Two types of surface states in topological crystalline insulators

Topological crystalline insulators (TCIs) are new states of matter whose topological distinction relies on the crystal symmetry of periodic solids. The first material realization of TCIs has recently been predicted and observed in IV-VI semiconductor SnTe and related alloys. By combining k . p theory and band structure calculation, we present a unified approach to study topological surface states on various crystal surfaces of these TCI materials based on the electronic structure of the bulk. Depending on the surface orientation, we find two types of surface states with qualitatively different properties. In particular, the (111) surface states consist of four Dirac cones centered at (Gamma) over bar and (M) over bar, while Dirac cones on (001) and (110) surfaces are located at non-time-reversal-invariant momenta. The latter types of surface states exhibit a Lifshitz transition as a function of Fermi energy, which is accompanied by a Van Hove singularity in the density of states arising from saddle points in the band structure.