Curvature-induced anisotropic spin-orbit splitting in carbon nanotubes

We have theoretically explored the spin-orbit interaction in carbon nanotubes. We show that, besides the dependences on chirality and diameter, the effects of spin-orbit coupling are anisotropic: spin-orbit splitting is larger for the higher valence or the lower electron band depending on the specific tube. Different tube behaviors can be grouped in three families, according to the so-called chiral index. Curvature-induced changes in the orbital hybridization have a crucial role, and they are shown to be family dependent. Our results explain recent experimental results which have evidenced the importance of spin-orbit effects in carbon nanotubes.