▎ 摘　　要

We have performed path-integral Monte Carlo calculations to study He-4 adsorption on a single graphene sheet. The He-4-substrate interaction was assumed to be a pairwise sum of the helium-carbon potentials constructed by Carlos and Cole to fit helium scattering data from a graphite surface. We employed both an anisotropic 6-12 Lennard-Jones potential and a spherical 6-12 potential. For both potentials, the first He-4 layer has the C-1/3 commensurate structure at a surface density of 0.0636 angstrom(-2). Vacancy states created in the C-1/3 commensurate solid, however, behave differently depending on the He-4-substrate interaction: a cluster of localized vacancies are formed with the fully anisotropic 6-12 pair potentials while mobile vacancies are found to induce finite superfluid fractions with the substrate potential based on only the isotropic parts of the inter-atomic pair potentials. For the second helium layer we find that exchange among He-4 adatoms results in quantum melting of a C-7/12 commensurate structure, which is registered to a first-layer triangular solid. The possible stabilization of this commensurate structure with the addition of He-3 impurities is discussed.