Density-functional studies of spin-orbit splitting in graphene on metals

Spin-orbit splitting in graphene on Ni, Au, or Ag (111) substrates was examined on the basis of density-functional theory. Graphene grown on the three metals was found to have Rashba splitting of a few or several tens of meV. The strong splitting obtained on Au or Ag substrates was mainly ascribed to effective hybridization of graphene $p_{z}$ state with Au or Ag $d_{z^{2}}$ states, rather than charge transfer as previously proposed. Our work provides theoretical understandings of the metal-induced Rashba effect in graphene.