Source code for tbmodels.kdotp

#
# (c) 2015-2018, ETH Zurich, Institut fuer Theoretische Physik
# Author: Dominik Gresch <greschd@gmx.ch>
"""
Defines the :class:`.KdotpModel` class for k.p models.
"""

import typing as ty

import numpy as np
import scipy.linalg as la

from fsc.export import export
from fsc.hdf5_io import subscribe_hdf5, SimpleHDF5Mapping


[docs]@export @subscribe_hdf5("tbmodels.kdotp_model", check_on_load=False) class KdotpModel(SimpleHDF5Mapping): """ A class describing a k.p model. Parameters ---------- taylor_coefficients: A mapping containing the taylor coefficients of the k.p model. The keys are tuples which describe the power of the k-vector components, and the values are the corresponding matrices. Example: (1, 0, 2): [[1, 0], [0, -1]] describes k_x * k_z**2 * sigma_z """ HDF5_ATTRIBUTES = ["taylor_coefficients"] def __init__( self, taylor_coefficients: ty.Mapping[ty.Tuple[int, ...], ty.Any] ) -> None: for mat in taylor_coefficients.values(): if not np.allclose(mat, np.array(mat).T.conj()): raise ValueError( f"The provided Taylor coefficient {mat} is not hermitian" ) self.taylor_coefficients = { tuple(key): np.array(mat, dtype=complex) for key, mat in taylor_coefficients.items() } def hamilton( self, k: ty.Union[ty.Sequence[float], ty.Sequence[ty.Sequence[float]]] ) -> np.ndarray: """ Calculates the Hamilton matrix for a given k-point or list of k-points. Parameters ---------- k : The k-point at which the Hamiltonian is evaluated. If a list of k-points is given, the result will be the corresponding list of Hamiltonians. """ k_array = np.array(k, ndmin=1) if k_array.ndim == 1: single_point = True k_array = k_array.reshape((1, -1)) else: single_point = False ham: np.ndarray = sum( np.prod(k_array ** k_powers, axis=-1).reshape(-1, 1, 1) * mat[np.newaxis, :, :] for k_powers, mat in self.taylor_coefficients.items() ) if single_point: return ham[0] return ham def eigenval( self, k: ty.Union[ty.Sequence[float], ty.Sequence[ty.Sequence[float]]] ) -> ty.Union[np.ndarray, ty.List[np.ndarray]]: """ Returns the eigenvalues at a given k point, or list of k-points. Parameters ---------- k : The k-point at which the Hamiltonian is evaluated. If a list of k-points is given, a corresponding list of eigenvalue arrays is returned. """ hamiltonians = self.hamilton(k) if hamiltonians.ndim == 3: return [la.eigvalsh(ham) for ham in hamiltonians] return la.eigvalsh(hamiltonians)