Power-Law Decay of Standing Waves on the Surface of Topological Insulators

TL;DR

This paper develops a theory for the decay of standing waves caused by surface state scattering in topological insulators, confirmed by STM experiments on Bi2Te3 and Bi2Se3 showing power-law decay behaviors.

Contribution

It introduces a general theoretical framework for standing wave decay in topological insulators and validates it with experimental STM data, revealing energy-dependent decay indices.

Findings

Decay index of -3/2 in Bi2Se3 matches theory

Decay index varies from -3/2 to -1 in Bi2Te3 with energy

Suppression of backscattering does not always lead to faster decay

Abstract

We propose a general theory on the standing waves (quasiparticle interference pattern) caused by the scattering of surface states off step edges in topological insulators, in which the extremal points on the constant energy contour of surface band play the dominant role. Experimentally we image the interference patterns on both Bi$_2$Te$_3$ and Bi$_2$Se$_3$ films by measuring the local density of states using a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi$_2$Se$_3$, only a single decay index of -3/2 exists; while in Bi$_2$Te$_3$ with strongly warped surface band, it varies from -3/2 to -1/2 and finally to -1 as the energy increases. The -1/2 decay indicates that the suppression of backscattering due to time-reversal symmetry does not necessarily lead to a spatial decay rate faster than that in the conventional two-dimensional electron system. Our formalism can also explain the characteristic scattering wave vectors of the standing wave caused by non-magnetic impurities on Bi$_2$Te$_3$.