Comparison of $H_{c2}(T,\theta)$ in Mg$_{1-x}$Al$_x$B$_2$ single crystals with the dirty-limit two-gap theory

TL;DR

This study investigates the temperature and angular dependence of the upper critical field in Mg$_{1-x}$Al$_x$B$_2$ single crystals, confirming the applicability of the dirty-limit two-gap theory and observing how Al doping affects anisotropy and impurity scattering.

Contribution

It demonstrates that the dirty-limit two-gap theory accurately describes $H_{c2}(T, heta)$ in Mg$_{1-x}$Al$_x$B$_2$ crystals and reveals how Al doping influences anisotropic impurity scattering and the two-gap nature.

Findings

$H_{c2}(T, heta)$ fits the two-gap theory well.

Increased Al doping enhances impurity scattering and reduces anisotropy.

Two-gap superconductivity persists up to $x=0.21$.

Abstract

We studied the temperature and the angular dependences of the upper critical field ($H_{c2}(T,\theta$)) of Mg$_{1-x}$Al$_x$B$_2$ single crystals ($x = 0.12$ and 0.21) and compared with the dirty-limit two-gap theory. We found that $H_{c2}(T,\theta)$'s were well described in a unified way by this theory. The obtained values of the parameters indicated that as the Al concentration was increased, anisotropic impurity scattering increased, making the $\sigma$ bands less anisotropic. Accordingly, the temperature dependence of the anisotropy ratio of $H_{c2}$ ($\gamma_H$) systematically decreased, and for $x=0.21$, $\gamma_H$ was nearly constant. Our results imply that Mg$_{1-x}$Al$_x$B$_2$ single crystals are in dirty-limit and that two-gap nature survives until $x = 0.21$.