Stationary phase approach to the quasiparticle interference on the surface of three dimensional strong topological insulators

TL;DR

This paper develops an analytic method using stationary phase to analyze quasiparticle interference on the surfaces of three-dimensional topological insulators, revealing how scattering and impurities affect local electronic states.

Contribution

It introduces a general analytic formulation for local density of states and Friedel oscillations based on symmetry and geometry, highlighting differences in magnetic impurity responses.

Findings

Distinct responses of surface states to magnetic versus nonmagnetic impurities.

Predicted power laws for Friedel oscillations near scattering points.

Proposed experimental setup to measure magnetic impurity effects.

Abstract

Constant energy contour (CEC) of the surface bands in topological insulators varies not only with materials but also at different energies. The quasiparticle interference caused by scattering-off from defects on the surface of topological insulators is an effective way to reveal the topologies of the CEC and can be probed by scanning tunneling microscopy (STM). Using stationary phase approach, a general analytic formulation of the local density of states as well as the power laws of the Friedel oscillation are present, based only on the time-reversal symmetry and the local geometry around the scattering end points on the CEC. Distinct response of surface states to magnetic impurities from that of nonmagnetic impurities is predicted in particular, which is proposed to be measured in a closed "magnetic wall" setup on the surface of topological insulators.