Impurity-induced subgap states in superconductors with inhomogeneous pairing

TL;DR

This paper investigates how impurities in inhomogeneous s-wave superconductors create multiple subgap states, revealing that even nonmagnetic impurities can induce Yu-Shiba-Rusinov states in such systems.

Contribution

It demonstrates that in superconductors with spatially varying order parameters, impurities induce multiple subgap states, extending the understanding beyond homogeneous cases.

Findings

A single impurity induces two Yu-Shiba-Rusinov states inside the minigap.

Subgap states can appear even with nonmagnetic impurities.

The result applies broadly to superconductors with real, inhomogeneous order parameters.

Abstract

We study subgap states induced by a single impurity in an s-wave superconductor with suppressed pairing. For concreteness, we consider a bulk superconductor containing a normal spherical region. We find that a point impurity in this system induces two Yu-Shiba-Rusinov states inside the minigap instead of one, which one would have in a homogeneous superconductor. Moreover, the subgap states appear even if the impurity is nonmagnetic. We prove that this result actually holds almost for any superconductor with a real and spatially inhomogeneous order parameter, if the quasiparticle spectrum is gapped.