Non-trivial spin-texture of the coaxial Dirac cones on the surface of topological crystalline insulator SnTe

TL;DR

This paper uses first principles calculations to analyze the unique spin-texture of surface states in SnTe, revealing a nontrivial mirror Chern number and proposing a simple model for the coaxial Dirac cones.

Contribution

It introduces a simple model of interacting coaxial Dirac cones to describe surface state dispersion and spin-texture in SnTe, highlighting the nontrivial mirror Chern number.

Findings

Surface states exhibit four Dirac cones along mirror intersections.

In-plane spin texture shows helicity with distortion due to cone interaction.

Mirror Chern number is -2, different from Z2 topological insulators.

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. While the out-of-the-plane spin polarization is 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 $Z_{2}$ 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 way to determine the nontrivial mirror Chern number.