2006/06/30 by Daniel Huertas‐Hernando, D. Huertas-Hernando, F. Guinea +2 · 9 citations
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.74.155426
published as Phys. Rev. B 74, 155426 (2006) (15 pages) · Final version. Published in Physical Review B
openalex publication_date 2006/10/24 · arxiv created 2006/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A continuum model for the effective spin-orbit interaction in graphene is derived from a tight-binding model which includes the \ensuremathπ and \ensuremathσ bands. We analyze the combined effects of the intra-atomic spin-orbit coupling, curvature, and applied electric field, using perturbation theory. We recover the effective spin-orbit Hamiltonian derived recently from group theoretical arguments by Kane and Mele. We find, for flat graphene, that the intrinsic spin-orbit coupling \ensuremathΔint\ensuremath∝\ensuremathΔ2 and the Rashba coupling due to a perpendicular electric field E, \ensuremathΔE\ensuremath∝\ensuremathΔ, where \ensuremathΔ is the intra-atomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term \ensuremathΔcurv\ensuremath∝\ensuremathΔ. For the values of E and curvature profile reported in actual samples of graphene, we find that \ensuremathΔint<\ensuremathΔE\ensuremath\lesssim\ensuremathΔcurv. The effect of spin-orbit coupling on derived materials of graphenelike fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only \ensuremathΔint is important. Both for nanotubes and nanotube caps \ensuremathΔcurv is in the order of a few Kelvins. We reproduce the known appearance of a gap and spin-splitting in the energy spectrum of nanotubes due to the spin-orbit coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the localized states at the cap, which could allow spin-dependent field-effect emission.