster.py

def from_dict(self, input_dict: Dict[str, Union[float, str]]):
    """Set the parameters from a dictionary and recalculate the parameters.

    Parameters:
        input_dict (dict): The dictionary containing the SK parameters. The keys are the parameter names and the
            values are the parameter values. The keys are:
            `a`, `lamb_x`, `lamb_m`, `material`, `theta`,
            `delta_p`, `delta_z`, `delta_0`, `delta_1`, `delta_2`,
            `v_0_pps`, `v_0_ppp`,
            `v_1_e_pds`, `v_1_e_pdp`, `v_1_o_pds`, `v_1_o_pdp`,
            `v_2_e_pps`, `v_2_e_ppp`, `v_2_e_pps_tb`, `v_2_e_ppp_tb`,
            `v_2_o_pps`, `v_2_o_ppp`, `v_2_o_pps_tb`, `v_2_o_ppp_tb`,
            `v_2_e_dds`, `v_2_e_ddp`, `v_2_e_ddd`,
            `v_2_o_ddp`, `v_2_o_ddd`,
            `v_3_e_pds`, `v_3_e_pdp`, `v_3_o_pds`, `v_3_o_pdp`,
            `v_4_e_pds`, `v_4_e_pdp`, `v_4_o_pds`, `v_4_o_pdp`,
            `v_5_e_pps`, `v_5_e_ppp`, `v_5_e_pps_tb`, `v_5_e_ppp_tb`,
            `v_5_o_pps`, `v_5_o_ppp`, `v_5_o_pps_tb`, `v_5_o_ppp_tb`,
            `v_5_e_dds`, `v_5_e_ddp`, `v_5_e_ddd`,
            `v_5_o_ddp`, `v_5_o_ddd`,
            `v_6_e_pps`, `v_6_e_ppp`, `v_6_e_pps_tb`, `v_6_e_ppp_tb`,
            `v_6_o_pps`, `v_6_o_ppp`, `v_6_o_pps_tb`, `v_6_o_ppp_tb`,
            `v_6_e_dds`, `v_6_e_ddp`, `v_6_e_ddd`,
            `v_6_o_ddp` and `v_6_o_ddd`"""
    self._recalculate_params_bool = False
    super().from_dict(input_dict)
    self._recalculate_params_bool = True
    self._recalculate_params()

SKSimpleParametersList

Bases: SKParametersList

Class to store the simplified SK paramters (no even/odd).

Source code in tmdybinding/parameters/slater_koster.py

class SKSimpleParametersList(SKParametersList):
    """Class to store the simplified SK paramters (no even/odd)."""
    def __init__(self, input_dict: Optional[Dict[str, Union[str, Optional[float]]]] = None):
        """Initializes the SKSimpleParametersList object.

        Parameters:
            input_dict (dict): Dictionary with the SK paramters. The keus are the parameter names and the values are the
                parameter values. The parameter names are:
                `a`, `material`, `lamb_x`, `lamb_m`, `theta`,
                `delta_p`, `delta_z`, `delta_0`, `delta_1`, `delta_2`,
                `v_0_pps`, `v_0_ppp`,
                `v_1_pds`, `v_1_pdp`,
                `v_2_dds`, `v_2_ddp`, `v_2_ddd`, `v_2_pps`, `v_2_ppp`, `v_2_pps_tb`, `v_2_ppp_tb`,
                `v_3_pds`, `v_3_pdp`,
                `v_4_pds`, `v_4_pdp`,
                `v_5_dds`, `v_5_ddp`, `v_5_ddd`, `v_5_pps`, `v_5_ppp`, `v_5_pps_tb`, `v_5_ppp_tb`,
                `v_6_dds`, `v_6_ddp`, `v_6_ddd`, `v_6_pps`, `v_6_ppp`, `v_6_pps_tb` and `v_6_ppp_tb`."""
        super().__init__(None)
        sk_simple_params = [
            *[f"v_{n}_pd{i}" for n in ("1", "3", "4") for i in ("s", "p")],
            *[f"v_{n}_pp{i}{t}" for n in ("2", "5", "6") for i in ("s", "p") for t in ("", "_tb")],
            *[f"v_{n}_dd{i}" for n in ("2", "5", "6") for i in ("s", "p", "d")]
        ]

        sk_simple_params_names = [
            *[rf"$V^{{{n}}}_{{pd{i}}}$" for n in ("1", "3", "4") for i in (r"\sigma", r"\pi")],
            *[rf"$V^{{{n}}}_{{pp{i}{t}}}$" for n in ("2", "5", "6") for i in (r"\sigma", r"\pi") for t in ("", ",tb")],
            *[rf"$V^{{{n}}}_{{dd{i}}}$" for n in ("2", "5", "6") for i in (r"\sigmas", r"\pi", r"\delta")]
        ]
        self._sk_simple_params_dict: dict = dict(zip(
            sk_simple_params,
            [FloatParameter(name=p_name) for p_name in sk_simple_params_names]
        ))

        if input_dict is not None:
            self.from_dict(input_dict)

    def _recalculate_params(self):
        if self._recalculate_params_bool:
            # h1
            self._sk_params_dict["v_1_e_pds"].param = self["v_1_pds"]
            self._sk_params_dict["v_1_o_pds"].param = self["v_1_pds"]
            self._sk_params_dict["v_1_e_pdp"].param = self["v_1_pdp"]
            self._sk_params_dict["v_1_o_pdp"].param = self["v_1_pdp"]
            # h2
            self._sk_params_dict["v_2_e_dds"].param = self["v_2_dds"]
            self._sk_params_dict["v_2_e_ddp"].param = self["v_2_ddp"]
            self._sk_params_dict["v_2_o_ddp"].param = self["v_2_ddp"]
            self._sk_params_dict["v_2_e_ddd"].param = self["v_2_ddd"]
            self._sk_params_dict["v_2_o_ddd"].param = self["v_2_ddd"]
            self._sk_params_dict["v_2_e_pps"].param = self["v_2_pps"]
            self._sk_params_dict["v_2_o_pps"].param = self["v_2_pps"]
            self._sk_params_dict["v_2_e_ppp"].param = self["v_2_ppp"]
            self._sk_params_dict["v_2_o_ppp"].param = self["v_2_ppp"]
            self._sk_params_dict["v_2_e_pps_tb"].param = self["v_2_pps_tb"]
            self._sk_params_dict["v_2_o_pps_tb"].param = self["v_2_pps_tb"]
            self._sk_params_dict["v_2_e_ppp_tb"].param = self["v_2_ppp_tb"]
            self._sk_params_dict["v_2_o_ppp_tb"].param = self["v_2_ppp_tb"]
            # h3
            self._sk_params_dict["v_3_e_pds"].param = self["v_3_pds"]
            self._sk_params_dict["v_3_o_pds"].param = self["v_3_pds"]
            self._sk_params_dict["v_3_e_pdp"].param = self["v_3_pdp"]
            self._sk_params_dict["v_3_o_pdp"].param = self["v_3_pdp"]
            # h4
            self._sk_params_dict["v_4_e_pds"].param = self["v_4_pds"]
            self._sk_params_dict["v_4_o_pds"].param = self["v_4_pds"]
            self._sk_params_dict["v_4_e_pdp"].param = self["v_4_pdp"]
            self._sk_params_dict["v_4_o_pdp"].param = self["v_4_pdp"]
            # h5
            self._sk_params_dict["v_5_e_dds"].param = self["v_5_dds"]
            self._sk_params_dict["v_5_e_ddp"].param = self["v_5_ddp"]
            self._sk_params_dict["v_5_o_ddp"].param = self["v_5_ddp"]
            self._sk_params_dict["v_5_e_ddd"].param = self["v_5_ddd"]
            self._sk_params_dict["v_5_o_ddd"].param = self["v_5_ddd"]
            self._sk_params_dict["v_5_e_pps"].param = self["v_5_pps"]
            self._sk_params_dict["v_5_o_pps"].param = self["v_5_pps"]
            self._sk_params_dict["v_5_e_ppp"].param = self["v_5_ppp"]
            self._sk_params_dict["v_5_o_ppp"].param = self["v_5_ppp"]
            self._sk_params_dict["v_5_e_pps_tb"].param = self["v_5_pps_tb"]
            self._sk_params_dict["v_5_o_pps_tb"].param = self["v_5_pps_tb"]
            self._sk_params_dict["v_5_e_ppp_tb"].param = self["v_5_ppp_tb"]
            self._sk_params_dict["v_5_o_ppp_tb"].param = self["v_5_ppp_tb"]
            # h6
            self._sk_params_dict["v_6_e_dds"].param = self["v_6_dds"]
            self._sk_params_dict["v_6_e_ddp"].param = self["v_6_ddp"]
            self._sk_params_dict["v_6_o_ddp"].param = self["v_6_ddp"]
            self._sk_params_dict["v_6_e_ddd"].param = self["v_6_ddd"]
            self._sk_params_dict["v_6_o_ddd"].param = self["v_6_ddd"]
            self._sk_params_dict["v_6_e_pps"].param = self["v_6_pps"]
            self._sk_params_dict["v_6_o_pps"].param = self["v_6_pps"]
            self._sk_params_dict["v_6_e_ppp"].param = self["v_6_ppp"]
            self._sk_params_dict["v_6_o_ppp"].param = self["v_6_ppp"]
            self._sk_params_dict["v_6_e_pps_tb"].param = self["v_6_pps_tb"]
            self._sk_params_dict["v_6_o_pps_tb"].param = self["v_6_pps_tb"]
            self._sk_params_dict["v_6_e_ppp_tb"].param = self["v_6_ppp_tb"]
            self._sk_params_dict["v_6_o_ppp_tb"].param = self["v_6_ppp_tb"]
            super()._recalculate_params()

    @property
    def _unique_params_dict(self) -> List[dict]:
        return [self._general_params_dict, self._onsite_sk_params_dict, self._sk_simple_params_dict]

    @property
    def _protected_params_dict(self) -> Optional[List[dict]]:
        return [self._sk_params_dict, self._energy_params_dict]

__init__(input_dict=None)

Initializes the SKSimpleParametersList object.

