By performing first-principles calculations, we studied hexagonal-boron-nitride (hBN)-supported graphene, in which moiré structures are formed due to lattice mismatch or interlayer rotation. A series of graphene/hBN systems has been studied to reveal the evolution of properties with respect to different twisting angles (21.78°, 13.1°, 9.43°, 7.34°, 5.1°, and 3.48°). Although AA- and AB-stacked graphene/hBN are gapped at the Dirac point by about 50 meV, the energy gap of the moiré graphene/hBN, which is much more asymmetric, is only about several meV. Although the Dirac cone of graphene residing in the wide gap of hBN is not much affected, the calculated Fermi velocity is found to decrease with the increase in the moiré super lattice constant due to charge transfer. The periodic potential imposed by hBN modulated charge distributions in graphene, leading to the shift of graphene bands. In agreement with experiments, there are dips in the calculated density of states, which get closer and closer to the Fermi energy as the moiré lattice grows larger.
Keywords: Fermi velocity; boron nitride; charge transfer; density of states; graphene.