import numpy as np
from ase.units import Bohr, _hbar, _e, _me, _eps0
from gpaw.mpi import world
[docs]def get_chi_tensor(
nlodata,
freqs=[1.0], eta=0.05,
ftol=1e-4, Etol=1e-6, eshift=0.0,
band_n=None, out_name=None):
"""
Calculate full linear susceptibility tensor for nonmagnetic semiconductors;
array will be saved to disk if out_name is given.
Parameters
----------
nlodata
Data object of type NLOData.
freqs
Excitation frequency array (a numpy array or list).
eta
Broadening, a number or an array (default 0.05 eV).
Etol, ftol
Tolerance in energy and occupancy 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.
Returns
-------
np.ndarray:
Full linear susceptibility tensor (3, 3, nw).
"""
freqs = np.array(freqs)
nw = len(freqs)
w_lc = freqs + 1j * eta
# Load the required data
k_info = nlodata.distribute()
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))
np.save(out_name, 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