Proximity-induced topological phases in bilayer graphene

We study the band structure of phases induced by depositing bilayer graphene on a transition metal dichalcogenide monolayer. Tight-binding and low-energy effective Hamiltonian calculations show that it is possible to induce topologically nontrivial phases that should exhibit spin Hall effect in these systems. We classify bulk insulating phases through calculation of the Z${}_2$ invariant, which unequivocally identifies the topology of the structure. The study of these and similar hybrid systems under applied gate voltage opens the possibility for tunable topological structures in real experimental systems.