Elastic scattering of surface states on three-dimensional topological insulators

Topological insulators as new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states which are protected by time-reversal symmetry. We propose the interference patterns caused by elastic scattering of defects or impurities are dominated by surface states at the extremal points on the constant energy contour. Within such formalism, we summarize our recent theoretical investigations on elastic scattering of topological surface states by various imperfections, including the non-magnetic impurities, magnetic impurities, step-edges, and various other defects, in comparison with recent related experiments in typical topological materials such as BiSb alloys, Bi$_2$Te$_3$ and Bi$_2$Se$_3$ crystals.