Anisotropy parameters of superconducting MgB$_2$

TL;DR

This paper reviews the macroscopic superconducting anisotropy of MgB$_2$, modeling it with a two-gap anisotropic s-wave approach, and discusses how different anisotropy ratios vary with temperature and their implications.

Contribution

It applies a weak coupling two-gap anisotropic s-wave model to describe MgB$_2$'s anisotropy and analyzes the temperature dependence of critical field and penetration depth ratios.

Findings

The ratio of upper critical fields $ ext{ } ext{ } ightarrow ext{ }  ext{ }$ increases with decreasing temperature.

The ratio of London penetration depths $ ext{ } ext{ } ightarrow ext{ }  ext{ }$ decreases to about 1.1 at T=0.

Possible macroscopic effects of $ ext{ } ext{ } e  ext{ }$ are discussed.

Abstract

Data on macroscopic superconducting anisotropy of MgB$_2$ are reviewed. The data are described within a weak coupling two-gaps anisotropic s-wave model of superconductivity. The calculated ratio of the upper critical fields $\gamma_H=H_{c2,ab}/H_{c2,c}$ increases with decreasing temperature in agreement with available data, whereas the calculated ratio of London penetration depths $\gamma_{\lambda}=\lambda_c/\lambda_{ab}$ decreases to reach $\approx 1.1$ at T=0. Possible macroscopic consequences of $\gamma_{\lambda}\ne\gamma_H$ are discussed.