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

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${}_3$.

4 pages, 3 figures

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• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Surface States Protected From Backscattering by Chiral Spin Texture

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