Nontrivial spin texture of the coaxial Dirac cones on the surface of topological crystalline insulator SnTe

Abstract

We present first-principles calculations of the nontrivial surface states and their spin textures in the topological crystalline insulator SnTe. The surface state dispersion on the [001] surface exhibits four Dirac cones centered along the intersection of the mirror plane and the surface plane. We propose a simple model of two interacting coaxial Dirac cones to describe both the surface state dispersion and the associated spin texture. The out-of-plane spin polarization is found to be zero due to the crystalline and time-reversal symmetries. The in-plane spin texture shows helicity with some distortion due to the interaction of the two coaxial Dirac cones, indicating a nontrivial mirror Chern number of $\ensuremath{-}2$, distinct from the value of $\ensuremath{-}1$ in a ${Z}_{2}$ topological insulator such as Bi/Sb alloys or Bi${}_{2}$Se${}_{3}$. The surface state dispersion and its spin texture would provide an experimentally accessible signature for determining the nontrivial mirror Chern number.