Parameters:

Name	Type	Description	Default
input_dict	dict	Dictionary with the SK paramters. The keus are the parameter names and the values are the parameter values. The parameter names are: a, material, lamb_x, lamb_m, theta, delta_p, delta_z, delta_0, delta_1, delta_2, v_0_pps, v_0_ppp, v_1_pds, v_1_pdp, v_2_dds, v_2_ddp, v_2_ddd, v_2_pps, v_2_ppp, v_2_pps_tb, v_2_ppp_tb, v_3_pds, v_3_pdp, v_4_pds, v_4_pdp, v_5_dds, v_5_ddp, v_5_ddd, v_5_pps, v_5_ppp, v_5_pps_tb, v_5_ppp_tb, v_6_dds, v_6_ddp, v_6_ddd, v_6_pps, v_6_ppp, v_6_pps_tb and v_6_ppp_tb.	None

Source code in tmdybinding/parameters/slater_koster.py

def __init__(self, input_dict: Optional[Dict[str, Union[str, Optional[float]]]] = None):
    """Initializes the SKSimpleParametersList object.

    Parameters:
        input_dict (dict): Dictionary with the SK paramters. The keus are the parameter names and the values are the
            parameter values. The parameter names are:
            `a`, `material`, `lamb_x`, `lamb_m`, `theta`,
            `delta_p`, `delta_z`, `delta_0`, `delta_1`, `delta_2`,
            `v_0_pps`, `v_0_ppp`,
            `v_1_pds`, `v_1_pdp`,
            `v_2_dds`, `v_2_ddp`, `v_2_ddd`, `v_2_pps`, `v_2_ppp`, `v_2_pps_tb`, `v_2_ppp_tb`,
            `v_3_pds`, `v_3_pdp`,
            `v_4_pds`, `v_4_pdp`,
            `v_5_dds`, `v_5_ddp`, `v_5_ddd`, `v_5_pps`, `v_5_ppp`, `v_5_pps_tb`, `v_5_ppp_tb`,
            `v_6_dds`, `v_6_ddp`, `v_6_ddd`, `v_6_pps`, `v_6_ppp`, `v_6_pps_tb` and `v_6_ppp_tb`."""
    super().__init__(None)
    sk_simple_params = [
        *[f"v_{n}_pd{i}" for n in ("1", "3", "4") for i in ("s", "p")],
        *[f"v_{n}_pp{i}{t}" for n in ("2", "5", "6") for i in ("s", "p") for t in ("", "_tb")],
        *[f"v_{n}_dd{i}" for n in ("2", "5", "6") for i in ("s", "p", "d")]
    ]

    sk_simple_params_names = [
        *[rf"$V^{{{n}}}_{{pd{i}}}$" for n in ("1", "3", "4") for i in (r"\sigma", r"\pi")],
        *[rf"$V^{{{n}}}_{{pp{i}{t}}}$" for n in ("2", "5", "6") for i in (r"\sigma", r"\pi") for t in ("", ",tb")],
        *[rf"$V^{{{n}}}_{{dd{i}}}$" for n in ("2", "5", "6") for i in (r"\sigmas", r"\pi", r"\delta")]
    ]
    self._sk_simple_params_dict: dict = dict(zip(
        sk_simple_params,
        [FloatParameter(name=p_name) for p_name in sk_simple_params_names]
    ))

    if input_dict is not None:
        self.from_dict(input_dict)

StrainParametersList

Bases: ParametersList

List of strain parameters.

Source code in tmdybinding/parameters/strain.py

class StrainParametersList(ParametersList):
    """List of strain parameters."""

    def __init__(self, input_dict: Optional[Dict[str, Union[float, List[float]]]] = None, max_order: int = 1):
        super().__init__(None)
        self.max_order = max_order
        strain_params = []
        strain_params_names = []

        # biaxial and uniaxial strain parameters
        for strain_type in ("b", "u", "s"):
            for order_idx in range(1, self.max_order+1):
                strain_part = f"{strain_type}_{str(order_idx)}"
                strain_part_name = rf"{strain_type},{str(order_idx)}"
                if not strain_type == "s":
                    for param_key, param_float in self._energy_params_dict.items():
                        strain_params.append(rf"{param_key}_{strain_part}")
                        check_for = r"$\epsilon_" if "eps_" in param_key else r"$u_"
                        split_idx, split_len = len(check_for), 1
                        param_name = param_float.name
                        pre_name = param_name[:split_idx]
                        idx_name = param_name[split_idx:split_idx+split_len]
                        pst_name = param_name[split_idx+split_len:]
                        assert pre_name == check_for, f"Expected {check_for}, got {pre_name}"
                        strain_params_names.append(rf"{pre_name}{{{idx_name},{strain_part_name}}}{pst_name}")
                else:
                    params_shear = [
                        *[f"u_{u}_{i}_m_e_{strain_part}" for u in ("1", "3", "4") for i in range(5, 9)],
                        *[f"u_{u}_{i}_m_o_{strain_part}" for u in ("1", "3", "4") for i in range(3, 6)],
                        *[f"u_{u}_{i}_{m}_e_{strain_part}" for u in ("2", "6") for i in ("1", "2", "4") for m in ("m", "x")],
                        *[f"u_{u}_{i}_x_o_{strain_part}" for u in ("2", "6") for i in ("1", "2", "4")],
                        *[f"u_{u}_{i}_m_o_{strain_part}" for u in ("2", "6") for i in range(1, 2)],
                        *[f"u_{u}_{i}_m_e_{strain_part}" for u in "5" for i in ("2", "4", "7", "8")],
                        *[f"u_{u}_{i}_x_{r}_{strain_part}" for u in "5" for i in ("1", "4", "7", "8") for r in ("e", "o")],
                        *[f"u_{u}_{i}_m_o_{strain_part}" for u in "5" for i in ("1", "3")],
                    ]
                    params_names_shear = [
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},e}}$" for u in ("1", "3", "4") for i in range(5, 9)],
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},o}}$" for u in ("1", "3", "4") for i in range(3, 6)],
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},{m}e}}$" for u in ("2", "6") for i in ("1", "2", "4") for m in ("M", "X")],
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},Xo}}$" for u in ("2", "6") for i in ("1", "2", "4")],
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},Mo}}$" for u in ("2", "6") for i in range(1, 2)],
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},Me}}$" for u in "5" for i in ("2", "4", "7", "8")],
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},X{r}}}$" for u in "5" for i in ("2", "4", "7", "8") for r in ("e", "o")],
                        *[rf"$u_{{{u},{strain_part_name}}}^{{{i},Mo}}$" for u in "5" for i in ("1", "3")],
                    ]
                    strain_params.extend(params_shear)
                    strain_params_names.extend(params_names_shear)


        # shear strain parameters, only hoppings as onsite are given by the uniaxial parameters
        self._strain_params_dict: dict = dict(zip(
            strain_params,
            [FloatParameter(name=p_name) for p_name in strain_params_names]
        ))


        if input_dict is not None:
            self.from_dict(input_dict)

    @property
    def _unique_params_dict(self) -> List[dict]:
        return [self._general_params_dict, self._energy_params_dict, self._strain_params_dict]

StringParameter dataclass

Bases: Parameter

Class to store one separate string parameter

Source code in tmdybinding/parameters/symmetry_group.py

@dataclass
class StringParameter(Parameter):
    """Class to store one separate string parameter"""
    param: Optional[str] = None

TmdMatrices

Construct the TMD hopping matrices

Source code in tmdybinding/tmd_hopping_matrices.py

class TmdMatrices:
    """Construct the TMD hopping matrices"""
    def __init__(self, params: ParametersList):
        """Initialize the TMD hopping matrices

        Parameters:
            params (ParametersList): The parameters for the TMD lattice."""
        self.params = params

    @staticmethod
    def _t_n_e(u_0, u_1, u_2, u_3, u_4) -> np.ndarray:
        """The hopping matrices for the first-, third- and fourth-nearest neighbours from the even metal orbitals"""
        return np.array([[0, 0, u_0], [u_1, u_2, 0], [u_3, u_4, 0]])

    @staticmethod
    def _t_n_o(u_0, u_1, u_2) -> np.ndarray:
        """The hopping matrices for the first-, third- and fourth-nearest neighbours from the odd metal orbitals"""
        return np.array([[u_0, 0], [0, u_1], [0, u_2]])

    @staticmethod
    def _t_m_xr(u_0, u_1, u_2, u_3, u_4, u_5) -> np.ndarray:
        """The hopping matrices for the second- and sixth-nearest neighbours from the chalcogen orbitals"""
        return np.array([[u_0, u_1, u_2], [-u_1, u_3, u_4], [-u_2, u_4, u_5]])

    @staticmethod
    def _t_m_me(u_0, u_1, u_2, u_3, u_4, u_5) -> np.ndarray:
        """The hopping matrices for the second-, fifth- and sixth-nearest neighbours from the even metal orbitals"""
        return np.array([[u_0, u_1, u_2], [u_1, u_3, u_4], [-u_2, -u_4, u_5]])

    @staticmethod
    def _t_m_mo(u_0, u_1, u_2) -> np.ndarray:
        """The hopping matrices for the second-, fifth- and sixth-nearest neighbours from the odd metal orbitals"""
        return np.array([[u_0, u_1], [-u_1, u_2]])

    @staticmethod
    def _t_5_me(u_0, u_1, u_3, u_5, u_6) ->np.ndarray:
        """The hopping matrix for the fifth-nearest neighbours from the even metal orbitals"""
        return np.array([[u_0, -u_1, 0.0], [-u_6, u_3, 0.0], [0.0, 0.0, u_5]])

    @staticmethod
    def _t_5_mo(u_0, u_2) -> np.ndarray:
        """The hopping matrix for the fifth-nearest neighbours from the odd metal orbitals"""
        return np.diag((u_2, u_0))

    @staticmethod
    def _t_5_xr(u_0, u_2, u_3, u_5, u_6) -> np.ndarray:
        """The hopping matrices for the fifth-nearest neighbours from the chalcogen orbitals"""
        return np.array([[u_3, 0, 0], [0, u_0, u_2], [0, u_6, u_5]])

    @property
    def e_xe(self) -> np.ndarray:
        """The hopping matrix for the even chalcogen orbitals"""
        return np.diag((self.params["eps_0_x_e"], self.params["eps_0_x_e"], self.params["eps_1_x_e"]))

    @property
    def e_xo(self) -> np.ndarray:
        """The hopping matrix for the odd chalcogen orbitals"""
        return np.diag((self.params["eps_0_x_o"], self.params["eps_0_x_o"], self.params["eps_1_x_o"]))

