Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures

Abstract In this work, we study the synergistic correlated states in two distinct types of interacting electronic systems coupled by interlayer Coulomb interactions. We propose that this scenario can be realized in a new type of Coulomb-coupled graphene-insulator heterostructures with gate tunable band alignment. We find that, by virtue of the interlayer Coulomb coupling between the interacting electrons in the two layers, intriguing correlated physics that is not seen in either individual layer emerges in a cooperative and synergistic manner. Specifically, as a result of the band alignment, charge carriers can be transferred between graphene and the substrate under the control of gate voltages, which can yield a long-wavelength electronic crystal at the surface of the substrate. This electronic crystal exerts a superlattice Coulomb potential on the Dirac electrons in graphene, which generates subbands with reduced non-interacting Fermi velocity. As a result, $e$-$e$ Coulomb interactions within graphene would play a more important role, giving rise to a gapped Dirac state at the charge neutrality point, accompanied by interaction-enhanced Fermi velocity. Moreover, the superlattice potential can give rise to topologically nontrivial subband structures which are tunable by superlattice's constant and anisotropy. Reciprocally, the electronic crystal formed in the substrate can be substantially stabilized in such coupled bilayer heterostructure by virtue of the cooperative interlayer Coulomb coupling. We further perform high-throughput first principles calculations to identify a number of promising insulating materials as candidate substrates for graphene to demonstrate these effects. Our findings provide new insights into the physics of correlated and topological electronic states in graphene-based heterostructures.