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

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) bands using computers. identify IR for the planar and buckled discuss difference between obtained non-SOC SOC calculations. In particular, we clarify at Dirac point where split because SOC. evaluate Z2 invariants based on identified IR, which suggests all systems topological insulators.