    @property
    def e_me(self) -> np.ndarray:
        """The hopping matrix for the even metal orbitals"""
        return np.diag((self.params["eps_0_m_e"], self.params["eps_1_m_e"], self.params["eps_1_m_e"]))

    @property
    def e_mo(self) -> np.ndarray:
        """The hopping matrix for the odd metal orbitals"""
        return np.diag((self.params["eps_0_m_o"], self.params["eps_0_m_o"]))

    @property
    def t_1_me(self) -> np.ndarray:
        """The first-nearest neighbour hopping matrix from the even metal orbitals"""
        return self._t_n_e(*[self.params[f"u_1_{i}_m_e"] for i in range(5)])

    @property
    def t_1_mo(self) -> np.ndarray:
        """The first-nearest neighbour hopping matrix from the odd metal orbitals"""
        return self._t_n_o(*[self.params[f"u_1_{i}_m_o"] for i in range(3)])

    @property
    def t_2_me(self) -> np.ndarray:
        """The second-nearest neighbour hopping matrix from the even metal orbitals"""
        return self._t_m_me(*[self.params[f"u_2_{i}_m_e"] for i in range(6)])

    @property
    def t_2_mo(self) -> np.ndarray:
        """The second-nearest neighbour hopping matrix from the odd metal orbitals"""
        return self._t_m_mo(*[self.params[f"u_2_{i}_m_o"] for i in range(3)])

    @property
    def t_2_xe(self) -> np.ndarray:
        """The second-nearest neighbour hopping matrix from the even chalcogen orbitals"""
        return self._t_m_xr(*[self.params[f"u_2_{i}_x_e"] for i in range(6)])

    @property
    def t_2_xo(self) -> np.ndarray:
        """The second-nearest neighbour hopping matrix from the odd chalcogen orbitals"""
        return self._t_m_xr(*[self.params[f"u_2_{i}_x_o"] for i in range(6)])

    @property
    def t_3_me(self) -> np.ndarray:
        """The third-nearest neighbour hopping matrix from the even metal orbitals"""
        return self._t_n_e(*[self.params[f"u_3_{i}_m_e"] for i in range(5)])

    @property
    def t_3_mo(self) -> np.ndarray:
        """The third-nearest neighbour hopping matrix from the odd metal orbitals"""
        return self._t_n_o(*[self.params[f"u_3_{i}_m_o"] for i in range(3)])

    @property
    def t_4_me(self) -> np.ndarray:
        """The fourth-nearest neighbour hopping matrix from the even metal orbitals"""
        return self._t_n_e(*[self.params[f"u_4_{i}_m_e"] for i in range(5)])

    @property
    def t_4_mo(self) -> np.ndarray:
        """The fourth-nearest neighbour hopping matrix from the odd metal orbitals"""
        return self._t_n_o(*[self.params[f"u_4_{i}_m_o"] for i in range(3)])

    @property
    def t_5_me(self) -> np.ndarray:
        """The fifth-nearest neighbour hopping matrix from the even metal orbitals"""
        return self._t_5_me(*[self.params[f"u_5_{i}_m_e"] for i in ("0", "1", "3", "5", "6")])

    @property
    def t_5_mo(self) -> np.ndarray:
        """The fifth-nearest neighbour hopping matrix from the odd metal orbitals"""
        return self._t_5_mo(*[self.params[f"u_5_{i}_m_o"] for i in ("0", "2")])

    @property
    def t_5_xe(self) -> np.ndarray:
        """The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals"""
        return self._t_5_xr(*[self.params[f"u_5_{i}_x_e"] for i in ("0", "2", "3", "5", "6")])

    @property
    def t_5_xo(self) -> np.ndarray:
        """The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals"""
        return self._t_5_xr(*[self.params[f"u_5_{i}_x_o"] for i in ("0", "2", "3", "5", "6")])

    @property
    def t_6_me(self) -> np.ndarray:
        """The sixth-nearest neighbour hopping matrix from the even metal orbitals"""
        return self._t_m_me(*[self.params[f"u_6_{i}_m_e"] for i in range(6)])

    @property
    def t_6_mo(self) -> np.ndarray:
        """The sixth-nearest neighbour hopping matrix from the odd metal orbitals"""
        return self._t_m_mo(*[self.params[f"u_6_{i}_m_o"] for i in range(3)])

    @property
    def t_6_xe(self) -> np.ndarray:
        """The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals"""
        return self._t_m_xr(*[self.params[f"u_6_{i}_x_e"] for i in range(6)])

    @property
    def t_6_xo(self) -> np.ndarray:
        """The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals"""
        return self._t_m_xr(*[self.params[f"u_6_{i}_x_o"] for i in range(6)])

e_me: np.ndarray property

The hopping matrix for the even metal orbitals

e_mo: np.ndarray property

The hopping matrix for the odd metal orbitals

e_xe: np.ndarray property

The hopping matrix for the even chalcogen orbitals

e_xo: np.ndarray property

The hopping matrix for the odd chalcogen orbitals

t_1_me: np.ndarray property

The first-nearest neighbour hopping matrix from the even metal orbitals

t_1_mo: np.ndarray property

The first-nearest neighbour hopping matrix from the odd metal orbitals

t_2_me: np.ndarray property

The second-nearest neighbour hopping matrix from the even metal orbitals

t_2_mo: np.ndarray property

The second-nearest neighbour hopping matrix from the odd metal orbitals

t_2_xe: np.ndarray property

The second-nearest neighbour hopping matrix from the even chalcogen orbitals

t_2_xo: np.ndarray property

The second-nearest neighbour hopping matrix from the odd chalcogen orbitals

t_3_me: np.ndarray property

The third-nearest neighbour hopping matrix from the even metal orbitals

t_3_mo: np.ndarray property

The third-nearest neighbour hopping matrix from the odd metal orbitals

t_4_me: np.ndarray property

The fourth-nearest neighbour hopping matrix from the even metal orbitals

t_4_mo: np.ndarray property

The fourth-nearest neighbour hopping matrix from the odd metal orbitals

t_5_me: np.ndarray property

The fifth-nearest neighbour hopping matrix from the even metal orbitals

t_5_mo: np.ndarray property

The fifth-nearest neighbour hopping matrix from the odd metal orbitals

t_5_xe: np.ndarray property

The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals

t_5_xo: np.ndarray property

The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals

t_6_me: np.ndarray property

The sixth-nearest neighbour hopping matrix from the even metal orbitals

t_6_mo: np.ndarray property

The sixth-nearest neighbour hopping matrix from the odd metal orbitals

t_6_xe: np.ndarray property

The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals

t_6_xo: np.ndarray property

The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals

__init__(params)

Initialize the TMD hopping matrices

Parameters:

Name	Type	Description	Default
params	ParametersList	The parameters for the TMD lattice.	required

Source code in tmdybinding/tmd_hopping_matrices.py

def __init__(self, params: ParametersList):
    """Initialize the TMD hopping matrices

    Parameters:
        params (ParametersList): The parameters for the TMD lattice."""
    self.params = params

TmdNN123456MeoXeo

Bases: AbstractLattice

11 bands model for metal and chalcogen orbitals with all the hoppings up to sixth nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN123456MeoXeo(AbstractLattice):
    """11 bands model for metal and chalcogen orbitals with all the hoppings up to sixth nearest-neighbor hopping"""
    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2, 1, -1], "X": [1, -1, 0, 1, -1, 0]},
            orbs={"M": ["dz2", "dx2y2", "dxy", "dxz", "dyz"], "X": ["pxe", "pye", "pze", "pxo", "pyo", "pzo"]},
            group={"M": [0, 1, 1, 2, 2], "X": [0, 0, 1, 2, 2, 3]}
        )
        super().__init__(orbital=orbital, params=all["MoS2"], lattice_name="11 bands 6NN model",
                         n_v=6, n_b=11)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]

    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = self.block_diag(t_m.e_me, t_m.e_mo)
        h_0_x = self.block_diag(t_m.e_xe, t_m.e_xo)
        h_1_m = self.block_diag(t_m.t_1_me, t_m.t_1_mo)
        h_2_m = self.block_diag(t_m.t_2_me, t_m.t_2_mo)
        h_2_x = self.block_diag(t_m.t_2_xe, t_m.t_2_xo)
        h_3_m = self.block_diag(t_m.t_3_me, t_m.t_3_mo)
        h_4_m = self.block_diag(t_m.t_4_me, t_m.t_4_mo)
        h_5_m = self.block_diag(t_m.t_5_me, t_m.t_5_mo)
        h_5_x = self.block_diag(t_m.t_5_xe, t_m.t_5_xo)
        h_6_m = self.block_diag(t_m.t_6_me, t_m.t_6_mo)
        h_6_x = self.block_diag(t_m.t_6_xe, t_m.t_6_xo)
        keys = ["h_0_m", "h_0_c", "h_1_m", "h_2_m", "h_2_c", "h_3_m", "h_4_m", "h_5_m", "h_5_c", "h_6_m", "h_6_c",
                "a", "lamb_m", "lamb_c"]
        values = [h_0_m, h_0_x, h_1_m, h_2_m, h_2_x, h_3_m, h_4_m, h_5_m, h_5_x, h_6_m, h_6_x,
                  self.params["a"], self.params["lamb_m"], self.params["lamb_x"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdNN123MeoXeo

Bases: AbstractLattice

11 bands model for metal and chalcogen orbitals with the first-, second- and third-nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN123MeoXeo(AbstractLattice):
    """11 bands model for metal and chalcogen orbitals with the first-, second- and third-nearest-neighbor hopping"""
    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2, 1, -1], "X": [1, -1, 0, 1, -1, 0]},
            orbs={"M": ["dz2", "dx2y2", "dxy", "dxz", "dyz"], "X": ["pxe", "pye", "pze", "pxo", "pyo", "pzo"]},
            group={"M": [0, 1, 1, 2, 2], "X": [0, 0, 1, 2, 2, 3]}
        )
        super().__init__(orbital=orbital, params=fang["MoS2"], lattice_name="11 bands 3NN model",
                         n_v=6, n_b=11)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]

