Synergistic interplay between Dirac fermions and long-wavelength orders in graphene-insulator heterostructures

In this work, we study the physical properties of a new type of heterostructure system consisted of graphene placed on top of a band-aligned insulating substrate. By virtue of the band alignment, charge carriers can be transferred between graphene and the surface of the substrate under the control of gate voltages, which may yield a long-wavelength charge order at the surface of the substrate through Wigner-crystallization mechanism. The long-wavelength charge order in turn exerts a superlattice Coulomb potential to the Dirac electrons in graphene, which reduces the non-interacting Fermi velocity such that e-e Coulomb interactions would play an important role. Consequently, the Dirac points are spontaneously gapped out by e-e interactions. Meanwhile, the Fermi velocities around the Dirac points are drastically enhanced due to interaction effects, which can give rise to large Landau-level spacing with robust quantization plateaux of Hall resistivity under weak magnetic fields and at high temperatures. We have further performed high-throughput first principles calculations, and found a number of promising insulating materials as candidate substrates for graphene to demonstrate such effects.