Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

Here we report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI), Pb1$${-}$$xSnxSe, as a function of various material parameters including composition x, temperature T , and crystal structure. Our spectroscopic data demonstrate the electronic ground-state condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states’ response to circularly polarized light. Our results show that each material parameter can tune the system between the trivial and topological phase in a distinct way, unlike that seen in Bi2Se3 and related compounds, leading to a rich topological phase diagram. Our systematic studies of the TCI Pb1$${-}$$xSnxSe are a valuable materials guide to realize new topological phenomena.