    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = self.block_diag(t_m.e_me, t_m.e_mo)
        h_0_x = self.block_diag(t_m.e_xe, t_m.e_xo)
        h_1_m = self.block_diag(t_m.t_1_me, t_m.t_1_mo)
        h_2_m = self.block_diag(t_m.t_2_me, t_m.t_2_mo)
        h_2_x = self.block_diag(t_m.t_2_xe, t_m.t_2_xo)
        h_3_m = self.block_diag(t_m.t_3_me, t_m.t_1_mo * 0)
        keys = ["h_0_m", "h_0_c", "h_1_m", "h_2_m", "h_2_c", "h_3_m",
                "a", "lamb_m", "lamb_c"]
        values = [h_0_m, h_0_x, h_1_m, h_2_m, h_2_x, h_3_m,
                  self.params["a"], self.params["lamb_m"], self.params["lamb_x"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdNN125MeoXeo

Bases: AbstractLattice

11 bands model for metal and chalcogen orbitals with the first-, second- and fifth- nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN125MeoXeo(AbstractLattice):
    """11 bands model for metal and chalcogen orbitals with the first-, second- and fifth- nearest-neighbor hopping"""
    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2, 1, -1], "X": [1, -1, 0, 1, -1, 0]},
            orbs={"M": ["dz2", "dx2y2", "dxy", "dxz", "dyz"], "X": ["pxe", "pye", "pze", "pxo", "pyo", "pzo"]},
            group={"M": [0, 1, 1, 2, 2], "X": [0, 0, 1, 2, 2, 3]}
        )
        super().__init__(orbital=orbital, params=dias["MoS2"], lattice_name="11 bands 5NN model",
                         n_v=6, n_b=11)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]

    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = self.block_diag(t_m.e_me, t_m.e_mo)
        h_0_x = self.block_diag(t_m.e_xe, t_m.e_xo)
        h_1_m = self.block_diag(t_m.t_1_me, t_m.t_1_mo)
        h_2_m = self.block_diag(t_m.t_2_me, t_m.t_2_mo)
        h_2_x = self.block_diag(t_m.t_2_xe, t_m.t_2_xo)
        h_5_m = self.block_diag(t_m.t_5_me, t_m.t_5_mo)
        h_5_x = self.block_diag(t_m.t_5_xe, t_m.t_5_xo)
        keys = ["h_0_m", "h_0_c", "h_1_m", "h_2_m", "h_2_c", "h_5_m", "h_5_c",
                "a", "lamb_m", "lamb_c"]
        values = [h_0_m, h_0_x, h_1_m, h_2_m, h_2_x, h_5_m, h_5_x,
                  self.params["a"], self.params["lamb_m"], self.params["lamb_x"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdNN12MeXe

Bases: AbstractLattice

6 bands model for even metal and chalcogen orbitals with the first- and second-nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN12MeXe(AbstractLattice):
    """6 bands model for even metal and chalcogen orbitals with the first- and second-nearest-neighbor hopping"""
    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2], "X": [1, -1, 0]},
            orbs={"M": ["dz2", "dx2y2", "dxy"], "X": ["pxe", "pye", "pze"]},
            group={"M": [0, 2, 2], "X": [0, 0, 1]}
        )
        super().__init__(orbital=orbital, params=jorissen["MoS2"], lattice_name="6 bands 2NN model",
                         n_v=3, n_b=6)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]

    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = t_m.e_me
        h_0_x = t_m.e_xe
        h_1_m = t_m.t_1_me
        h_2_m = t_m.t_2_me
        h_2_x = t_m.t_2_xe
        keys = ["h_0_m", "h_0_c", "h_1_m", "h_2_m", "h_2_c", "a", "lamb_m", "lamb_c"]
        values = [h_0_m, h_0_x, h_1_m, h_2_m, h_2_x, self.params["a"], self.params["lamb_m"], self.params["lamb_x"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdNN12MeoXeo

Bases: AbstractLattice

3 bands model for metal and chalocogen orbitals with the first- and second-nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN12MeoXeo(AbstractLattice):
    """3 bands model for metal and chalocogen orbitals with the first- and second-nearest-neighbor hopping"""
    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2, 1, -1], "X": [1, -1, 0, 1, -1, 0]},
            orbs={"M": ["dz2", "dx2y2", "dxy", "dxz", "dyz"], "X": ["pxe", "pye", "pze", "pxo", "pyo", "pzo"]},
            group={"M": [0, 1, 1, 2, 2], "X": [0, 0, 1, 2, 2, 3]}
        )
        super().__init__(orbital=orbital, params=cappelluti["MoS2"], lattice_name="11 bands 2NN model",
                         n_v=6, n_b=11)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]
    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = self.block_diag(t_m.e_me, t_m.e_mo)
        h_0_x = self.block_diag(t_m.e_xe, t_m.e_xo)
        h_1_m = self.block_diag(t_m.t_1_me, t_m.t_1_mo)
        h_2_m = self.block_diag(t_m.t_2_me, t_m.t_2_mo)
        h_2_x = self.block_diag(t_m.t_2_xe, t_m.t_2_xo)
        keys = ["h_0_m", "h_0_c", "h_1_m", "h_2_m", "h_2_c", "a", "lamb_m", "lamb_c"]
        values = [h_0_m, h_0_x, h_1_m, h_2_m, h_2_x, self.params["a"], self.params["lamb_m"], self.params["lamb_x"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdNN256Me

Bases: AbstractLattice

3 bands model for even metal orbitals with the second-, fifth- and sixth-nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN256Me(AbstractLattice):
    """3 bands model for even metal orbitals with the second-, fifth- and sixth-nearest-neighbor hopping"""

    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2]},
            orbs={"M": ["dz2", "dx2y2", "dxy"]},
            group={"M": [0, 1, 1]}
        )
        super().__init__(orbital=orbital, params=liu6["MoS2"], lattice_name="3 bands 6NN model",
                         n_v=0, n_b=3)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]
    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = t_m.e_me
        h_2_m = t_m.t_2_me
        h_5_m = t_m.t_5_me
        h_6_m = t_m.t_6_me
        keys = ["h_0_m", "h_2_m", "h_5_m", "h_6_m", "a", "lamb_m"]
        values = [h_0_m, h_2_m, h_5_m, h_6_m, self.params["a"], self.params["lamb_m"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdNN256Meo

Bases: AbstractLattice

5 bands model for metal orbitals with the second-, fifth- and sixth-nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN256Meo(AbstractLattice):
    """5 bands model for metal orbitals with the second-, fifth- and sixth-nearest-neighbor hopping"""
    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2, 1, -1]},
            orbs={"M": ["dz2", "dx2y2", "dxy", "dxz", "dyz"]},
            group={"M": [0, 1, 1, 2, 2]}
        )
        super().__init__(orbital=orbital, params=wu["MoS2"], lattice_name="5 bands 6NN model",
                         n_v=0, n_b=5)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]

    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = self.block_diag(t_m.e_me, t_m.e_mo)
        h_2_m = self.block_diag(t_m.t_2_me, t_m.t_2_mo)
        h_5_m = self.block_diag(t_m.t_5_me, t_m.t_5_mo)
        h_6_m = self.block_diag(t_m.t_6_me, t_m.t_6_mo)
        keys = ["h_0_m", "h_2_m", "h_5_m", "h_6_m", "a", "lamb_m"]
        values = [h_0_m, h_2_m, h_5_m, h_6_m, self.params["a"], self.params["lamb_m"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdNN2Me

Bases: AbstractLattice

3 bands model for even metal orbitals with the second nearest-neighbor hopping

Source code in tmdybinding/tmd_lattice.py

class TmdNN2Me(AbstractLattice):
    """3 bands model for even metal orbitals with the second nearest-neighbor hopping"""
    def __init__(self, **kwargs):
        orbital = LatticeOrbitals(
            l_number={"M": [0, 2, -2]},
            orbs={"M": ["dz2", "dx2y2", "dxy"]},
            group={"M": [0, 1, 1]}
        )
        super().__init__(orbital=orbital, params=liu2["MoS2"], lattice_name="3 bands 2NN model",
                         n_v=0, n_b=3)
        [setattr(self, var, kwargs[var]) for var in [*kwargs]]

    def _generate_matrices(self):
        t_m = TmdMatrices(self.params)
        h_0_m = t_m.e_me
        h_2_m = t_m.t_2_me
        keys = ["h_0_m", "h_2_m", "a", "lamb_m"]
        values = [h_0_m, h_2_m, self.params["a"], self.params["lamb_m"]]
        self.lattice_params.set_params(dict([(key, value) for key, value in zip(keys, values)]))

TmdStrainMatrices

Bases: TmdMatrices

Construct the strained TMD hopping matrices

Source code in tmdybinding/tmd_strain.py

class TmdStrainMatrices(TmdMatrices):
    """Construct the strained TMD hopping matrices"""

    def __init__(self, params: StrainParametersList):
        """Initialize the strained TMD hopping matrices

        Parameters:
            params (StrainParametersList): The parameters for the strained TMD lattice."""
        super().__init__(params)
        self.params: StrainParametersList = params

    @staticmethod
    def _e_xr_u(u_0, u_1) -> np.ndarray:
        """The onsite matrix for the chalcogen orbitals under uniaxial strain"""
        return np.array([[u_0, 0, 0], [0, -u_0, u_1], [0, u_1, 0]])

    @staticmethod
    def _e_me_u(u_0, u_1) -> np.ndarray:
        """The onsite matrix for the even metal orbitals under uniaxial strain"""
        return np.array([[0, u_0, 0], [u_0, -u_1, 0], [0, 0, u_1]])

    @staticmethod
    def _e_mo_u(u_0) -> np.ndarray:
        """The onsite matrix for the odd metal orbitals under uniaxial strain"""
        return np.array([[u_0, 0], [0, -u_0]])

    @staticmethod
    def _e_xr_s(u_0, u_1) -> np.ndarray:
        """The onsite matrix for the chalcogen orbitals under shear strain"""
        return np.array([[0, -u_0, -u_1], [-u_0, 0, 0], [-u_1, 0, 0]])

    @staticmethod
    def _e_me_s(u_0, u_1) -> np.ndarray:
        """The onsite matrix for the even metal orbitals under shear strain"""
        return np.array([[0, 0, -u_0], [0, 0, -u_1], [-u_0, -u_1, 0]])

    @staticmethod
    def _e_mo_s(u_0) -> np.ndarray:
        """The onsite matrix for the odd metal orbitals under shear strain"""
        return np.array([[0, -u_0], [-u_0, 0]])

