Spin-orbit splitting in graphene on metallic substrates

Substrate-induced spin-orbit splitting in graphene on Ni, Au and Ag(111) is examined on the basis of density-functional theory. The Rashba splitting of pi bands along the Gamma M direction of the graphene surface Brillouin zone in graphene on Ni(111) is found to be very small (a few millielectronvolts), consistent with the experimental report of Rader et al. Instead, very strong Rashba splitting (near 100 meV) can be obtained for graphene with a certain stretch distortion on a Au substrate. It can be ascribed to the effective match in energy between the C 2p and Au 5d bands, obtained from the analysis of densities of states. The net charge transfer between the graphene and the substrates just affects the spin-orbit effect indirectly. The small spin-orbit splitting induced by the Ag substrates indicates that heavy metals do not always produce large SO splitting. Our findings provide important insights that are useful for understanding the metal-induced Rashba effect in graphene.