Z2 invariant protected bound states in topological insulators

TL;DR

This paper demonstrates that vacancies in topological insulators can induce Z2-protected bound states within the band gap, which are topologically protected and may influence the material's transport properties.

Contribution

It provides an exact solution showing how vacancies induce topologically protected bound states in topological insulators, highlighting their robustness and potential impact on electronic transport.

Findings

Vacancies induce in-gap bound states in topological insulators.

Bound states are protected by Z2 topology and coexist with surface states.

Imperfections can influence transport properties via these bound states.

Abstract

We present an exact solution of a modifed Dirac equation for topological insulator in the presence of a hole or vacancy to demonstrate that vacancies may induce bound states in the band gap of topological insulators. They arise due to the Z_2 classification of time-reversal invariant insulators, thus are also topologically-protected like the edge states in the quantum spin Hall effect and the surface states in three-dimensional topological insulators. Coexistence of the in-gap bound states and the edge or surface states in topological insulators suggests that imperfections may affect transport properties of topological insulators via additional bound states near the system boundary.