106 lines
2.8 KiB
Python
106 lines
2.8 KiB
Python
import numpy as np
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import pynam.dielectric.sigma_nam
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import pynam.dielectric.low_k_nam
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from typing import Tuple
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FIXED_LARGE_MOMENTUM = 1e8
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class DedimensionalisedParameters(object):
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def __init__(
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self,
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omega: float,
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sigma_n: float,
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tau: float,
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v_f: float,
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temp: float,
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critical_temp: float,
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c_light: float):
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gap = 0
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if temp < critical_temp:
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# else, problems will happen
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gap = 3.06 * np.sqrt(critical_temp * (critical_temp - temp))
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self.xi = omega / gap
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self.nu = 1 / (tau * gap)
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self.t = temp / gap
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self.a = omega * v_f / (c_light * gap)
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self.b = sigma_n / omega
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class NamDielectricCoefficients(object):
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def __init__(self, a: float, b: float, c: float, d: float):
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self.a = a
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self.b = b
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self.c = c
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self.d = d
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self.u_l = np.real((-self.c + 1j * self.d) / (-self.a + 1j * self.b))
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def eps(self, u_c: float):
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def piecewise_eps(u: float):
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# todo add check for u_c vs u_l
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if u < self.u_l:
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return -self.a + 1j * self.b
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elif self.u_l < u < u_c:
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return 1 + (-self.c + 1j * self.d) / u
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else:
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return 1
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return piecewise_eps
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def get_dedimensionalised_parameters(
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omega: float,
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sigma_n: float,
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tau: float,
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v_f: float,
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temp: float,
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critical_temp: float,
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c_light: float) -> DedimensionalisedParameters:
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return DedimensionalisedParameters(omega, sigma_n, tau, v_f, temp, critical_temp, c_light)
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def get_small_momentum_coefficients(dedim_params: DedimensionalisedParameters) -> Tuple[float, float]:
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prefactor = 4j * np.pi * dedim_params.b
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s = pynam.dielectric.low_k_nam.sigma_nam_alk(dedim_params.xi, 0, dedim_params.nu, dedim_params.t)
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conductivity = prefactor * s
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return -np.real(conductivity), np.imag(conductivity)
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def get_big_momentum_coefficients(dedim_params: DedimensionalisedParameters) -> Tuple[float, float]:
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prefactor = 4j * np.pi * dedim_params.b * FIXED_LARGE_MOMENTUM / dedim_params.a
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s = pynam.dielectric.sigma_nam.sigma_nam(dedim_params.xi,
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FIXED_LARGE_MOMENTUM,
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dedim_params.nu,
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dedim_params.t)
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conductivity = prefactor * s
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return -np.real(conductivity), np.imag(conductivity)
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def get_nam_dielectric_coefficients(
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omega: float,
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sigma_n: float,
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tau: float,
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v_f: float,
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temp: float,
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crit_temp: float,
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c_light: float) -> NamDielectricCoefficients:
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"""Gets a NamDielectricCoefficients object, using SI unit parameters
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:param omega: frequency
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:param sigma_n: normal state conductivity
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:param tau: tau in Hz
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:param v_f: Fermi velocity, in m/s
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:param temp: temperature in Hz
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:param crit_temp: critical temperature, in Hz
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:param c_light: speed of light, meters per second
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:return:
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"""
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dedim = get_dedimensionalised_parameters(omega, sigma_n, tau, v_f, temp, crit_temp, c_light)
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a, b = get_small_momentum_coefficients(dedim)
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c, d = get_big_momentum_coefficients(dedim)
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return NamDielectricCoefficients(a, b, c, d)
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