Robustness of unconventional $s$-wave superconducting states against disorder

TL;DR

This paper develops a theory to analyze how unconventional $s$-wave superconducting states in multiband systems respond to disorder, revealing enhanced resilience in certain topological superconductors.

Contribution

It introduces a general framework for impurity effects on multiband $s$-wave states, highlighting their robustness compared to single-band predictions.

Findings

Unconventional $s$-wave states are more resilient to disorder in multiband systems.

Application to YPtBi and Cu$_x$Bi$_2$Se$_3$ shows enhanced robustness.

Superconducting fitness quantifies the robustness of $s$-wave states.

Abstract

We investigate the robustness against disorder of superconductivity in multiband systems where the fermions have four internal degrees of freedom. This permits unconventional $s$-wave pairing states, which may transform nontrivially under crystal symmetries. Using the self-consistent Born approximation, we develop a general theory for the effect of impurities on the critical temperature, and find that the presence of these novel $s$-wave channels significantly modifies the conclusions of single-band theories. We apply our theory to two candidate topological superconductors, YPtBi and Cu$_x$Bi$_2$Se$_3$, and show that the novel $s$-wave states display an enhanced resilience against disorder, which extends to momentum-dependent pairing states with the same crystal symmetry. The robustness of the $s$-wave states can be quantified in terms of their superconducting fitness, which can be readily evaluated for model systems.