Chen Fang, Matthew J. Gilbert, Su-Yang Xu, B. Andrei Bernevig, M. Zahid Hasan
We theoretically study the quasiparticle interference (QPI) of the surface states in crystalline topological insulators which possess mirror symmetry and time-reversal symmetry, by analyzing the Fourier transformed local density of states (FT-LDOS), $\rho(\bq,\omega)$ around a single static impurity on the surface. We show that the symmetries in the QPI pattern are determined by the transformation properties of the impurity under mirror reflections and time-reversal. We study the singularities in $\rho(\bq,\omega)$ and show that while the presence of singularities in $\rho(\bq,\omega)$ depends on the geometric features of the iso-energy contour at $\omega$, the \emph{absence} of certain singularities denotes the scattering forbidden by underlying symmetries. We apply the general analysis to the QPI on the $<{001}>$-surface of Pb$_{1-x}$Sn$_x$Te and predict all vanishing singularities in $\rho(\bq,\omega)$. The model-independent analysis is supported by numerical calculations of $\rho(\bq,\omega)$ around a single point charge impurity using an effective four-band model. We demonstrate that QPI can also be used to probe the Lifshitz transition of the surface states observed in recent ARPES experiment.
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http://arxiv.org/abs/1212.3285
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