Electronic structures of graphene/boron nitride sheet superlattices

Single-sheet graphene/boron nitride superlattices (SLs) are studied by a first-principles density functional theory approach to form a basic understanding for engineering a graphene band gap. The formation energy and electronic properties of SLs with different orientations (armchair or zigzag boundary) and stripe widths (2.16-14.80 angstrom) are studied. The trends of the formation energy with respect to the stripe widths and orientations are explained by the differences in bond energies and simple coulombic forces between ions. Regarding the electronic properties, it is found that not all SLs have a nonzero band gap. The band gap size and band edge locations can be explained by the Brillouin zone folding, the symmetry of SLs, and the effects from the graphene/boron nitride edges. The factors that cause the band gap opening and those that lift it are analyzed and discussed. The detailed electronic states near the band edges of each SL group are analyzed by directly plotting the charge densities, as well as utilizing a simple tight-binding model to resolve their characteristics.