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• W2084266112 abstract "A continuum model for the effective spin-orbit interaction in graphene is derived from a tight-binding model which includes the $ensuremath{pi}$ and $ensuremath{sigma}$ 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 ${ensuremath{Delta}}_{mathrm{int}}ensuremath{propto}{ensuremath{Delta}}^{2}$ and the Rashba coupling due to a perpendicular electric field $mathcal{E}$, ${ensuremath{Delta}}_{mathcal{E}}ensuremath{propto}ensuremath{Delta}$, where $ensuremath{Delta}$ 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 ${ensuremath{Delta}}_{mathrm{curv}}ensuremath{propto}ensuremath{Delta}$. For the values of $mathcal{E}$ and curvature profile reported in actual samples of graphene, we find that ${ensuremath{Delta}}_{mathrm{int}}<{ensuremath{Delta}}_{mathcal{E}}ensuremath{lesssim}{ensuremath{Delta}}_{mathrm{curv}}$. The effect of spin-orbit coupling on derived materials of graphenelike fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only ${ensuremath{Delta}}_{mathrm{int}}$ is important. Both for nanotubes and nanotube caps ${ensuremath{Delta}}_{mathrm{curv}}$ 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." @default.
• W2084266112 created "2016-06-24" @default.
• W2084266112 creator A5047460618 @default.
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• W2084266112 date "2006-10-24" @default.
• W2084266112 modified "2023-10-13" @default.
• W2084266112 title "Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps" @default.
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• W2084266112 doi "https://doi.org/10.1103/physrevb.74.155426" @default.
• W2084266112 hasPublicationYear "2006" @default.
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