Intrinsic spin-orbit interactions in flat and curved graphene nanoribbons

[EN] Recent theoretical and experimental works on carbon nanotubes and graphene samples have revealed that spin-orbit interactions, though customarily ignored in carbon-based materials, are more important and complex than it was thought. We study the intrinsic spin-orbit coupling effects on graphene nanoribbons, both flat and bent. Calculations are performed within the tight-binding model with the inclusion of a four-orbital basis set; thereby the full symmetry of the honeycomb lattice and the hybridization of σ and π bands are considered. In addition to the zero-energy π-edge states, σ-derived edge states are found for the three investigated ribbon geometries. The σ states are also spin filtered and localized at the boundaries of the ribbons. The calculated spin-orbit splittings are larger for the σ- than for the π-derived edge states. Due to this enhancement, spin-orbit splittings of the σ states reach values of the order of a few Kelvin. These spin-filtered edge states are robust under σ-π hybridization and curvature effects. © 2011 American Physical Society.This work has been partially supported by the Spanish DGES under Grants No. MAT2006-05122, No. FIS2008-00124, and No. MAT2009-14578-C03-03