Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets

Hongki Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, Leonard Kleinman, A. H. MacDonald

Published 2006-06-20, updated 2006-10-20Version 4

Starting from a microscopic tight-binding model and using second order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength $\xi$ and first order in the external electric field $E$ perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at E=0 is second order in $\xi$. The spin-orbit terms in the low-energy effective Hamiltonian have the form proposed recently by Kane and Mele. \textit{Ab initio} electronic structure calculations were performed as a partial check on the validity of the tight-binding model.