Effects of Rashba spin–orbit interaction and inhomogeneous magnetic field on the eigenstates in a quantum wire

Using an efficient expanded basis method, we have studied the effects of Rashba spin–orbit interaction (SOI) and a laterally inhomogeneous magnetic field on the eigenstates of spin-polarized electrons in a quantum wire. Our numerical results show that inhomogeneous magnetic field can significantly modify the energy spectrum as compared with uniform magnetic field. The spatial distributions of probability and spin densities across the wire have also been investigated. We find that in the presence of only Rashba SOI, i.e., without magnetic field, the component of spin density parallel to the propagating direction vanishes for all the states and the other two spin components exhibit even (or odd) symmetry and oscillating behaviors across the wire. Under the interplay of Rashba SOI and nonuniform magnetic field, the distributions of both the probability and spin densities show a variety of localized behavior. The spin polarizations of electrons strongly depends on the wave number of the propagating state.