Ginzburg-Landau Expansion and the Slope of the Upper Critical Field in Disordered Superconductors with Anisotropic Pairing

TL;DR

This paper analyzes how the slope of the upper critical magnetic field near the critical temperature varies with disorder in superconductors, providing a method to distinguish pairing symmetries in complex materials.

Contribution

It introduces a Ginzburg-Landau expansion approach to relate the slope of $H_{c2}$ to impurity concentration, differentiating between $d$-wave and anisotropic $s$-wave pairing.

Findings

In $d$-wave superconductors, $|dH_{c2}/dT|_{T_{c}}$ decreases rapidly with impurities.

In anisotropic $s$-wave superconductors, $|dH_{c2}/dT|_{T_{c}}$ increases with disorder.

Strong disorder results align with the dirty superconductor theory.

Abstract

It is demonstrated that the slope of the upper critical field $|dH_{c2}/dT|_{T_{c}}$ in superconductors with $d$-wave pairing drops rather fast with concentration of normal impurities, while in superconductors with anisotropic $s$-wave pairing $|dH_{c2}/dT|_{T_{c}}$ grows, and in the limit of strong disorder is described by the known dependences of the theory of ``dirty'' superconductors. This allows to use the measurements of $H_{c2}$ in disordered superconductors to discriminate between these different types of pairing in high-temperature and heavy-fermion superconductors.