Abstract
Proximity effects resulting from depositing a graphene layer on a transition-metal dichalcogenide substrate layer change the dynamics of the electronic states in graphene, inducing spin-orbit coupling and staggered potential effects. An effective Hamiltonian that describes different symmetry-breaking terms in graphene, while preserving time-reversal invariance, shows that an inverted mass band-gap regime is possible. The competition of different perturbation terms causes a transition from an inverted mass phase to a staggered gap in the bilayer heterostructure as seen in its phase diagram. A tight-binding calculation of the bilayer validates the effective model parameters. A relative gate voltage between the layers may produce such a phase transition in experimentally accessible systems. The phases are characterized in terms of Berry curvature and valley Chern numbers, demonstrating that the system may exhibit quantum spin Hall and valley Hall effects.