Topological and correlated states in spin-orbit coupled graphene-insulator heterostructures

In this work, we theoretically study the topological and correlated states in band-aligned graphene-insulator heterostructures systems including spin-orbit coupling (SOC) effects. Typical examples include graphene-transition metal dichalcogenide (TMD) heterostructures. On the one hand, the band edges are energetically close to the Dirac point in graphene, which may induce charge transfer between the two layers. The transferred charges in the TMD layer may form long-wavelength electronic crystal at sufficiently low carrier densities, which exerts a superlattice potential to the graphene layer through interlayer Coulomb coupling. As a result, the Fermi velocity of Dirac fermions in graphene would be reduced due to scatterings by the superlattice Coulomb potential, which thus boosts electron-electron interaction effects in graphene layer. On the other hand, TMD can induce proximity SOC in graphene, which would generate topological subbands with nonzero valley Chern numbers if considering effects of both SOC and long-wavelength Coulomb potential. We further study the interacting ground states based on unrestricted Hartree-Fock calculations including the Coulomb screening effects from the remote bands, and find a variety of symmetry-breaking ground states. Within the same theoretical framework, we also investigate the electronic structures, topological properties, and interaction effects in coupled bilayer graphene-TMD heterostructures.