Density of states in gapped superconductors with pairing-potential impurities

TL;DR

This paper investigates how pairing-potential impurities and disorder affect the density of states in gapped superconductors, revealing conditions for Andreev states and the impact of gap anisotropy on spectral features.

Contribution

It derives and solves equations for quasiclassical Green functions to analyze impurity effects on the density of states in superconductors with small gap anisotropy.

Findings

Isolated impurities with suppressed pairing support infinite Andreev states in isotropic gaps.

Increasing impurity concentration broadens the density of states from a sharp gap to a smeared singularity.

Gap anisotropy makes the density of states sensitive to potential disorder and affects Andreev state localization.

Abstract

We study the density of states in disordered s-wave superconductors with a small gap anisotropy. Disorder comes in the form of common nonmagnetic scatterers and pairing-potential impurities, which interact with electrons via an electric potential and a local distortion of the superconducting gap. A set of equations for the quasiclassical Green functions is derived and solved. Within one spin sector, pairing-potential impurities and weak spin-polarized magnetic impurities have essentially the same effect on the density of states. We show that if the gap is isotropic, an isolated impurity with suppressed pairing supports an infinite number of Andreev states. With growing impurity concentration, the energy-dependent density of states evolves from a sharp gap edge with an impurity band below it to a smeared BCS singularity in the so-called universal limit. If a gap anisotropy is present, the density of states becomes sensitive to ordinary potential disorder, and the existence of of Andreev states localized at pairing-potential impurities requires special conditions. An unusual feature related to the anisotropy is a nonmonotonic dependence of the gap edge smearing on impurity concentration.