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

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".