Theory of quasiparticle interference in mirror-symmetric two-dimensional systems and its application to surface states of topological crystalline insulators

We study symmetry-protected features in the quasiparticle interference (QPI) pattern of two-dimensional (2D) systems with mirror symmetries and time-reversal symmetry, around a single static point impurity. We show that, in the Fourier-transformed local density of states (FT-LDOS) rho(q,omega), while the position of high-intensity peaks generically depends on the geometric features of the iso-energy contour at energy omega, the absence of certain peaks is guaranteed by the opposite mirror eigenvalues of the two Bloch states that are (i) on the mirror-symmetric lines in the Brillouin zone (BZ) and (ii) separated by scattering vector q. We apply the general result to the QPI on the < 001 > surface of the topological crystalline insulator Pb1-xSnx Te and predict all vanishing peaks in rho(q,omega). The model-independent analysis is supported by numerical calculations using an effective four-band model derived from symmetry analysis.