    @staticmethod
    def _t_n_e_s(u_5, u_6, u_7, u_8) -> np.ndarray:
        """The hopping matrices for the first-, third- and fourth-nearest neighbours from the even metal orbitals under shear strain"""
        return np.array([[u_5, u_6, 0], [0, 0, u_7], [0, 0, u_8]])

    @staticmethod
    def _t_n_o_s(u_3, u_4, u_5) -> np.ndarray:
        """The hopping matrices for the first-, third- and fourth-nearest neighbours from the odd metal orbitals under shear strain"""
        return np.array([[0, u_3], [u_4, 0], [u_5, 0]])

    @staticmethod
    def _t_m_xr_s(u_1, u_2, u_4) -> np.ndarray:
        """The hopping matrices for the second- and sixth-nearest neighbours from the chalcogen orbitals under shear strain"""
        return np.array([[0, u_1, u_2], [u_1, 0, u_4], [u_2, -u_4, 0]])

    @staticmethod
    def _t_m_me_s(u_1, u_2, u_4) -> np.ndarray:
        """The hopping matrices for the second-, fifth- and sixth-nearest neighbours from the even metal orbitals under shear strain"""
        return np.array([[0, u_1, u_2], [-u_1, 0, u_4], [u_2, u_4, 0]])

    @staticmethod
    def _t_m_mo_s(u_1) -> np.ndarray:
        """The hopping matrices for the second-, fifth- and sixth-nearest neighbours from the odd metal orbitals under shear strain"""
        return np.array([[0, u_1], [u_1, 0]])

    @staticmethod
    def _t_5_me_s(u_2, u_4, u_7, u_8) -> np.ndarray:
        """The hopping matrix for the fifth-nearest neighbours from the even metal orbitals under shear strain"""
        return np.array([[0, 0, u_2], [0, 0, u_4], [u_7, u_8, 0]])

    @staticmethod
    def _t_5_mo_s(u_1, u_3) -> np.ndarray:
        """The hopping matrix for the fifth-nearest neighbours from the odd metal orbitals under shear strain"""
        return np.array([[0, u_1], [u_3, 0]])

    @staticmethod
    def _t_5_xr_s(u_1, u_4, u_7, u_8) -> np.ndarray:
        """The hopping matrices for the fifth-nearest neighbours from the chalcogen orbitals under shear strain"""
        return np.array([[0, u_1, u_4], [u_7, 0, 0], [u_8, 0, 0]])

    @property
    def e_xe_b(self) -> list[np.ndarray]:
        """The hopping matrix for the even chalcogen orbitals under biaxial strain"""
        return [
            np.diag((
                self.params[f"eps_0_x_e_b_{order_idx}"],
                self.params[f"eps_0_x_e_b_{order_idx}"],
                self.params[f"eps_1_x_e_b_{order_idx}"]
            ))
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_xo_b(self) -> list[np.ndarray]:
        """The hopping matrix for the odd chalcogen orbitals under biaxial strain"""
        return [
            np.diag((
                self.params[f"eps_0_x_o_b_{order_idx}"],
                self.params[f"eps_0_x_o_b_{order_idx}"],
                self.params[f"eps_1_x_o_b_{order_idx}"]
            ))
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_me_b(self) -> list[np.ndarray]:
        """The hopping matrix for the even metal orbitals under biaxial strain"""
        return [
            np.diag((
                self.params[f"eps_0_m_e_b_{order_idx}"],
                self.params[f"eps_1_m_e_b_{order_idx}"],
                self.params[f"eps_1_m_e_b_{order_idx}"]
            ))
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_mo_b(self) -> list[np.ndarray]:
        """The hopping matrix for the odd metal orbitals under biaxial strain"""
        return [
            np.diag((
                self.params[f"eps_0_m_e_b_{order_idx}"],
                self.params[f"eps_0_m_e_b_{order_idx}"]
            ))
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_xe_u(self) -> list[np.ndarray]:
        """The hopping matrix for the even chalcogen orbitals under uniaxial strain"""
        return [self._e_xr_u(
            self.params[f"eps_0_x_e_u_{order_idx}"],
            self.params[f"eps_1_x_e_u_{order_idx}"]
        ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_xo_u(self) -> list[np.ndarray]:
        """The hopping matrix for the odd chalcogen orbitals under uniaxial strain"""
        return [
            self._e_xr_u(
                self.params[f"eps_0_x_o_u_{order_idx}"],
                self.params[f"eps_1_x_o_u_{order_idx}"]
            )
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_me_u(self) -> list[np.ndarray]:
        """The hopping matrix for the even metal orbitals under uniaxial strain"""
        return [
            self._e_me_u(
                self.params[f"eps_0_m_e_u_{order_idx}"],
                self.params[f"eps_1_m_e_u_{order_idx}"]
            )
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_mo_u(self) -> list[np.ndarray]:
        """The hopping matrix for the odd metal orbitals under uniaxial strain"""
        return [
            self._e_mo_u(
                self.params[f"eps_0_m_o_u_{order_idx}"]
            )
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_xe_s(self) -> list[np.ndarray]:
        """The hopping matrix for the even chalcogen orbitals under shear strain"""
        return [
            self._e_xr_s(
                self.params[f"eps_0_x_e_u_{order_idx}"],
                self.params[f"eps_1_x_e_u_{order_idx}"]
            )
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_xo_s(self) -> list[np.ndarray]:
        """The hopping matrix for the odd chalcogen orbitals under shear strain"""
        return [
            self._e_xr_s(
                self.params[f"eps_0_x_o_u_{order_idx}"],
                self.params[f"eps_1_x_o_u_{order_idx}"]
            )
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_me_s(self) -> list[np.ndarray]:
        """The hopping matrix for the even metal orbitals under shear strain"""
        return [
            self._e_me_s(
                self.params[f"eps_0_m_e_u_{order_idx}"],
                self.params[f"eps_1_m_e_u_{order_idx}"]
            )
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def e_mo_s(self) -> list[np.ndarray]:
        """The hopping matrix for the odd metal orbitals under shear strain"""
        return [
            self._e_mo_s(
                self.params[f"eps_0_m_o_u_{order_idx}"]
            )
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_1_me_b(self) -> list[np.ndarray]:
        """The first-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain"""
        return [
            self._t_n_e(*[self.params[f"u_1_{i}_m_e_b_{order_idx}"] for i in range(5)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_1_mo_b(self) -> list[np.ndarray]:
        """The first-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain"""
        return [
            self._t_n_o(*[self.params[f"u_1_{i}_m_o_b_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_me_b(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain"""
        return [
            self._t_m_me(*[self.params[f"u_2_{i}_m_e_b_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_mo_b(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain"""
        return [
            self._t_m_mo(*[self.params[f"u_2_{i}_m_o_b_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_xe_b(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the even chalcogen orbitals under biaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_2_{i}_x_e_b_{order_idx}"] for i in range(6)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_xo_b(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the odd chalcogen orbitals under biaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_2_{i}_x_o_b_{order_idx}"] for i in range(6)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_3_me_b(self) -> list[np.ndarray]:
        """The third-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain"""
        return [
            self._t_n_e(*[self.params[f"u_3_{i}_m_e_b_{order_idx}"] for i in range(5)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_3_mo_b(self) -> list[np.ndarray]:
        """The third-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain"""
        return [
            self._t_n_o(*[self.params[f"u_3_{i}_m_o_b_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_4_me_b(self) -> list[np.ndarray]:
        """The fourth-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain"""
        return [
            self._t_n_e(*[self.params[f"u_4_{i}_m_e_b_{order_idx}"] for i in range(5)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_4_mo_b(self) -> list[np.ndarray]:
        """The fourth-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain"""
        return [
            self._t_n_o(*[self.params[f"u_4_{i}_m_o_b_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_me_b(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain"""
        return [
            self._t_5_me(*[self.params[f"u_5_{i}_m_e_b_{order_idx}"] for i in ("0", "1", "3", "5", "6")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_mo_b(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain"""
        return [
            self._t_5_mo(*[self.params[f"u_5_{i}_m_o_b_{order_idx}"] for i in ("0", "2")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_xe_b(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals under biaxial strain"""
        return [
            self._t_5_xr(*[self.params[f"u_5_{i}_x_e_b_{order_idx}"] for i in ("0", "2", "3", "5", "6")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_xo_b(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals under biaxial strain"""
        return [
            self._t_5_xr(*[self.params[f"u_5_{i}_x_o_b_{order_idx}"] for i in ("0", "2", "3", "5", "6")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_me_b(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain"""
        return [
            self._t_m_me(*[self.params[f"u_6_{i}_m_e_b_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_mo_b(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain"""
        return [
            self._t_m_mo(*[self.params[f"u_6_{i}_m_o_b_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_xe_b(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals under biaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_6_{i}_x_e_b_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_xo_b(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals under biaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_6_{i}_x_o_b_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_1_me_u(self) -> list[np.ndarray]:
        """The first-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain"""
        return [
            self._t_n_e(*[self.params[f"u_1_{i}_m_e_u_{order_idx}"] for i in range(5)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_1_mo_u(self) -> list[np.ndarray]:
        """The first-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain"""
        return [
            self._t_n_o(*[self.params[f"u_1_{i}_m_o_u_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_me_u(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain"""
        return [
            self._t_m_me(*[self.params[f"u_2_{i}_m_e_u_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_mo_u(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain"""
        return [
            self._t_m_mo(*[self.params[f"u_2_{i}_m_o_u_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_xe_u(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the even chalcogen orbitals under uniaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_2_{i}_x_e_u_{order_idx}"] for i in range(6)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_xo_u(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the odd chalcogen orbitals under uniaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_2_{i}_x_o_u_{order_idx}"] for i in range(6)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_3_me_u(self) -> list[np.ndarray]:
        """The third-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain"""
        return [
            self._t_n_e(*[self.params[f"u_3_{i}_m_e_u_{order_idx}"] for i in range(5)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_3_mo_u(self) -> list[np.ndarray]:
        """The third-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain"""
        return [
            self._t_n_o(*[self.params[f"u_3_{i}_m_o_u_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_4_me_u(self) -> list[np.ndarray]:
        """The fourth-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain"""
        return [
            self._t_n_e(*[self.params[f"u_4_{i}_m_e_u_{order_idx}"] for i in range(5)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_4_mo_u(self) -> list[np.ndarray]:
        """The fourth-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain"""
        return [
            self._t_n_o(*[self.params[f"u_4_{i}_m_o_u_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_me_u(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain"""
        return [
            self._t_5_me(*[self.params[f"u_5_{i}_m_e_u_{order_idx}"] for i in ("0", "1", "3", "5", "6")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_mo_u(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain"""
        return [
            self._t_5_mo(*[self.params[f"u_5_{i}_m_o_u_{order_idx}"] for i in ("0", "2")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_xe_u(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals under uniaxial strain"""
        return [
            self._t_5_xr(*[self.params[f"u_5_{i}_x_e_u_{order_idx}"] for i in ("0", "2", "3", "5", "6")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_xo_u(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals under uniaxial strain"""
        return [
            self._t_5_xr(*[self.params[f"u_5_{i}_x_o_u_{order_idx}"] for i in ("0", "2", "3", "5", "6")])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_me_u(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain"""
        return [
            self._t_m_me(*[self.params[f"u_6_{i}_m_e_u_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_mo_u(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain"""
        return [
            self._t_m_mo(*[self.params[f"u_6_{i}_m_o_u_{order_idx}"] for i in range(3)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_xe_u(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals under uniaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_6_{i}_x_e_u_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_xo_u(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals under uniaxial strain"""
        return [
            self._t_m_xr(*[self.params[f"u_6_{i}_x_o_u_{order_idx}"] for i in range(6)])
            for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_1_me_s(self) -> list[np.ndarray]:
        """The first-nearest neighbour hopping matrix from the even metal orbitals under shear strain"""
        return [
            self._t_n_e_s(*[self.params[f"u_1_{i}_m_e_s_{order_idx}"] for i in range(5, 9)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_1_mo_s(self) -> list[np.ndarray]:
        """The first-nearest neighbour hopping matrix from the odd metal orbitals under shear strain"""
        return [
            self._t_n_o_s(*[self.params[f"u_1_{i}_m_o_s_{order_idx}"] for i in range(3, 6)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_me_s(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the even metal orbitals under shear strain"""
        return [
            self._t_m_me_s(*[self.params[f"u_2_{i}_m_e_s_{order_idx}"] for i in [1, 2, 4]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_mo_s(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the odd metal orbitals under shear strain"""
        return [
            self._t_m_mo_s(*[self.params[f"u_2_{i}_m_o_s_{order_idx}"] for i in [1]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_xe_s(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the even chalcogen orbitals under shear strain"""
        return [
            self._t_m_xr_s(*[self.params[f"u_2_{i}_x_e_s_{order_idx}"] for i in [1, 2, 4]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_2_xo_s(self) -> list[np.ndarray]:
        """The second-nearest neighbour hopping matrix from the odd chalcogen orbitals under shear strain"""
        return [
            self._t_m_xr_s(*[self.params[f"u_2_{i}_x_o_s_{order_idx}"] for i in [1, 2, 4]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_3_me_s(self) -> list[np.ndarray]:
        """The third-nearest neighbour hopping matrix from the even metal orbitals under shear strain"""
        return [
            self._t_n_e_s(*[self.params[f"u_3_{i}_m_e_s_{order_idx}"] for i in range(5, 9)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_3_mo_s(self) -> list[np.ndarray]:
        """The third-nearest neighbour hopping matrix from the odd metal orbitals under shear strain"""
        return [
            self._t_n_o_s(*[self.params[f"u_3_{i}_m_o_s_{order_idx}"] for i in range(3, 6)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_4_me_s(self) -> list[np.ndarray]:
        """The fourth-nearest neighbour hopping matrix from the even metal orbitals under shear strain"""
        return [
            self._t_n_e_s(*[self.params[f"u_4_{i}_m_e_s_{order_idx}"] for i in range(5, 9)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_4_mo_s(self) -> list[np.ndarray]:
        """The fourth-nearest neighbour hopping matrix from the odd metal orbitals under shear strain"""
        return [
            self._t_n_o_s(*[self.params[f"u_4_{i}_m_o_s_{order_idx}"] for i in range(3, 6)]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_me_s(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the even metal orbitals under shear strain"""
        return [
            self._t_5_me_s(*[self.params[f"u_5_{i}_m_e_s_{order_idx}"] for i in [2, 4, 7, 8]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_mo_s(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the odd metal orbitals under shear strain"""
        return [
            self._t_5_mo_s(*[self.params[f"u_5_{i}_m_o_s_{order_idx}"] for i in [1, 3]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_xe_s(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals under shear strain"""
        return [
            self._t_5_xr_s(*[self.params[f"u_5_{i}_x_e_s_{order_idx}"] for i in [1, 4, 7, 8]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_5_xo_s(self) -> list[np.ndarray]:
        """The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals under shear strain"""
        return [
            self._t_5_xr_s(*[self.params[f"u_5_{i}_x_o_s_{order_idx}"] for i in [1, 4, 7, 8]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_me_s(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the even metal orbitals under shear strain"""
        return [
            self._t_m_me_s(*[self.params[f"u_6_{i}_m_e_s_{order_idx}"] for i in [1, 2, 4]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_mo_s(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the odd metal orbitals under shear strain"""
        return [
            self._t_m_mo_s(*[self.params[f"u_6_{i}_m_o_s_{order_idx}"] for i in [1]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_xe_s(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals under shear strain"""
        return [
            self._t_m_xr_s(*[self.params[f"u_6_{i}_x_e_s_{order_idx}"] for i in [1, 2, 4]]
            ) for order_idx in range(1, self.params.max_order+1)]

