hyperfine.superconductivity.pippard.K_Pippard

hyperfine.superconductivity.pippard.K_Pippard(q: Annotated[float, slice(0, None, None)], T: Annotated[float, slice(0, None, None)], T_c: Annotated[float, slice(0, None, None)], Delta_0: Annotated[float, slice(0, None, None)], lambda_L: Annotated[float, slice(0, None, None)], l: Annotated[float, slice(0, None, None)], xi_0: Annotated[float, slice(0, None, None)], alpha: Annotated[float, slice(0, None, None)] = 1.0) → float

Evaluate the Pippard response function.

Parameters:

• q – wavevector (1/nm).

• T – Absolute temperature (K).

• T_c – Superconducting transition temperature (K).

• Delta_0 – Superconducting gap energy at 0 K (eV).

• lambda_L – London penetration depth (nm).

• l – electron mean-free-path (nm).

• xi_0 – Pippard coherence length at 0 K (nm).

• alpha – numerical constant on the order of unity.

Returns:

The Pippard response function K(q) at q.

Example

import numpy as np
import matplotlib.pyplot as plt
from hyperfine.superconductivity import pippard

q = np.logspace(-4, 4, 200)
args = (0.0, 10.0, 1.43e-3, 30.0, 300.0, 40.0)
k = np.array([pippard.K_Pippard(qq, *args) for qq in q])
plt.plot(q, k, "-")
plt.xlabel("$q$ (nm$^{-1}$)")
plt.ylabel(r"$K_{\mathrm{Pippard}}(q)$ (nm$^{-2}$)")
plt.xscale("log")
plt.yscale("log")
plt.show()

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