Band structures of carbon nanotube with spin-orbit coupling interaction

When spin and orbit are independent, the two equivalent dispersion cones (K and K´) yield a four-fold-degenerate electronic energy spectrum in clean nanotubes. Many work groups reported the split of level degeneracy in graphene and carbon nanotube. Recently, McEuen et al.[1] reported measurements demonstrating that in clean nanotubes the spin and orbital (SO) motion of electrons are coupled, which breaking the four-fold degeneracy of a single electron.