Impurity Effects on Superconductivity on Surfaces of Topological Insulators

TL;DR

This paper investigates the stability of superconductivity on topological insulator surfaces against impurities, revealing robustness against time-reversal symmetric impurities and analyzing the nature of the superconducting state.

Contribution

It combines Abrikosov-Gor'kov theory and real-space Bogoliubov-de Gennes calculations to show the stability of surface superconductivity against impurities and clarifies its topological nature.

Findings

Superconductivity on TI surfaces is stable against small TRS impurity concentrations.

Superconductivity remains stable against strong TRS impurities.

The surface SC is not a topological superconductor.

Abstract

A two-dimensional superconductor (SC) on surfaces of topological insulators (TIs) is a mixture of s-wave and helical p-wave components when induced by s-wave interactions, since spin and momentum are correlated. On the basis of the Abrikosov-Gor'kov theory, we reveal that unconventional SCs on the surfaces of TIs are stable against time-reversal symmetric (TRS) impurities within a region of small impurity concentration. Moreover, we analyze the stability of the SC on the surfaces of TIs against impurities beyond the perturbation theory by solving the real-space Bogoliubov-de Gennes equation for an effective tight-binding model of a TI. We find that the SC is stable against strong TRS impurities. The behaviors of bound states around an impurity suggest that the SC on the surfaces of TIs is not a topological SC.