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

TL;DR

This paper investigates how proximity effects from a Cu(111) surface influence graphene's electronic and spin-orbit properties using density functional theory, revealing strong distance-dependent spin-orbit coupling and a proximity-induced orbital gap.

Contribution

It provides a detailed DFT-based analysis of proximity-induced orbital and spin-orbit effects in graphene on Cu(111), including a model Hamiltonian fit and exploration of distance dependence.

Findings

Proximity effects cause a 20 meV orbital gap in graphene.

Spin-orbit coupling parameters strongly depend on the graphene-Cu distance.

Band inversion occurs when graphene is pressed closer to copper.

Abstract

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