Source code for gpaw.nlopt.linear

import numpy as np
from ase.units import Bohr, _hbar, _e, _me, _eps0

from gpaw.nlopt.basic import load_data
from gpaw.mpi import world

[docs]def get_chi_tensor( freqs=[1.0], eta=0.05, ftol=1e-4, Etol=1e-6, eshift=0.0, band_n=None, mml_name='mml.npz', out_name=None): """ Calculate full linear susceptibility tensor for nonmagnetic semiconductors. Input: freqs Excitation frequency array (a numpy array or list) eta Broadening, a number or an array (default 0.05 eV) Etol, ftol Tol. in energy and fermi to consider degeneracy eshift Bandgap correction band_n List of bands in the sum (default 0 to nb) out_name If it is given: output filename mml_name The momentum filename (default 'mml.npz') Output: chi_vvl The output tensor (3, 3, nw) chi.npy If specified: array containing the spectrum and freqs """ freqs = np.array(freqs) nw = len(freqs) w_lc = freqs + 1j * eta # Load the required data k_info = load_data(mml_name=mml_name) if k_info: tmp = list(k_info.values())[0] nb = len(tmp[1]) if band_n is None: band_n = list(range(nb)) # Initialize the outputs sum_vvl = np.zeros((3, 3, nw), complex) # Do the calculations for _, (we, f_n, E_n, p_vnn) in k_info.items(): tmp = np.zeros((3, 3, nw), complex) for v1 in range(3): for v2 in range(v1, 3): sum_l = calc_chi( w_lc, f_n, E_n, p_vnn, [v1, v2], band_n, ftol, Etol, eshift=eshift) tmp[v1, v2] = sum_l tmp[v2, v1] = sum_l # Add it to previous with a weight sum_vvl += tmp * we world.sum(sum_vvl) # Make the output in SI unit dim_sigma = 1j * _e**2 * _hbar / (_me**2 * (2 * np.pi)**3) dim_chi = 1j * _hbar / (_eps0 * _e) dim_sum = (_hbar / (Bohr * 1e-10))**2 / \ (_e**2 * (Bohr * 1e-10)**3) dim_SI = dim_sigma * dim_chi * dim_sum chi_vvl = dim_SI * sum_vvl # Save it to the file if world.rank == 0 and out_name is not None: tmp = chi_vvl.reshape(9, nw) lin = np.vstack((freqs, tmp)), lin) return chi_vvl
def calc_chi( w_l, f_n, E_n, p_vnn, pol_v, band_n=None, ftol=1e-4, Etol=1e-6, eshift=0): """ Loop over bands for computing the response Input: w_l Complex frequency array f_n Fermi levels E_n Energies p_vnn Momentum matrix elements pol_v Tensor element band_n Band list Etol, ftol Tol. in energy and fermi to consider degeneracy eshift Bandgap correction Output: sum_l Output sum value (array with length of w_l) """ # Initialize variables nb = len(f_n) if band_n is None: band_n = list(range(nb)) sum_l = np.zeros(w_l.size, complex) # Loop over bands for nni in band_n: for mmi in band_n: # Use TRS to reduce if mmi <= nni: continue fnm = f_n[nni] - f_n[mmi] Emn = E_n[mmi] - E_n[nni] + fnm * eshift if np.abs(fnm) < ftol or np.abs(Emn) < Etol: continue # *2 for real, /2 for TRS, *2 for m<n sum_l += 2 * fnm * np.real( p_vnn[pol_v[0], nni, mmi] * p_vnn[pol_v[1], mmi, nni]) \ / (Emn * (w_l**2 - Emn**2)) return sum_l