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Topological crystalline insulators (TCI) are new topological phases of matterprotected by crystal symmetry of solids. Recently, the first realization of TCIhas been predicted and observed in IV-VI semiconductor SnTe and related alloysPb_{1-x}Sn_{x}(Te, Se). By combining k.p theory and band structure calculation,we present a unified approach to study topological surface states on variouscrystal surfaces of TCI in IV-VI semiconductors. We explicitly derive k.pHamiltonian for topological surface states from electronic structure of thebulk, thereby providing a microscopic understanding of bulk-boundarycorrespondence in TCI. Depending on the surface orientation, we find two typesof surface states with qualitatively different properties. In particular, wepredict that (111) surface states consist of four Dirac cones centered attime-reversal-invariant momenta {\Gamma} and M, while (110) surface statesconsist of Dirac cones at non-time-reversal-invariant momenta, similar to(001). Moreover, both (001) and (110) surface states exhibit a Lifshitztransition as a function of Fermi energy, which is accompanied by a Van-Hovesingularity in density of states arising from saddle points in the bandstructure.

Surface States of Topological Crystalline Insulators in IV-VI Semiconductors