Time-Reversal Quantum Spin Hall Phase is distinct from the Z2 Topological Insulator

Abstract For a time-reversal symmetric system, the quantum spin Hall phase is assumed to be the same as the Z2 topological insulator phase in the existing literature. The spin Chern number Cs is supposed to yield the same topological classification as the Z2 invariant. Here, by investigating the topological electronic structures of monolayer α-phase group V elements, we uncover the presence of a topological phase in α-Sb, which can be characterized by a spin Chern number Cs=2, even though it is Z2 trivial. Although both being classified as trivial insulators by the existing topological classification schemes, we demonstrate the existence of a phase transition between α-As and Sb, which is induced by band inversions at two generic k points. In the absence of spin-orbit coupling (SOC), α-As is a trivial insulator, while α-Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of the SOC gaps out the Dirac points and induces a nontrivial Berry curvature, endowing α-Sb with a high spin Chern number of Cs=2. We further show that monolayer α-Sb exhibits either a gapless band structure or a gapless spin spectrum on its edges as expected from topological considerations.