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

TL;DR

This study combines DFT and model Hamiltonian approaches to analyze how copper adatoms induce spin-orbit coupling in graphene, revealing that Cu p and d orbitals significantly contribute to the effect.

Contribution

It provides a detailed theoretical analysis of orbital and spin-orbit effects of Cu adatoms on graphene, including new tight-binding models and quantitative estimates of induced spin-orbit coupling.

Findings

Spin-orbit coupling induced by Cu adatoms is in the tens of meV range.

Cu adatoms act as resonant impurities with lifetimes of 50-100 fs.

Both p and d orbitals of Cu are crucial for spin-orbit effects.

Abstract

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