Spin Splitting in Quasi-One Dimensional Systems

Abstract

Spin-orbit induced phenomena in quasi-one-dimensional systems are analyzed with the help of double line groups and their irreducible representations. Orbital band splitting and removal of the spin degeneracy are found to be incompatible with vertical mirror symmetry, as well as with simultaneous invariance under the time reversal and horizontal (roto) reflections. This singles out systems with the first and the fifth family line group symmetry as the only candidates for spin polarized currents; direction of electron spin polarization is also determined by the system symmetry. When applied to carbon nanotubes the developed theory enlightens a number of interesting results concerning the band topology and spin polarization of bands.