Material realization of topological crystalline insulators: Role of strain and spin-orbit coupling

Taking into consideration of the mirror symmetry gives rise to a new phase of quantum matter, called topological crystalline insulator (TCI). Here, using SnTe and PbTe as the examples, we give detailed insight into the effects of spin-orbit coupling (SOC) and strain on the formation of the TCI. A strain-induced band inversion, without any SOC, is shown. The SOC, however, is indispensable for achieving the TCI phase in real materials and can promote the process of the band inversion. Detailed surface state analysis reveals that topological surface state is thickness dependent and the Dirac point can locate precise on or slightly away from the mirror-symmetry point. Our results pave a way of the material realization of new topological crystalline insulator.