Scattering from Surface Step Edges in Strong Topological Insulators

TL;DR

This paper analyzes how surface step edges in strong topological insulators affect electron scattering and LDOS decay, revealing faster decay rates than in conventional 2D electron gases due to topological protection.

Contribution

It provides a theoretical analysis of scattering processes at step edges in STIs, showing decay rates of LDOS modulations and the effects of generic step edges, which were not previously detailed.

Findings

LDOS modulations decay no slower than 1/x near perfect step edges

Decay of LDOS oscillations at generic step edges follows a x^{-3/2} law

Surface states exhibit suppressed backscattering due to topological protection

Abstract

We study the characteristics of scattering processes at step edges on the surfaces of Strong Topological Insulators (STI), arising from restrictions imposed on the $S$-matrix \emph{solely} by time reversal symmetry and translational invariance along the step edge. We show that the `perfectly reflecting' step edge that may be defined with these restrictions allow modulations in the Local Density of States (LDOS) near the step edge to decay no slower than $1/x$, where $x$ is the distance from the step edge. This is faster than in 2D Electron Gases (2DEG) --- where the LDOS decays as $1/\sqrt{x}$ --- and shares the same cause as the suppression of backscattering in STI surface states. We also calculate the scattering at a delta function scattering potential and argue that \emph{generic} step edges will produce a $x^{-3/2}$ decay of LDOS oscillations. Experimental implications are also discussed.