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We study symmetry protected features in the quasiparticle interference (QPI)pattern of 2D systems with mirror symmetries and time-reversal symmetry, arounda single static point impurity. We show that, in the Fourier transformed localdensity of states (FT-LDOS), $\rho(\bq,\omega)$, while the position of highintensity peaks generically depends on the geometric features of the iso-energycontour at energy $\omega$, the \emph{absence} of certain peaks is guaranteedby the opposite mirror eigenvalues of the two Bloch states that are (i) on themirror symmetric lines in the Brillouin zone (BZ) and (ii) separated byscattering vector $\bq$. We apply the general result to the QPI on the $ <{001}>$-surface of topological crystalline insulator Pb$_{1-x}$Sn$_x$Te and predictall vanishing peaks in $\rho(\bq,\omega)$. The model-independent analysis issupported by numerical calculations using an effective four-band model derivedfrom symmetry analysis.

Theory of quasiparticle interference in mirror symmetric 2D systems and its application to surface states of topological crystalline insulators