High Spin-Chern-Number Insulator Phase in α-Antimonene

We report on a new topological phase characterized by a high-number quantized spin Hall conductivity in α-Sb, which we have found in investigating the electronic structures of monolayer α-phase group V elements. This distinct topological phase is invisible in the symmetry-based topological quantum chemistry (TQC) and symmetry indicators (SIs). Since α-As and Sb share the same band representations at high-symmetry points, they are both trivial insulators in terms of TQC and SIs. However, we demonstrate that there is a topological phase transition between As and Sb that involves a band-gap closing at two <i>k</i>-points on the high-symmetry line X-Γ-X. In the absence of spin-orbit coupling (SOC), As is a trivial insulator, while Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of S_z-conserved SOC gaps out the DPs and induces a nontrivial Berry curvature and drives Sb into the new high-spin Chern number topological phase. The band structure of α-Bi differs from that of Sb by a band inversion at Γ, transforming Bi into a Z₂ topological insulator. Our study shows that quantized spin Hall conductivity can serve as a topological invariant beyond the Z₂ topological invariant for characterizing the topological phases.