Many-impurity scattering on the surface of a topological insulator

TL;DR

This paper compares two theoretical methods, SCBA and CPA, to analyze how non-magnetic impurities affect the surface states of topological insulators, revealing that SCBA overestimates impurity effects.

Contribution

It provides a detailed comparison between SCBA and CPA methods for impurity scattering, highlighting the limitations of SCBA in topological insulator surface states.

Findings

SCBA overestimates impurity impact compared to CPA.

Differences between methods grow with increased disorder.

CPA offers a more accurate single-site approximation for disordered surface states.

Abstract

We theoretically address the impact of a random distribution of non-magnetic impurities on the surface states formed at the interface between a trivial and a topological insulator. The interaction of electrons with the impurities is accounted for by a separable pseudo-potential method that allows us to obtain closed expressions for the density of states. Spectral properties of surface states are assessed by means of the Green's function averaged over disorder realizations. For comparison purposes, the configurationally averaged Green's function is calculated by means of two different self-consistent methods, namely the self-consistent Born approximation (SCBA) and the coherent potential approximation (CPA). The latter is often regarded as the best single-site theory for the study of the spectral properties of disordered systems. However, although a large number of works employ the SCBA for the analysis of many-impurity scattering on the surface of a topological insulator, CPA studies of the same problem are scarce in the literature. In this work we find that the SCBA overestimates the impact of the random distribution of impurities on the spectral properties of surface states compared to the CPA predictions. The difference is more pronounced when increasing the magnitude of the disorder.