    @property
    def t_6_xo_s(self) -> list[np.ndarray]:
        """The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals under shear strain"""
        return [
            self._t_m_xr_s(*[self.params[f"u_6_{i}_x_o_s_{order_idx}"] for i in [1, 2, 4]]
            ) for order_idx in range(1, self.params.max_order+1)]

e_me_b: list[np.ndarray] property

The hopping matrix for the even metal orbitals under biaxial strain

e_me_s: list[np.ndarray] property

The hopping matrix for the even metal orbitals under shear strain

e_me_u: list[np.ndarray] property

The hopping matrix for the even metal orbitals under uniaxial strain

e_mo_b: list[np.ndarray] property

The hopping matrix for the odd metal orbitals under biaxial strain

e_mo_s: list[np.ndarray] property

The hopping matrix for the odd metal orbitals under shear strain

e_mo_u: list[np.ndarray] property

The hopping matrix for the odd metal orbitals under uniaxial strain

e_xe_b: list[np.ndarray] property

The hopping matrix for the even chalcogen orbitals under biaxial strain

e_xe_s: list[np.ndarray] property

The hopping matrix for the even chalcogen orbitals under shear strain

e_xe_u: list[np.ndarray] property

The hopping matrix for the even chalcogen orbitals under uniaxial strain

e_xo_b: list[np.ndarray] property

The hopping matrix for the odd chalcogen orbitals under biaxial strain

e_xo_s: list[np.ndarray] property

The hopping matrix for the odd chalcogen orbitals under shear strain

e_xo_u: list[np.ndarray] property

The hopping matrix for the odd chalcogen orbitals under uniaxial strain

t_1_me_b: list[np.ndarray] property

The first-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain

t_1_me_s: list[np.ndarray] property

The first-nearest neighbour hopping matrix from the even metal orbitals under shear strain

t_1_me_u: list[np.ndarray] property

The first-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain

t_1_mo_b: list[np.ndarray] property

The first-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain

t_1_mo_s: list[np.ndarray] property

The first-nearest neighbour hopping matrix from the odd metal orbitals under shear strain

t_1_mo_u: list[np.ndarray] property

The first-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain

t_2_me_b: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain

t_2_me_s: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the even metal orbitals under shear strain

t_2_me_u: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain

t_2_mo_b: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain

t_2_mo_s: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the odd metal orbitals under shear strain

t_2_mo_u: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain

t_2_xe_b: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the even chalcogen orbitals under biaxial strain

t_2_xe_s: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the even chalcogen orbitals under shear strain

t_2_xe_u: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the even chalcogen orbitals under uniaxial strain

t_2_xo_b: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the odd chalcogen orbitals under biaxial strain

t_2_xo_s: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the odd chalcogen orbitals under shear strain

t_2_xo_u: list[np.ndarray] property

The second-nearest neighbour hopping matrix from the odd chalcogen orbitals under uniaxial strain

t_3_me_b: list[np.ndarray] property

The third-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain

t_3_me_s: list[np.ndarray] property

The third-nearest neighbour hopping matrix from the even metal orbitals under shear strain

t_3_me_u: list[np.ndarray] property

The third-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain

t_3_mo_b: list[np.ndarray] property

The third-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain

t_3_mo_s: list[np.ndarray] property

The third-nearest neighbour hopping matrix from the odd metal orbitals under shear strain

t_3_mo_u: list[np.ndarray] property

The third-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain

t_4_me_b: list[np.ndarray] property

The fourth-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain

t_4_me_s: list[np.ndarray] property

The fourth-nearest neighbour hopping matrix from the even metal orbitals under shear strain

t_4_me_u: list[np.ndarray] property

The fourth-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain

t_4_mo_b: list[np.ndarray] property

The fourth-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain

t_4_mo_s: list[np.ndarray] property

The fourth-nearest neighbour hopping matrix from the odd metal orbitals under shear strain

t_4_mo_u: list[np.ndarray] property

The fourth-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain

t_5_me_b: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain

t_5_me_s: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the even metal orbitals under shear strain

t_5_me_u: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain

t_5_mo_b: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain

t_5_mo_s: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the odd metal orbitals under shear strain

t_5_mo_u: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain

t_5_xe_b: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals under biaxial strain

t_5_xe_s: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals under shear strain

t_5_xe_u: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the even chalcogen orbitals under uniaxial strain

t_5_xo_b: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals under biaxial strain

t_5_xo_s: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals under shear strain

t_5_xo_u: list[np.ndarray] property

The fifth-nearest neighbour hopping matrix from the odd chalcogen orbitals under uniaxial strain

t_6_me_b: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the even metal orbitals under biaxial strain

t_6_me_s: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the even metal orbitals under shear strain

t_6_me_u: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the even metal orbitals under uniaxial strain

t_6_mo_b: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the odd metal orbitals under biaxial strain

t_6_mo_s: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the odd metal orbitals under shear strain

t_6_mo_u: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the odd metal orbitals under uniaxial strain

t_6_xe_b: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals under biaxial strain

t_6_xe_s: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals under shear strain

t_6_xe_u: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the even chalcogen orbitals under uniaxial strain

t_6_xo_b: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals under biaxial strain

t_6_xo_s: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals under shear strain

t_6_xo_u: list[np.ndarray] property

The sixth-nearest neighbour hopping matrix from the odd chalcogen orbitals under uniaxial strain

__init__(params)

Initialize the strained TMD hopping matrices

Parameters:

Name	Type	Description	Default
params	StrainParametersList	The parameters for the strained TMD lattice.	required

Source code in tmdybinding/tmd_strain.py

def __init__(self, params: StrainParametersList):
    """Initialize the strained TMD hopping matrices

    Parameters:
        params (StrainParametersList): The parameters for the strained TMD lattice."""
    super().__init__(params)
    self.params: StrainParametersList = params

VariableStorage

Class for saving the matrices and variables in the AbstractLattice-class. There are also checks for a consistent model, where the sizes of the matrices, the included hoppings and the onsite matrices are checked.

