Electronic structure and scanning tunneling microscopy images of heterostructures consisting of graphene and carbon-doped hexagonal boron nitride layers

We perform first-principles total-energy calculations within the framework of the density-functional theory to investigate electronic properties of graphene/C-doped hexagonal boron nitride (h-BN) heterostructures. We consider both the monolayer h-BN case and the trilayer h-BN case. From the electronic-structure analysis, it is found that substitutional doping of the C atom at the B site and that at the N site in underlying h-BN lead to asymmetric charge carrier concentrations in the graphene layer, indicating the importance of the impurity atom in the h-BN substrate and its polarity in the electronic transport properties of graphene/h-BN heterostructures. We also find that simulated scanning tunneling microscopy (STM) images of the graphene surface on the C-doped h-BN layer at the B site and that at the N site are considerably different from each other in both monolayer and trilayer h-BN cases. While the B site doping of the C atom in h-BN substrate layers essentially does not change the STM image of the graphene surface on the pristine h-BN, the C atom doped at the N site considerably modifies the STM image of graphene even in the case of the doping in the third layer of the trilayer h-BN. Therefore, when the graphene in used as a cover layer to the h-BN layered materials and thin films, the STM should be a useful tool to detect the acceptor C atoms in the h-BN not only at the topmost surface layer but also at second and third layers. We clarify the origin of these characteristic features of the STM images in terms of spatial distributions of the local density of states induced by the dopant C atom.