Ginzburg-Landau Expansion and the Slope of the Upper Critical Field in Superconductors with Anisotropic Normal Impurity Scattering

TL;DR

This paper derives a Ginzburg-Landau expansion for anisotropic superconductors with impurities, revealing how the slope of the upper critical field varies with disorder and pairing symmetry.

Contribution

It introduces a new theoretical framework for understanding the effects of anisotropic impurity scattering on the upper critical field in superconductors.

Findings

In d-wave superconductors, the slope of Hc2(T) shows nonlinear dependence on impurity concentration.

In s-wave superconductors, the slope approaches the isotropic limit regardless of scattering anisotropy.

The stability of d-wave pairing increases with anisotropic impurity scattering.

Abstract

Ginzburg-Landau expansion for superconductors with anisotropic $s-$ and $d-$wave pairing is derived in the presence of anisotropic normal impurity scattering which makes $d-$pairing state more stable under disordering. It is demonstrated that the slope of the upper critical field $|dH_{c2}/dT|_{T_{c}}$ in superconductors with $d-$wave pairing has nonlinear dependence on disorder, i.e. for the low anisotropic scattering rate it drops rather fast with concentration of normal impurities, but as anisotropy of scattering increases it features initial nonlinear growth, approaches a maximum and drops again, vanishing at the critical impurity concentration. In superconductors with anisotropic $s-$wave pairing $|dH_{c2}/dT|_{T_{c}}$ grows, approaching the known asymptotic behavior, characteristic of usual isotropic case irrespective to the scattering anisotropy.