Macroscopic anisotropy in superconductors with anisotropic gaps

TL;DR

This paper demonstrates that superconducting anisotropy in materials with anisotropic gaps varies with temperature and cannot be summarized by a single number, especially in the case of MgB₂ with two gaps.

Contribution

It provides a theoretical analysis of macroscopic anisotropy in anisotropic-gap superconductors, including temperature dependence and specific models like MgB₂.

Findings

Anisotropy parameter γ(T) varies with temperature.

γ(T) increases with T in MgB₂.

Single-number characterization is insufficient for anisotropic-gap superconductors.

Abstract

It is shown within the weak-coupling model that the macroscopic superconducting anisotropy for materials with the gap varying on the Fermi surface cannot be characterized by a single number, unlike the case of clean materials with isotropic gaps. For clean uniaxial materials, the anisotropy parameter $\gamma (T)$ defined as the ratio of London penetration depths, $\lambda_c/\lambda_{ab}$, is evaluated for all $T$'s. Within the two-gap model of MgB$_2$, $\gamma (T)$ is an increasing function of $T$.