Critical temperature and superfluid density suppression in disordered high-$T_c$ cuprate superconductors

TL;DR

This paper shows that traditional theories underestimate the resilience of high-$T_c$ cuprate superconductors' critical temperature and superfluid density against disorder, emphasizing the importance of spatial variations in the order parameter.

Contribution

It introduces a numerical approach that accounts for spatial variations of the order parameter, revealing a weaker suppression of $T_c$ and superfluid density than predicted by conventional theories.

Findings

Suppression of $T_c$ is weaker than AG theory predicts.

Spatial variation of the order parameter is crucial in disordered high-$T_c$ cuprates.

Results align well with experimental observations.

Abstract

We argue that the standard Abrikosov-Gorkov (AG) type theory of $T_c$ in disordered $d$-wave superconductors breaks down in short coherence length high-$T_c$ cuprates. Numerical calculations within the Bogoliubov-de Gennes formalism demonstrate that the correct description of such systems must allow for the spatial variation of the order parameter, which is strongly suppressed in the vicinity of impurities but mostly unaffected elsewhere. Suppression of $T_c$ as measured with respect to the attendant decrease in the superfluid density is found to be significantly weaker than that predicted by the AG theory, in good agreement with experiment.