Graphene monolayers on GaN(0001)

•DFT calculations predict perfect graphene monolayer can be obtained over GaN(0001).•Graphene maintains its hexagonal honeycomb structure with the CC bonds intact.•Dirac cones indicate preservation of the graphene π-network.•Stable structures were obtained for a wide range of Ga chemical potentials.•GaN(0001) is an excellent substrate for supporting graphene layers. The epitaxial growth of graphene on GaN(0001) surfaces is studied by first principles total energy calculations. The idea is to understand how defect-free graphene can be grown on substrates. It is found that the most stable structures were a 4×4(0001) GaN/3√3×3√3 graphene and a 2√3×2√3(0001) GaN Northrup bilayer/√21×√21 graphene, grown under N- and Ga-rich conditions, respectively. In these structures, graphene maintains its hexagonal honeycomb structure with the CC bonds intact. Preservation of the π-network for the graphene layers was demonstrated by the presence of Dirac cones. The band structures for both the N- and Ga-rich configurations show metallic characteristics and the Ga-rich configuration is slightly magnetic. This demonstrates that GaN(0001) is an excellent substrate for supporting graphene layers.