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) $\rho (\mathbf{q},\omega )$, 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 $\mathbf{q}$. We apply the general result to the QPI on the $\langle 001\rangle$ surface of the topological crystalline insulator Pb${}_{1-x}$Sn${}_x$Te and predict all vanishing peaks in $\rho (\mathbf{q},\omega )$. The model-independent analysis is supported by numerical calculations using an effective four-band model derived from symmetry analysis.

• Received 25 December 2012

DOI:https://doi.org/10.1103/PhysRevB.88.125141