Spin-orbit coupling and electron spin resonance for interacting electrons in carbon nanotubes

We review the theoretical description of spin-orbit (SO) scattering and electron spin resonance (ESR) in carbon nanotubes. Particular emphasis is laid on the effects of electron-electron interactions. The SO coupling is derived and the resulting ESR spectrum is analysed using both the effective low-energy field theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard ladders. For single-wall tubes, the field theoretical description predicts a double-peak spectrum linked to the existence of spin-charge separation. The numerical analysis basically confirms this picture, but also predicts additional features in finite-size samples.