Impact of topology on the impurity effects in extended $s$-wave superconductors with spin-orbit coupling

TL;DR

This study explores how the topology of extended s-wave superconductors with spin-orbit coupling influences impurity-induced subgap states, revealing that potential impurities can serve as indicators of topological superconductivity.

Contribution

It demonstrates the presence of impurity bound states only in topological phases and links impurity effects to topological edge states, offering a new method to detect topological superconductivity.

Findings

Subgap impurity states exist only in topological phases.

Potential impurities do not create zero-energy states, unlike magnetic impurities.

Superconducting gaps are resilient to finite disorder in topological phases.

Abstract

We investigate the impact of topology on the existence of impurity subgap states in a time-reversal-invariant superconductor with an extended $s$-wave pairing and strong spin-orbit coupling. By simply tuning the chemical potential we access three distinct phases: topologically trivial $s$-wave, topologically non-trivial $s_\pm$-wave, and nodal superconducting phase. For a single potential impurity we find subgap impurity bound states in the topological phase, but notably no subgap states in the trivial phase. These subgap impurity states have always finite energies for any strength of the potential scattering and subsequently, the superconducting gap in the topological $s_\pm$-wave phase survives but is attenuated in the presence of finite disorder. By creating islands of potential impurities we smoothly connect the single impurity results to topological edge states of impurity island. On the other hand, magnetic impurities lead to the formation of Yu-Shiba-Rusinov states in both the trivial and topological phases, which even reach zero energy at certain scattering strengths. We thus propose that potential impurities can be a very valuable tool to detect time-reversal-invariant topological superconductivity.