Topological insulators are a class of quantum materials in which time-reversal symmetry, relativistic effects and an inverted band structure result in the occurrence of electronic metallic states on the surfaces of insulating bulk crystals. These helical states exhibit a Dirac-like energy dispersion across the bulk bandgap, and they are topologically protected. Recent theoretical results have suggested the existence of topological crystalline insulators (TCIs), a class of topological insulators in which crystalline symmetry replaces the role of time-reversal symmetry in ensuring topological protection. In this study we show that the narrow-gap semiconductor Pb(1-x)Sn(x)Se is a TCI for x  =  0.23. Temperature-dependent angle-resolved photoelectron spectroscopy demonstrates that the material undergoes a temperature-driven topological phase transition from a trivial insulator to a TCI. These experimental findings add a new class to the family of topological insulators, and we anticipate that they will lead to a considerable body of further research as well as detailed studies of topological phase transitions.

The recent discovery of a topological phase transition in IV-VI narrow-gap semiconductors has revitalized the decades-old interest in the bulk band inversion occurring in these materials. Here we systematically study the (001) surface states of Pb 1−x Sn x Se mixed crystals by means of angle-resolved photoelectron spectroscopy in the parameter space 0 x 0.37 and 300 K T 9 K. Using the surface-state observations, we monitor directly the topological phase transition in this solid solution and gain valuable information on the evolution of the underlying fundamental band gap of the system. In contrast to common model expectations, the band-gap evolution appears to be nonlinear as a function of the studied parameters, resulting in the measuring of a discontinuous band-inversion process. This finding signifies that the anticipated gapless bulk state is in fact not a stable configuration and that the topological phase transition therefore exhibits features akin to a first-order transition.

We study the nature of (001) surface states in Pb0.73Sn0.27Se in the newly discovered topologicalcrystalline-insulator (TCI) phase as well as the corresponding topologically trivial state above the band-gap-inversion temperature. Our calculations predict not only metallic surface states with a nontrivial chiral spin structure for the TCI case, but also nonmetallic (gapped) surface states with nonzero spin polarization when the system is a normal insulator. For both phases, angle-and spinresolved photoelectron spectroscopy measurements provide conclusive evidence for the formation of these (001) surface states in Pb0.73Sn0.27Se, as well as for their chiral spin structure.

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