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

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 -2, distinct from the value of -1 in a Z₂ topological insulator such as Bi/Sb alloys or Bi₂Se₃. The surface state dispersion and its spin texture would provide an experimentally accessible signature for determining the nontrivial mirror Chern number.