Intrinsic spin–orbit interaction in carbon nanotubes and curved nanoribbons

We present a theoretical study of spin–orbit interaction effects on single wall carbon nanotubes and curved graphene nanoribbons by means of a realistic multiorbital tight-binding model, which takes into account the full symmetry of the honeycomb lattice. Several effects relevant to spin–orbit interaction, namely, the importance of chirality, curvature, and a family-dependent anisotropic conduction and valence band splitting are identified. We show that chiral nanotubes and nanoribbons exhibit spin-split states. Curvature-induced orbital hybridization is crucial to understand the experimentally observed anisotropic spin–orbit splittings in carbon nanotubes. In fact, spin–orbit interaction is important in curved graphene nanoribbons, since the induced spin-splitting on the edge states gives rise to spin-filtered states.

► We have studied intrinsic spin–orbit interactions in carbon nanotubes and curved graphene ribbons. ► We show the importance of chirality, curvature and family-dependent behaviour in these systems. ► The anisotropy in the induced spin-splitting in chiral nanotubes and ribbons is directly related to σ−πσ−π hybridization.