Stationary phase approximation approach to the quasiparticle interference on the surface of a strong topological insulator

TL;DR

This paper develops an analytic method using stationary phase approximation to analyze quasiparticle interference patterns on the surface of strong topological insulators, revealing unique signatures of magnetic impurities.

Contribution

It introduces a general analytic formulation of the local density of states for topological insulator surfaces, highlighting the effects of magnetic impurities.

Findings

Power laws of Friedel oscillations depend on the shape of the energy contour.

Magnetic impurities produce distinct interference signatures compared to nonmagnetic ones.

Predicted unique signatures of magnetic impurities in surface states.

Abstract

Topological insulators have surface states with unique spin-orbit coupling. With impurities on the surface, the quasiparticle interference pattern is an effective way to reveal the topological nature of the surface states, which can be probed by the scanning tunneling microscopy. In this paper, we present a general analytic formulation of the local density of states using the stationary phase approximation. The power laws of Friedel oscillations are discussed for a constant energy contour with a generic shape. In particular, we predict unique signature of magnetic impurities in comparison with nonmagnetic impurities for a surface state trapped in a "magnetic wall".