Composition and stacking dependent topology in bilayers from the graphene family

We present a compositional and structural investigation of silicene, germanene, and stanene bilayers from first principles. Due to the staggering of the individual layers, several stacking patterns are possible, most of which are not available to the bilayer graphene. This structural variety, in conjunction with the presence of the spin-orbit coupling, unveils a diversity of the electronic properties, with the appearance of distinct band features, including orbital hybridization and band inversion. We show that for particular cases, the intrinsic spin Hall response exhibits signatures of nontrivial electronic band topology, making these structures promising candidates to probe Dirac-like physics.