Electronic band structures of group-IV two-dimensional materials: Spin-orbit coupling and group theoretical analysis

Abstract

Band structures of group-IV two-dimensional materials are studied by carrying out first-principles calculations including spin-orbit coupling (SOC). We propose a method that identifies irreducible representations (IR) of bands by using computers. We identify IR for the planar and buckled structures and discuss the difference between bands obtained by non-SOC and SOC calculations. In particular, we clarify IR at the Dirac point where the bands split because of the SOC. We evaluate the Z2 invariants based on identified IR, which suggests that all the systems are topological insulators.