Spin–orbit interaction in bent carbon nanotubes: resonant spin transitions

We develop an effective tight-binding Hamiltonian for spin–orbit (SO) interaction in bent carbon nanotubes (CNT) for the electrons forming the π bonds between the nearest neighbor atoms. We account for the bend of the CNT and the intrinsic spin–orbit interaction which introduce mixing of π and σ bonds between the p z orbitals along the CNT. The effect contributes to the main origin of the SO coupling—the folding of the graphene plane into the nanotube. We discuss the bend-related contribution of the SO coupling for resonant single-electron spin and charge transitions in a double quantum dot. We report that although the effect of the bend-related SO coupling is weak for the energy spectra, it produces a pronounced increase of the spin transition rates driven by an external electric field. We find that spin-flipping transitions driven by alternate electric fields have usually larger rates when accompanied by charge shift from one dot to the other. Spin-flipping transition rates are non-monotonic functions of the driving amplitude since they are masked by stronger spin-conserving charge transitions. We demonstrate that the fractional resonances—counterparts of multiphoton transitions for atoms in strong laser fields—occurring in electrically controlled nanodevices already at moderate ac amplitudes—can be used to maintain the spin-flip transitions.