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

In this work, we theoretically study the electronic structure, topological properties, and interaction effects of the low-energy Dirac electrons in band-aligned heterostructures consisted of graphene and some correlated insulating substrates. By virtue of the band alignment, charge carriers can be transferred from graphene to the insulating substrate under the control of gate voltages. This may yield a long-wavelength charge order at the surface of the substrate through the 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 interactions leading to a sublattice polarized insulator state. Meanwhile, the Fermi velocities around the Dirac points are drastically enhanced to more than twice of the bare value by interaction effects, which can give rise to large Landau-level spacing with robust quantization plateaus of Hall resistivity under weak magnetic fields and at high temperatures. We have further performed high-throughput first principles calculations, and suggested a number of promising insulating materials as candidate substrates for graphene, which could realize the gapped Dirac state concomitant with low-field, high-temperature quantum Hall effects.Comment: Main text: 7 pages with 3 figures and 2 tables; Supplement info: 16 pages with 8 figures and 4 table