Impurity-induced bound states in superconductors with topological order

TL;DR

This paper investigates how impurities induce bound states in topological superconductors, providing a method to identify topological phases through impurity effects without surface analysis.

Contribution

It classifies Bogoliubov-de Gennes Hamiltonians using the $F$-function to determine impurity-induced bound states in topological superconductors.

Findings

Impurities induce localized states in the superconducting gap.

The $F$-function predicts the presence or absence of bound states.

Bound states persist across impurity strengths.

Abstract

The study of classical spins in topological insulators [Phys. Rev. B {\bf 80}, 115216 (2009)] is generalized to topological superconductors. Based on the characteristic features of the so-called $F$-function, Bogoliubov-de Gennes Hamiltonian for superconductors is classified to positive, negative, and zero "gap" categories for topologically trivial and nontrivial phases of a topological superconductor as well as a BCS superconductor respectively. It is found that the $F$-function determines directly the presence or absence of localized excited states, induced by bulk classical spins and nonmagnetic impurities, in superconducting gap and their persistence with respect to impurity strength. Our results provide an alternative way to identify topologically insulating and superconducting phases in experiments while without resorting to the surface properties.