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We present a combined DFT and model Hamiltonian analysis of spin-orbitcoupling in graphene induced by copper adatoms in the bridge and top positions,representing isolated atoms in the dilute limit. The orbital physics in bothsystems is found to be surprisingly similar, given the fundamental differencein the local symmetry. In both systems the Cu p and d contributions at theFermi level are very similar. Based on the knowledge of orbital effects weidentify that the main cause of the locally induced spin-orbit couplings are Cup and d orbitals. By employing the DFT+U formalism as an analysis tool we findthat both the p and d orbital contributions are equally important to spin-orbitcoupling, although p contributions to the density of states are much higher. Wefit the DFT data with phenomenological tight-binding models developedseparately for the top and bridge positions. Our model Hamiltonians describethe low-energy electronic band structure in the whole Brillouin zone and allowus to extract the size of the spin-orbit interaction induced by the local Cuadatom to be in the tens of meV. By application of the phenomenological modelsto Green's function techniques, we find that copper atoms act as resonantimpurities in graphene with large lifetimes of 50 and 100~fs for top andbridge, respectively.

Copper adatoms on graphene: theory of orbital and spin-orbital effects