  The Coulomb interaction is widely known to enhance the effective mass of
interacting particles and therefore tends to favor a localized state at
commensurate filling. Here, we will show that, in contrast to this consensus,
in a van der Waals heterostructure consisting of graphene and hexagon boron
nitride (h-BN), the onsite Coulomb repulsion will at first destroy the
localized state. This is due to the fact that the onsite Coulomb repulsion
tends to suppress the asymmetry between neighboring carbons induced by h-BN
substrate. We corroborate this surprising phenomenon by solving a tight-binding
model with onsite Coulomb repulsion treated within coherent potential
approximation, where hopping parameters are derived from density functional
theory calculations based on the graphene/h-BN heterostructure. Our results
indicate that both gapless and gapped states observed experimentally in
graphene/h-BN heterostructures can be understood after a realistic value of the
onsite Coulomb repulsion as well as different interlayer distances are taken
into account. Finally, we propose ways to enhance the gapped state which is
essential for potential application of graphene to next-generation electronics.
Furthermore, we argue that band gap suppressed by many-body effect should
happen in other van der Waals heterostructures.