Source code in tmdybinding/tmd_abstract_lattice.py

class VariableStorage:
    """
    Class for saving the matrices and variables in the AbstractLattice-class.
    There are also checks for a consistent model, where the sizes of the matrices, the included hoppings and the onsite
    matrices are checked.
    """

    def __init__(self, params_dict: Optional[dict] = None):
        """Make a VariableStorage object with the given parameters. If no parameters are given, the parameters are None.

        Parameters:
            params_dict (Optional[dict]): The parameters for the lattice model.
                The dictionary entries must be in the format `"name": parameter`.
                The possible parameters are `"h_0_m"`, `"h_0_c"`, `"h_1_m"`, `"h_2_m"`, `"h_2_c"`, `"h_3_m"`, `"h_4_m"`,
                `"h_5_m"`, `"h_5_c"`, `"h_6_m"`, `"h_6_c"`, `"a"`, `"lamb_m"` and `"lamb_c"`.
        """
        self.__h_0_m = None
        self.__h_0_c = None
        self.__h_1_m = None
        self.__h_2_m = None
        self.__h_2_c = None
        self.__h_3_m = None
        self.__h_4_m = None
        self.__h_5_m = None
        self.__h_5_c = None
        self.__h_6_m = None
        self.__h_6_c = None
        self.__a = None
        self.__lamb_m = None
        self.__lamb_c = None
        self.__keys = [
            "h_0_m", "h_0_c",
            "h_1_m",
            "h_2_m", "h_2_c",
            "h_3_m",
            "h_4_m",
            "h_5_m", "h_5_c",
            "h_6_m", "h_6_c",
            "a", "lamb_m", "lamb_c"
        ]
        if params_dict is not None:
            self.set_params(params_dict)

    @staticmethod
    def _params_check(params_dict: dict, param_name: str) -> Optional[np.ndarray]:
        if param_name in params_dict.keys():
            if params_dict[param_name] is not None:
                return np.array(params_dict[param_name])
        return None

    def set_params(self, params_dict: dict, keep: bool = True):
        """Set the parameters for the lattice model.

        Parameters:
            params_dict (dict): The parameters for the lattice model.
                The dictionary entries must be in the format `"name": parameter`.
                The possible parameters are `"h_0_m"`, `"h_0_c"`, `"h_1_m"`, `"h_2_m"`, `"h_2_c"`, `"h_3_m"`, `"h_4_m"`,
                `"h_5_m"`, `"h_5_c"`, `"h_6_m"`, `"h_6_c"`, `"a"`, `"lamb_m"` and `"lamb_c"`.
            keep (bool): If True, the parameters that are not included in the `param_dict`are kept as they are.
                If False, the parameters that are not given are set to None.
        """
        params = self.to_dict() if keep else {}
        for name in params_dict.keys():
            assert str(name) in self.__keys, f"key {name} not in expected hoppings, possible wrong name"
            params[name] = params_dict[name]
        self._component_check(params)
        self._shape_check(params)
        self.__h_0_m = self._params_check(params, "h_0_m")
        self.__h_0_c = self._params_check(params, "h_0_c")
        self.__h_1_m = self._params_check(params, "h_1_m")
        self.__h_2_m = self._params_check(params, "h_2_m")
        self.__h_2_c = self._params_check(params, "h_2_c")
        self.__h_3_m = self._params_check(params, "h_3_m")
        self.__h_4_m = self._params_check(params, "h_4_m")
        self.__h_5_m = self._params_check(params, "h_5_m")
        self.__h_5_c = self._params_check(params, "h_5_c")
        self.__h_6_m = self._params_check(params, "h_6_m")
        self.__h_6_c = self._params_check(params, "h_6_c")
        self.__a = self._params_check(params, "a")
        self.__lamb_m = self._params_check(params, "lamb_m")
        self.__lamb_c = self._params_check(params, "lamb_c")

    def _make_bools(self, params_dict: dict):
        return [self._attr_check(name, params_dict) for name in self.__keys]

    def _component_check(self, params_dict: dict):
        (m_bool, c_bool,
         h_1_m_bool,
         h_2_m_bool, h_2_c_bool,
         h_3_m_bool,
         h_4_m_bool,
         h_5_m_bool, h_5_c_bool,
         h_6_m_bool, h_6_c_bool) = self._make_bools(params_dict)[:-3]
        assert m_bool or c_bool, "not X nor M in model"
        assert not (not m_bool and h_1_m_bool), "not M in model and 1st hopping from M"
        assert not (not c_bool and h_1_m_bool), "not M in model and 1st hopping to X"
        assert not (not m_bool and h_2_m_bool), "not M in model and 2nd hopping from/to M"
        assert not (not c_bool and h_2_c_bool), "not M in model and 2nd hopping from/to X"
        assert not (not m_bool and h_3_m_bool), "not M in model and 3rd hopping from M"
        assert not (not c_bool and h_3_m_bool), "not M in model and 3rd hopping to X"
        assert not (not m_bool and h_4_m_bool), "not M in model and 4rd hopping from M"
        assert not (not c_bool and h_4_m_bool), "not M in model and 4rd hopping to X"
        assert not (not m_bool and h_5_m_bool), "not M in model and 5th hopping from/to M"
        assert not (not c_bool and h_5_c_bool), "not M in model and 5th hopping from/to X"
        assert not (not m_bool and h_6_m_bool), "not M in model and 6th hopping from/to M"
        assert not (not c_bool and h_6_c_bool), "not M in model and 6th hopping from/to X"
        assert h_1_m_bool or h_2_c_bool or h_2_m_bool or h_3_m_bool or h_4_m_bool or h_5_c_bool or h_5_m_bool or \
               h_6_c_bool or h_6_m_bool, "no hoppings specified in the model"

    def _shape_check(self, params_dict: dict):
        (m_bool, c_bool,
         h_1_m_bool,
         h_2_m_bool, h_2_c_bool,
         h_3_m_bool,
         h_4_m_bool,
         h_5_m_bool, h_5_c_bool,
         h_6_m_bool, h_6_c_bool) = self._make_bools(params_dict)[:-3]
        if m_bool:
            m_shape = self._check_shape(params_dict["h_0_m"])
            if h_1_m_bool:
                assert np.shape(params_dict["h_1_m"])[1] == m_shape, "shape 1st hopping from M not correct"
            if h_2_m_bool:
                assert np.shape(params_dict["h_2_m"])[0] == m_shape, "shape 2nd hopping to M not correct"
                assert np.shape(params_dict["h_2_m"])[1] == m_shape, "shape 2nd hopping from M not correct"
            if h_3_m_bool:
                assert np.shape(params_dict["h_3_m"])[1] == m_shape, "shape 3rd hopping from M not correct"
            if h_4_m_bool:
                assert np.shape(params_dict["h_4_m"])[1] == m_shape, "shape 4rd hopping from M not correct"
            if h_5_m_bool:
                assert np.shape(params_dict["h_5_m"])[0] == m_shape, "shape 5th hopping to M not correct"
                assert np.shape(params_dict["h_5_m"])[1] == m_shape, "shape 5th hopping from M not correct"
            if h_6_m_bool:
                assert np.shape(params_dict["h_6_m"])[0] == m_shape, "shape 6th hopping to M not correct"
                assert np.shape(params_dict["h_6_m"])[1] == m_shape, "shape 6th hopping from M not correct"
        if c_bool:
            c_shape = self._check_shape(params_dict["h_0_c"])
            if h_1_m_bool:
                assert np.shape(params_dict["h_1_m"])[0] == c_shape, "shape 1st hopping to X not correct"
            if h_2_c_bool:
                assert np.shape(params_dict["h_2_c"])[0] == c_shape, "shape 2nd hopping to X not correct"
                assert np.shape(params_dict["h_2_c"])[1] == c_shape
            if h_3_m_bool:
                assert np.shape(params_dict["h_3_m"])[0] == c_shape, "shape 3rd hopping to X not correct"
            if h_4_m_bool:
                assert np.shape(params_dict["h_4_m"])[0] == c_shape, "shape 4rd hopping to X not correct"
            if h_5_c_bool:
                assert np.shape(params_dict["h_5_c"])[0] == c_shape, "shape 5th hopping to X not correct"
                assert np.shape(params_dict["h_5_c"])[1] == c_shape, "shape 5th hopping from X not correct"
            if h_6_c_bool:
                assert np.shape(params_dict["h_6_c"])[0] == c_shape, "shape 6th hopping to X not correct"
                assert np.shape(params_dict["h_6_c"])[1] == c_shape, "shape 6th hopping from X not correct"

    @staticmethod
    def _attr_check(name, params_dict: dict):
        if name in params_dict.keys():
            return params_dict[name] is not None
        else:
            return False

    @staticmethod
    def _check_shape(h_0):
        h_0_shape = np.shape(h_0)
        assert len(h_0_shape) < 3, "onsite energy too many dims (max 2 as matrix)"
        if len(h_0_shape) == 2:
            assert h_0_shape[0] == h_0_shape[1] or h_0_shape[0] == 1, "shape of x and y not the same for onsite energy"
            return h_0_shape[1]
        else:
            return h_0_shape[0]

    def to_dict(self) -> dict:
        """Return the parameters as a dictionary in the format `"name": parameter`."""
        dict_list = []
        for name in self.__keys:
            value = getattr(self, name)
            if value is not None:
                dict_list.append((name, value))
        return dict(dict_list)

