Energy dispersion relations of spin-split subbands in a quantum wire and electrostatic modulation of carrier spin polarization

Abstract

We numerically calculate the energy dispersion relations of the spin-split subbands in a quantum wire subjected to a transverse magnetic field in the presence of Rashba and Dresselhaus spin-orbit interactions. The spin splitting energy at zero wave vector is found to be neither equal to the bare Zeeman splitting nor linear in the magnetic field in any subband. This happens because the expectation value of the spin angular momentum operator varies along the width of the wire, causing a spatial modulation of the spin density. We also show that spin splitting energy is subband dependent and has a complex dependence on the external magnetic field. In some subbands, it can vanish entirely at nonzero values of the external magnetic field. The effective spin polarization of carriers in any subband can be changed in both magnitude and sign with an external electrostatic potential, applied, for example, via a gate terminal. This has practical applications in quantum computing and other areas.