Scattering from surface step edges in strong topological insulators

Abstract

We study the characteristics of scattering processes at step edges on the surfaces of strong topological insulators (STIs), arising from restrictions imposed on the $S$ matrix 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 two-dimensional 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 generic step edges will produce a ${x}^{\ensuremath{-}3/2}$ decay of LDOS oscillations. Experimental implications are also discussed.