Quantum spin Hall insulating phase in Nb–Ta double-layer honeycomb (DLHC) lattice

The recent experimental synthesis of AlSb in a double-layer honeycomb (DLHC) structure has sparked interest in studying a new type of two-dimensional (2D) material. This successful synthesis confirms the previous theoretical prediction that traditional semiconductors are stable in the DLHC structure within the ultrathin limit. In this study, we investigated six Nb–Ta-based compounds and considered their 2D wurtzite, 2D zinc blende, AA configuration, and DLHC structural configurations using first-principles calculations. Among these configurations, the DLHC structure is the most energetically favorable for all the investigated compounds. The phonon dispersions show that NbP, NbAs, TaP, and TaAs compounds have no significant negative frequencies, confirming their dynamic stability. Using the HSE06 hybrid functional approach, NbP, NbAs, TaP, and TaAs are found to host nontrivial phases (Z2 = 1) upon inclusion of spin–orbit coupling (SOC), with positive system bandgap ranging from 110 to 250 meV. For the representative compound NbAs, the nontrivial topology is rigorously established by an independent irreducible representation analysis using the Fu–Kane parity criterion, which reveals an SOC-driven band inversion at the Γ point and yields Z2 = 1 in full agreement with the Wannier charge center method. The presence of gapless edge states with explicit connectivity between time-reversal invariant momentum points, finite spin Berry curvature, and spin Hall conductivity further verifies the nontrivial topological nature of these compounds. Our results indicate that the Nb–Ta-based DLHC materials have potential applications in both topological and electronic devices.