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Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps | | D. Huertas-Hernando
; F. Guinea
; A. Brataas
; | | Date: |
22 Jun 2006 | | Subject: | Mesoscopic Systems and Quantum Hall Effect | | Abstract: | A continuum model for the effective spin orbit interaction in graphene is derived from a tight-binding model, which includes the $pi$ and $sigma$ bands. We analyze the combined effects of the intraatomic spin orbit coupling, curvature, and an 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 the intrinsic spin-orbit coupling $Hi propto Delta^ 2$ and for the Rashba coupling due to an electric field and for flat graphene $Delta_{cal E} propto Delta$, where $Delta$ is the intraatomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term $Delta_{
m curv} propto Delta$. For the values of $cal E$ and curvature profile reported in actual samples of graphene, we find that $Hi lesssim Delta_{cal E} <Delta_{
m curv}$. The effect of spin orbit coupling on derived materials of graphene like fullerenes, nanotubes, and nanotube caps, where curvature effects are important, is also studied. For fullerenes, only $Hi$ is important. Both for nanotubes and nanotube caps $Delta_R$ is of 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 for spin-dependent field-effect emission. | | Source: | arXiv, cond-mat/0606580 | | Services: | Forum | Review | PDF | Favorites | |
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