Ab initio studies of electronic and optical properties of graphene and graphene–BN interface

Atomic geometry, electronic states, and optical transitions for isolated monolayer, bilayer and trilayer graphene, and graphene grown on ultra-thin layers of hexagonal boron nitride (h-BN) have been studied theoretically by using the density functional theory and the planewave pseudopotential method. For monolayer graphene, the dispersion curve near the K point is linear with Dirac electronʹs speed of 0.9× 106 m/s. For bilayer graphene the lowest unoccupied energy band is characterised by a mixture of linear and quadratic behaviours, with a relative effective mass of 0.023. For trilayer graphene there are overlapping electron and hole bands near the Fermi level, with a relative electron effective mass of 0.0541. For a monolayer graphene on monolayer h-BN substrate, a small band gap of 57 meV is established. At Brillouin zone centre, the theoretically obtained direct transition of 6.3 eV for graphene is reduced to 5.7 eV for graphene/h-BN. Results are also presented for the interface between graphene and a multilayer h-BN.