Structural stability and topological surface states of the SnTe (111) surface

Abstract

We perform first-principles calculations to study the stability and electronic structure of the (111) surface of SnTe, a representative topological crystalline insulator (TCI). We find three stable surface phases, which support two qualitatively different types of topological surface states: type I with four Dirac points at $\overline{\ensuremath{\Gamma}}$ and three $\overline{\mathrm{M}}$ points and type II with two Dirac points nearby but not at $\overline{\ensuremath{\Gamma}}$. Their appearance can be controlled by varying growth conditions. Under an Sn-poor condition, the Te-terminated surface without reconstruction is stable, resulting in the type-I surface states. While under an Sn-rich condition, the (2$\ifmmode\times\else\texttimes\fi{}$1)-reconstructed Sn-terminated surface becomes more stable. The reconstruction folds the surface Brillouin zone and effectively induces interactions between the Dirac points at the $\overline{\ensuremath{\Gamma}}$ and $\overline{\mathrm{M}}$ points. Surface states thus change from type I to type II accompanied by a Lifshitz transition. Under intermediate growth conditions, the ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$)-reconstructed Sn-terminated surface gets stabilized, which recovers the type-I surface states. Our work suggests a promising alternative way to control the topological surface states of TCIs besides selecting different surface orientations.