Subgap states in disordered superconductors with strong magnetic impurities

TL;DR

This paper investigates how magnetic impurities and disorder affect the density of states in superconductors, revealing the smearing of spectral edges and subgap states through advanced theoretical methods.

Contribution

It introduces a beyond-mean-field approach using instantons in the replica sigma-model to analyze subgap states in disordered superconductors with magnetic impurities.

Findings

Calculated the smearing of spectral edges due to disorder fluctuations.

Reproduced known results in limiting cases for subgap DOS.

Showed how inhomogeneity in impurity concentration affects the DOS.

Abstract

We study the density of states (DOS) in diffusive superconductors with pointlike magnetic impurities of arbitrary strength described by the Poissonian statistics. The mean-field theory predicts a nontrivial structure of the DOS with the continuum of quasiparticle states and (possibly) the impurity band. In this approximation, all the spectral edges are hard, marking distinct boundaries between spectral regions of finite and zero DOS. Considering instantons in the replica sigma-model technique, we calculate the average DOS beyond the mean-field level and determine the smearing of the spectral edges due interplay of fluctuations of potential and nonpotential disorder. The latter, represented by inhomogeneity in the concentration of magnetic impurities, affects the subgap DOS in two ways: via fluctuations of the pair-breaking strength and via induced fluctuations of the order parameter. In limiting cases, we reproduce previously reported results for the subgap DOS in disordered superconductors with strong magnetic impurities.