Spin-orbit effects in carbon nanotubes – Analytical results

Energy spectra and transport properties of armchair nanotubes with curvature induced spin-orbit interaction are investigated thoroughly. The spin-orbit interaction consists of two terms: the first one preserves the spin symmetry in rotating frame, while the second one breaks it. It is found that the both terms are equally important: (i) at scattering on the potential step which mimics a long-range potential in the nanotubes; (ii) at transport via nanotube quantum dots. It is shown that an armchair nanotube with the first spin-orbit term works as an ideal spin-filter, while the second term produces a parasitic inductance.