Graphene-based heterostructures with moiré superlattice that preserve the Dirac cone: a first-principles study

In van der Waals heterostructures consisting of graphene and a substrate, lattice mismatch often leads to a moiré pattern with a huge supercell, preventing its treatment within first-principles calculations. Previous theoretical works considered mostly simple stacking models such as AB, AA with straining the lattice of graphene to match that of the substrate. Here, we propose a moiré superlattice build from graphene and porous graphene or graphyne like monolayers, having a lower interlayer binding energy, needing little strain in order to match the lattices. In contrast to the results from the simple stacking models, the present ab initio calculations for the moiré superlattices show different properties in lattice structure, energy, and band structures. For example, the Dirac cone at the K point is preserved and a linear energy dispersion near the Fermi level is obtained.