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

Dresselhaus spin-orbit coupling in [111]-oriented semiconductor nanowires