The contribution of bulk inversion asymmetry to the total spin-orbit coupling is commonly neglected for group III-V nanowires grown in the generic [111] direction. We have solved the complete Hamiltonian of the circular nanowire accounting for bulk inversion asymmetry via exact numerical diagonalization. Three different symmetry classes of angular momentum states exist, which reflects the threefold rotation symmetry of the crystal lattice about the [111] axis. A particular group of angular momentum states contains degenerate modes which are strongly coupled via the Dresselhaus Hamiltonian, which results in a significant energy splitting with increasing momentum. Hence, under certain conditions Dresselhaus spin-orbit coupling is relevant for [111] InAs and [111] InSb nanowires. We demonstrate momentum-dependent energy splittings and the impact of Dresselhaus spin-orbit coupling on the dispersion relation. In view of possible spintronics applications relying on bulk inversion asymmetry we calculate the spin expectation values and the spin texture as a function of the Fermi energy. Finally, we investigate the effect of an axial magnetic field on the energy spectrum and on the corresponding spin polarization.

We study the effects of spin-orbit coupling on the magnetoconductivity in diffusive cylindrical semiconductor nanowires. Following up on our former study on tubular semiconductor nanowires, we focus in this paper on nanowire systems where no surface accumulation layer is formed but instead the electron wave function extends over the entire cross section. We take into account the Dresselhaus spin-orbit coupling resulting from a zinc-blende lattice and the Rashba spin-orbit coupling, which is controlled by a lateral gate electrode. The spin relaxation rate due to Dresselhaus spin-orbit coupling is found to depend neither on the spin density component nor on the wire growth direction and is unaffected by the radial boundary. In contrast, the Rashba spin relaxation rate is strongly reduced for a wire radius that is smaller than the spin precession length. The derived model is fitted to the data of magnetoconductance measurements of a heavily doped back-gated InAs nanowire and transport parameters are extracted. At last, we compare our results to previous theoretical and experimental studies and discuss the occurring discrepancies.

Spin-momentum locking in a semiconductor device with strong spin-orbit coupling (SOC) is thought to be an important prerequisite for the formation of Majorana bound states. Such a helical state is predicted in one-dimensional (1D) nanowires subject to strong Rashba SOC and spin-mixing - its hallmark being a characteristic re-entrant behaviour in the conductance. Here, we report direct experimental observations of the re-entrant conductance feature, which reveals the formation of a helical liquid, in the lowest 1D subband of an InAs nanowire. Surprisingly, the feature is very prominent also in the absence of magnetic fields. This behaviour suggests that exchange interactions have a substantial impact on transport in our device. We attribute the opening of the pseudogap to spin-flipping two-particle backscattering. The all-electric origin of the ideal helical transport could have important implications for topological quantum computing.