Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly

Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moire potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replicas of the original Dirac cone and Hofstadter butterflies. Our large-scale tight-binding simulation reveals an unexpected coexistence of a relativistic and nonrelativistic Landau level structure. The presence of the zeroth Landau level and its associated butterfly is shown to be the unambiguous signature for the occurrence of the Dirac cone replica.