Suppression of spin - orbit effects in 1 D system

We report the absence of spin effects such as spin-galvanic effect, spin polarization and spin current under static electric field and inter-spin-subband absorption in 1D system with spin-orbit interaction of arbitrary form. It was also shown that the accounting for the direct interaction of electron spin with magnetic field violates this statement. The spin-orbit (SO) interaction in a 2D system underlies various spin control methods owing to the coupling between translational and spin degrees of freedom. Such effects have been studied as spin-galvanic effect [1]-[3], spin polarization [4]-[7] and spin current [8] under static electric field, spin polarization under action of electromagnetic wave [9]. The one dimensional system seems to be more suitable for this purpose due to more strong correlation between the spin and the wire direction. This stimulates to examine the similar problems in 1D systems. We consider the 1D Hamiltonian H = p 2 2m + V (x) + H SO (1) with the most general form of SO interaction H SO = {(a(x)σ), p}, (2) where σ are the Pauli matrices, the figure brackets denote the symmetrization procedure, vector a(x) is an arbitrary function of coordinate x along the wire. The Hamiltonian (2) originates from different approaches related with SO interaction in 1D systems. In general, it does not conserve the spin and hence one can expect the above mentioned effects in the frameworks of this Hamiltonian. However, we have found that in a strictly 1D system with the SO Hamiltonian (2) these effects vanish.