Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets

Details Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets

2006-06-20

arxiv.org/abs/cond-mat/0606504v4

Phys. Rev. B 74, 165310 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 2 figures; typos corrected, references updated

Scientific paper

10.1103/PhysRevB.74.165310

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.

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