Electronic structure near an impurity and terrace on the surface of a 3-dimensional topological insulator

TL;DR

This paper investigates the electronic structure near impurities and terraces on 3D topological insulator surfaces, revealing weak in-gap oscillations and decay behaviors consistent with Dirac fermion models, supported by lattice and analytical approaches.

Contribution

It provides a detailed theoretical analysis of impurity effects on surface states of 3D topological insulators using lattice and Dirac models, aligning with recent STM experiments.

Findings

LDOS oscillates significantly above the bulk gap

In-gap surface Dirac fermions show weak oscillations

LDOS decays faster than in normal metals, at least by 1/r

Abstract

Motivated by recent scanning tunneling microscopy experiments on surfaces of Bi$_{1-x}$Sb$_{x'}$\cite{yazdanistm,gomesstm} and Bi$_2$Te$_3$,\cite{kaptunikstm,xuestm} we theoretically study the electronic structure of a 3-dimensional (3D) topological insulator in the presence of a local impurity or a domain wall on its surface using a 3D lattice model. While the local density of states (LDOS) oscillates significantly in space at energies above the bulk gap, the oscillation due to the in-gap surface Dirac fermions are very weak. The extracted modulation wave number as a function of energy satisfies the Dirac dispersion for in-gap energies and follows the border of the bulk continuum above the bulk gap. We have also examined analytically the effects of the defects by using a pure Dirac fermion model for the surface states and found that the LDOS decays asymptotically faster at least by a factor of 1/r than that in normal metals, consistent with the results obtained from our lattice model.