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All-electrical manipulation of electron spin by the spin-orbit interaction in a semiconductor nanotube: analytical results

A possibility of controlled manipulation of electron spin states has been investigated for a cylindrical two-dimensional electron gas confined in a semiconductor nanotube/cylindrical nanowire with the Rashba spin-orbit interaction. We present analytical solutions for the two limiting cases, in which the spin-orbit interaction results from (A) the radial electric field and (B) the electric field applied along the axis z of the nanotube. In case (A), the superposition of the two lowest-energy bands corresponding to the opposite spins leads to the precession of electron spin around the nanowire axis. We have found that the direction of the spin precession changes from clockwise to counterclockwise if the energy of the injected electron achieves the value corresponding to the crossing of energy levels associated with the two components of the superposition state. In case (B), we have obtained the damped oscillations of the z spin component with the period that changes as a function of the coordinate z. We have also shown that the damped oscillations of the average value of the z spin component form beats localized along the nanowire axis.