Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
By D. Huertas-Hernando, Francisco Guinea, A. Brataas. 2006
739 citations recorded by the source corpus.
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 ${\ensuremath{\Delta}}_{\mathrm{int}}l{\ensuremath{\Delta}}_{\mathcal{E}}\ensuremath{\lesssim}{\ensuremath{\Delta}}_{\mathrm{curv}}$. 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.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/bd190ff876773867f0a55e91013d43ef96b3856e
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Citations in the corpus
- Quantum transport in carbon nanotubes (2014, background): “Indeed, spin-orbit coupling is comparatively weak in free carbon (3P0−3P1 splitting ∼ 2 meV (Kramida et al., 2013)), and almost completely suppressed near the Dirac points in flat graphene (Huertas-Hernando et al., 2006; Min et al., 2006).”
- Electronic transport in two-dimensional graphene (2010, background): “…graphene can be used as a component of more complicated structures by exploiting its spin Cho et al. (2007); Han et al. (2009); Hill et al. (2006); Huertas-Hernando et al. (2006, 2009); Józsa et al. (2009); Tombros et al. (2007) or valley Rycerz et al. (2007b) degeneracy or by patterning gates…”
- The electronic properties of graphene (2007, background): “Tight-binding (Huertas-Hernando et al., 2006; Zarea and Sandler, 2007) and band structure calculations (Min et al.”
- Colloquium : Spintronics in graphene and other two-dimensional materials (2019, background): “Second-order perturbation theory gives (Huertas-Hernando et al., 2006; Konschuh et al., 2010; Min et al., 2006) ∆KM = s∆ 2 SO 18V 2spσ ≈ 1 µeV, (3) where Vspσ ≈ 4.2 eV represents the hopping between px,y and s orbitals, s ≈ −7.3 eV is the energy of the latter measured with respect to the intrinsic…”
- Colloquium: Graphene spectroscopy (2014, background): “The curvature of the graphene sheet is predicted to enhance the Rashba splitting (Huertas-Hernando et al., 2006; Kuemmeth et al., 2008).”