Impurity Effects on Bound States in the Vortex Core of Topological S-wave Superconductor

TL;DR

This study investigates how impurities affect the bound states within vortex cores of topological s-wave superconductors, combining numerical and analytical methods to understand impurity scattering and vortex inequivalence.

Contribution

It introduces an improved numerical scheme and analytical approach to analyze impurity effects on vortex core states in topological s-wave superconductors, considering vortex inequivalence.

Findings

Impurity scattering rates depend on vortex type and impurity strength.

Analytical and numerical results show impurity effects alter the energy levels in vortex cores.

The study clarifies the origin of impurity scattering in topological superconductors.

Abstract

We study the impurity effects on the Caroli-de Gennes-Matricon (CdGM) states, particularly on the level spacings in a vortex core in topological s-wave superconductor (SC) by two means, numerically and analytically. The topological s-wave SC belongs to the same class as a chiral p-wave SC and thus there are two inequivalent vortices in terms of any symmetry operation. We take into account this inequivalence and numerically calculate the scattering rates based on an improved version of Kopnin-Kravtsov (iKK) scheme, which enables us to treat the discrete levels in the presence of white-noise disorder. We also construct the Andreev equation for the topological s-wave SC and obtain the Andreev bound states analytically. We use a correspondence between the wave functions for the Bogoliubov-de Gennes equation and the Andreev equation in the iKK scheme and deduce the formula of scattering rates described by the wave function for the Andreev equation. With this formula, we discuss the origin of impurity scattering rates for CdGM states of topological s-wave SC and the dependence on the types of vortices related to the inequivalence.