Stacking-induced type-II quantum spin Hall insulators with high spin Chern number in unconventional magnetism

Generally, stacking two monolayer type-I quantum spin Hall insulators gives rise to a trivial insulator. However, whether or not stacking two type-II quantum spin Hall insulators results in a trivial insulator has not yet been explored. In this letter, based on the calculations of lattice model, we demonstrate that stacking two type-II quantum spin Hall insulators does not yield a trivial insulator, but instead forms a quantum spin Hall insulator with high spin Chern number. In this phase, there are two pairs of topological edge states with opposite chirality and polarization coexisting in the boundary. Our calculations further reveal that the quantized spin Hall conductance of the bilayer is twice that of the monolayer. When U(1) symmetry is present, the high spin Chern number phase remains stable; when U(1) symmetry is broken, it persists over a broad parameter range. Furthermore, based on the first-principles electronic structure calculations, we propose that bilayer Nb$_2$SeTeO is a type-II quantum spin Hall insulator with high spin Chern number. Finally, extending this strategy to multilayer stacks naturally leads to quantum spin Hall insulator with larger spin Chern number. Our work not only deepens the distinction between type-I and type-II quantum spin Hall insulators, but also offers a route toward realizing highly quantized spin Hall conductance.