Abstract

Sublattice symmetry breaking has been identified as the necessary condition for bandgap opening in monolayer graphene-on-substrate heterostructures. In many of them, however, in spite of sublattice symmetry breaking, the Dirac cone of graphene remains preserved. Here, we report using first-principles density functional theory (DFT) and a simple tight-binding (TB) model that the presence of more than 50% symmetrically inequivalent carbon atoms is required to split the Dirac cone. Additionally, we find that the Dirac cone must also lie within the bandgap of the other 2D layer to get a semiconducting (nonmetallic) heterostructure. The robustness of these two criteria has been validated in a series of heterostructures of graphene. The simplicity and robustness of the proposed model provide a useful design principle for materials scientists and engineers, thus potentially expanding the applicability of graphene bilayer heterostructures to a multitude of semiconductor devices.