hyperfine.superconductivity.pippard.integrand_specular_profile

hyperfine.superconductivity.pippard.integrand_specular_profile(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[source]

Integrand for calculating the magnetic penetration depth.

The calculation assumes diffuse scattering of electrons at the material’s surface.

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 integrand at a given wavevector 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)
isp = np.array([pippard.integrand_specular_profile(qq, *args) for qq in q])
plt.plot(q, isp, "-")
plt.xlabel("$q$ (nm$^{-1}$)")
plt.ylabel("$I(q)$ (nm)")
plt.xscale("log")
plt.yscale("log")
plt.show()

(Source code, png, hires.png, pdf)

../_images/hyperfine-superconductivity-pippard-integrand_specular_profile-1.png