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We study orbital and spin-orbit proximity effects in graphene adsorbed to theCu(111) surface by means of density functional theory (DFT). The proximityeffects are caused mainly by the hybridization of graphene $\pi$ and copper dorbitals. Our electronic structure calculations agree well with theexperimentally observed features. We carry out a graphene-Cu(111) distancedependent study to obtain proximity orbital and spin-orbit coupling parameters,by fitting the DFT results to a robust low energy model Hamiltonian. We find astrong distance dependence of the Rashba and intrinsic proximity inducedspin-orbit coupling parameters, which are in the meV and hundreds of $\mu$eVrange, respectively, for experimentally relevant distances. The Dirac spectrumof graphene also exhibits a proximity orbital gap, of about 20 meV.Furthermore, we find a band inversion within the graphene states accompanied bya reordering of spin and pseudospin states, when graphene is pressed towardscopper.

Theory of electronic and spin-orbit proximity effects in graphene on Cu(111)