    @property
    def h_0_m(self) -> np.ndarray:
        """The onsite energy for the metal atom."""
        return self.__h_0_m

    @h_0_m.setter
    def h_0_m(self, value: np.ndarray):
        self.set_params({"h_0_m": value})

    @property
    def h_0_c(self) -> np.ndarray:
        """The onsite energy for the chalcogen atom."""
        return self.__h_0_c

    @h_0_c.setter
    def h_0_c(self, value: np.ndarray):
        self.set_params({"h_0_c": value})

    @property
    def h_1_m(self) -> np.ndarray:
        """The first nearest neighbour hopping from the metal atom."""
        return self.__h_1_m

    @h_1_m.setter
    def h_1_m(self, value: np.ndarray):
        self.set_params({"h_1_m": value})

    @property
    def h_2_m(self) -> np.ndarray:
        """The second-nearest neighbour hopping from the metal atom."""
        return self.__h_2_m

    @h_2_m.setter
    def h_2_m(self, value: np.ndarray):
        self.set_params({"h_2_m": value})

    @property
    def h_2_c(self) -> np.ndarray:
        """The second-nearest neighbour hopping from the chalcogen atom."""
        return self.__h_2_c

    @h_2_c.setter
    def h_2_c(self, value: np.ndarray):
        self.set_params({"h_2_c": value})

    @property
    def h_3_m(self) -> np.ndarray:
        """The third-nearest neighbour hopping from the metal atom."""
        return self.__h_3_m

    @h_3_m.setter
    def h_3_m(self, value: np.ndarray):
        self.set_params({"h_3_m": value})

    @property
    def h_4_m(self) -> np.ndarray:
        """The fourth-nearest neighbour hopping from the metal atom."""
        return self.__h_4_m

    @h_4_m.setter
    def h_4_m(self, value: np.ndarray):
        self.set_params({"h_4_m": value})

    @property
    def h_5_m(self) -> np.ndarray:
        """The fifth-nearest neighbour hopping from the metal atom."""
        return self.__h_5_m

    @h_5_m.setter
    def h_5_m(self, value: np.ndarray):
        self.set_params({"h_5_m": value})

    @property
    def h_5_c(self) -> np.ndarray:
        """The fifth-nearest neighbour hopping from the chalcogen atom."""
        return self.__h_5_c

    @h_5_c.setter
    def h_5_c(self, value: np.ndarray):
        self.set_params({"h_5_c": value})

    @property
    def h_6_m(self) -> np.ndarray:
        """The sixth-nearest neighbour hopping from the metal atom."""
        return self.__h_6_m

    @h_6_m.setter
    def h_6_m(self, value: np.ndarray):
        self.set_params({"h_6_m": value})

    @property
    def h_6_c(self) -> np.ndarray:
        """The sixth-nearest neighbour hopping from the chalcogen atom."""
        return self.__h_6_c

    @h_6_c.setter
    def h_6_c(self, value: np.ndarray):
        self.set_params({"h_6_c": value})

    @property
    def a(self) -> float:
        """The lattice constant."""
        return self.__a

    @a.setter
    def a(self, value: float):
        self.set_params({"a": value})

    @property
    def lamb_m(self) -> float:
        """The spin-orbit coupling for the metal atom."""
        return self.__lamb_m

    @lamb_m.setter
    def lamb_m(self, value: float):
        self.set_params({"lamb_m": value})

    @property
    def lamb_c(self) -> float:
        """The spin-orbit coupling for the chalcogen atom."""
        return self.__lamb_c

    @lamb_c.setter
    def lamb_c(self, value: float):
        self.set_params({"lamb_c": value})

a: float property writable

The lattice constant.

h_0_c: np.ndarray property writable

The onsite energy for the chalcogen atom.

h_0_m: np.ndarray property writable

The onsite energy for the metal atom.

h_1_m: np.ndarray property writable

The first nearest neighbour hopping from the metal atom.

h_2_c: np.ndarray property writable

The second-nearest neighbour hopping from the chalcogen atom.

h_2_m: np.ndarray property writable

The second-nearest neighbour hopping from the metal atom.

h_3_m: np.ndarray property writable

The third-nearest neighbour hopping from the metal atom.

h_4_m: np.ndarray property writable

The fourth-nearest neighbour hopping from the metal atom.

h_5_c: np.ndarray property writable

The fifth-nearest neighbour hopping from the chalcogen atom.

h_5_m: np.ndarray property writable

The fifth-nearest neighbour hopping from the metal atom.

h_6_c: np.ndarray property writable

The sixth-nearest neighbour hopping from the chalcogen atom.

h_6_m: np.ndarray property writable

The sixth-nearest neighbour hopping from the metal atom.

lamb_c: float property writable

The spin-orbit coupling for the chalcogen atom.

lamb_m: float property writable

The spin-orbit coupling for the metal atom.

__init__(params_dict=None)

Make a VariableStorage object with the given parameters. If no parameters are given, the parameters are None.

Parameters:

Name	Type	Description	Default
params_dict	Optional[dict]	The parameters for the lattice model. The dictionary entries must be in the format "name": parameter. The possible parameters are "h_0_m", "h_0_c", "h_1_m", "h_2_m", "h_2_c", "h_3_m", "h_4_m", "h_5_m", "h_5_c", "h_6_m", "h_6_c", "a", "lamb_m" and "lamb_c".	None

Source code in tmdybinding/tmd_abstract_lattice.py

def __init__(self, params_dict: Optional[dict] = None):
    """Make a VariableStorage object with the given parameters. If no parameters are given, the parameters are None.

    Parameters:
        params_dict (Optional[dict]): The parameters for the lattice model.
            The dictionary entries must be in the format `"name": parameter`.
            The possible parameters are `"h_0_m"`, `"h_0_c"`, `"h_1_m"`, `"h_2_m"`, `"h_2_c"`, `"h_3_m"`, `"h_4_m"`,
            `"h_5_m"`, `"h_5_c"`, `"h_6_m"`, `"h_6_c"`, `"a"`, `"lamb_m"` and `"lamb_c"`.
    """
    self.__h_0_m = None
    self.__h_0_c = None
    self.__h_1_m = None
    self.__h_2_m = None
    self.__h_2_c = None
    self.__h_3_m = None
    self.__h_4_m = None
    self.__h_5_m = None
    self.__h_5_c = None
    self.__h_6_m = None
    self.__h_6_c = None
    self.__a = None
    self.__lamb_m = None
    self.__lamb_c = None
    self.__keys = [
        "h_0_m", "h_0_c",
        "h_1_m",
        "h_2_m", "h_2_c",
        "h_3_m",
        "h_4_m",
        "h_5_m", "h_5_c",
        "h_6_m", "h_6_c",
        "a", "lamb_m", "lamb_c"
    ]
    if params_dict is not None:
        self.set_params(params_dict)

set_params(params_dict, keep=True)

Set the parameters for the lattice model.

Parameters:

Name	Type	Description	Default
params_dict	dict	The parameters for the lattice model. The dictionary entries must be in the format "name": parameter. The possible parameters are "h_0_m", "h_0_c", "h_1_m", "h_2_m", "h_2_c", "h_3_m", "h_4_m", "h_5_m", "h_5_c", "h_6_m", "h_6_c", "a", "lamb_m" and "lamb_c".	required
keep	bool	If True, the parameters that are not included in the param_dictare kept as they are. If False, the parameters that are not given are set to None.	True

Source code in tmdybinding/tmd_abstract_lattice.py

def set_params(self, params_dict: dict, keep: bool = True):
    """Set the parameters for the lattice model.

    Parameters:
        params_dict (dict): The parameters for the lattice model.
            The dictionary entries must be in the format `"name": parameter`.
            The possible parameters are `"h_0_m"`, `"h_0_c"`, `"h_1_m"`, `"h_2_m"`, `"h_2_c"`, `"h_3_m"`, `"h_4_m"`,
            `"h_5_m"`, `"h_5_c"`, `"h_6_m"`, `"h_6_c"`, `"a"`, `"lamb_m"` and `"lamb_c"`.
        keep (bool): If True, the parameters that are not included in the `param_dict`are kept as they are.
            If False, the parameters that are not given are set to None.
    """
    params = self.to_dict() if keep else {}
    for name in params_dict.keys():
        assert str(name) in self.__keys, f"key {name} not in expected hoppings, possible wrong name"
        params[name] = params_dict[name]
    self._component_check(params)
    self._shape_check(params)
    self.__h_0_m = self._params_check(params, "h_0_m")
    self.__h_0_c = self._params_check(params, "h_0_c")
    self.__h_1_m = self._params_check(params, "h_1_m")
    self.__h_2_m = self._params_check(params, "h_2_m")
    self.__h_2_c = self._params_check(params, "h_2_c")
    self.__h_3_m = self._params_check(params, "h_3_m")
    self.__h_4_m = self._params_check(params, "h_4_m")
    self.__h_5_m = self._params_check(params, "h_5_m")
    self.__h_5_c = self._params_check(params, "h_5_c")
    self.__h_6_m = self._params_check(params, "h_6_m")
    self.__h_6_c = self._params_check(params, "h_6_c")
    self.__a = self._params_check(params, "a")
    self.__lamb_m = self._params_check(params, "lamb_m")
    self.__lamb_c = self._params_check(params, "lamb_c")

to_dict()

Return the parameters as a dictionary in the format "name": parameter.

Source code in tmdybinding/tmd_abstract_lattice.py

def to_dict(self) -> dict:
    """Return the parameters as a dictionary in the format `"name": parameter`."""
    dict_list = []
    for name in self.__keys:
        value = getattr(self, name)
        if value is not None:
            dict_list.append((name, value))
    return dict(dict_list)

tests()

Run the package tests.

Source code in tmdybinding/__init__.py

def tests():
    """Run the package tests."""
    import pytest
    import pathlib
    import os
    from pybinding.utils.misc import cd
    import pybinding as pb

    module_path = pathlib.Path(__file__).parent

    args = []
    if (module_path / 'tests').exists():
        # tests are inside installed package -> use read-only mode
        args.append('--failpath=' + os.getcwd() + '/failed')
        with cd(module_path):
            args += ['-c', str(module_path / 'tests/local.cfg'), str(module_path)]
            error_code = pytest.main(args)
    else:
        # tests are in dev environment -> use development mode
        with cd(module_path.parent):
            error_code = pytest.main(args)

    return error_code or None