Power-law decay of standing waves on the surface of topological insulators

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 a dominant role. Experimentally, we image the interference patterns on both Bi2Te3 and Bi2Se3 films by measuring the local density of states with a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi2Se3, only a single decay index of -3/2 exists, while in Bi2Te3 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 better explain the characteristic scattering wave vectors of the standing wave caused by nonmagnetic impurities on Bi2Te3.