Two types of surface states in topological crystalline insulators

Abstract

Topological crystalline insulators (TCI) are new topological phases of matter protected by crystal symmetry of solids. Recently, the first realization of TCI has been predicted and observed in IV-VI semiconductor SnTe and related alloys Pb_{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 various crystal surfaces of TCI in IV-VI semiconductors. We explicitly derive k.p Hamiltonian for topological surface states from electronic structure of the bulk, thereby providing a microscopic understanding of bulk-boundary correspondence in TCI. Depending on the surface orientation, we find two types of surface states with qualitatively different properties. In particular, we predict that (111) surface states consist of four Dirac cones centered at time-reversal-invariant momenta {\Gamma} and M, while (110) surface states consist of Dirac cones at non-time-reversal-invariant momenta, similar to (001). Moreover, both (001) and (110) surface states exhibit a Lifshitz transition as a function of Fermi energy, which is accompanied by a Van-Hove singularity in density of states arising from saddle points in the band structure.