▎ 摘　　要

The synthesis of single-layer graphene sheets on metal surfaces can be carried out routinely nowadays. The energetic alignment of the graphene band structure, including the position of the Dirac point relative to the Fermi level of the metal, and subsequently, the doping level of the graphene sheet, depends crucially on the graphene-metal distance and the specific metal considered. These dependencies are studied with density-functional theory considering as typical metal surfaces Au(111), Ni(111), and Au/Ni(111). In the latter case, a single layer of gold is intercalated between the Ni(111) surface and the graphene sheet. We show that the energetic positions of eigenstates of helium adsorbed on a Au(111) surface exhibit a behavior with the adsorption distance qualitatively comparable to that of bands of physisorbed graphene. In both cases, the distance dependence of the energy of adsorbate bands can be explained by the effect of the surface dipole layer on the adsorbate bands and by electrostatic interactions caused by small charge rearrangements due to Pauli repulsion between metal surface and graphene. These charge rearrangements are neither caused by a charge transfer nor by chemical interactions due to conventional orbital interaction but have the effect to reduce the overlap of the surface charge density of the metal with the charge density of the adsorbate. The latter effect is known as pillow effect from molecules adsorbed on metal surfaces. Charge transfer between graphene and the metal substrate does occur but has an opposite effect to the surface dipole layer and Pauli repulsion, i.e., reduces the effect of the latter. For very large adsorption distances, this charge transfer vanishes in such a way that the Dirac point of graphene aligns with the metal Fermi energy. It is shown that the amount and character of graphene doping can be controlled by tuning the graphene-metal distance. For a proper description of the involved electrostatic potentials, a finite-slab correction had to be applied to them in order to take into account the finite size of the metal slabs used to model the substrate.