hopping_energy_modifier

hopping_energy_modifier(is_double: bool = False, is_complex: bool = False, phase: bool = False, **kwargs) → partial

Modify the hopping energy, e.g. to apply a magnetic field

Parameters:

is_doublebool

Requires the model to use double precision floating point values. Defaults to single precision otherwise.

is_complexbool

Requires the model to use complex numbers. Even if this is set to False, the model will automatically switch to complex numbers if it finds that a modifier has returned complex numbers for real input. Manually setting this argument to True will speed up model build time slightly, but it’s not necessary for correct operation.

phasebool

Define the phase of the reciprocal space so that the different eigenvectors have the same guage.

Notes

The function parameters must be a combination of any number of the following:

energyndarray

The hopping energy between two sites.

x1, y1, z1, x2, y2, z2ndarray

Positions of the two lattice sites connected by the hopping parameter.

hop_idsupport.alias.AliasIndex

Hopping identifier: can be checked for equality with hopping names specified in Lattice. For example, energy[hop_id == 't_nn'] *= 1.1 will only modify the energy of the hopping family named t_nn.

shiftndarray

Shift of x, y, z

The function must return:

ndarray

A modified hopping argument or an ndarray of the same dtype and shape.

Examples

def constant_magnetic_field(B):
    @pb.hopping_energy_modifier
    def f(energy, x1, y1, x2, y2):
        y = 0.5 * (y1 + y2) * 1e-9
        peierls = B * y * (x1 - x2) * 1e-9
        return energy * np.exp(1j * 2*pi/phi0 * peierls)
    return f

model = pb.Model(
    ... # lattice, shape, etc.
    constant_magnetic_field(B=10)
)