A systematic numerical investigation of spin-orbit fields in the conduction bands of III-V semiconductor nanowires is performed. Zinc-blende InSb nanowires are considered along [001], [011], and [111] directions, while wurtzite InAs nanowires are studied along [0001] and [1010] or [1120] directions. Robust multiband k · p Hamiltonians are solved by using plane wave expansions of realspace parameters. In all cases the linear and cubic spin-orbit coupling parameters are extracted for nanowire widths from 30 to 100 nm. Typical spin-orbit energies are on the µeV scale, except for InAs wurtzite nanowires grown along [1010] or [1120], in which the spin-orbit energy is about meV, largely independent of the wire diameter. Significant spin-orbit coupling is obtained by applying a transverse electric field, causing the Rashba effect. For an electric field of about 4 mV/nm the obtained spin-orbit energies are about 1 meV for both materials in all investigated growth directions. The most favorable system, in which the spin-orbit effects are maximal, are InAs WZ nanowires grown along [1010] or [1120], since here spin-orbit energies are giant (meV) already in the absence of electric field. The least favorable are InAs WZ nanowires grown along [0001], since here even the electric field does not increase the spin-orbit energies beyond 0.1 meV. The presented results should be useful for investigations of optical orientation, spin transport, weak localization, and superconducting proximity effects in semiconductor nanowires. arXiv:1802.06734v2 [cond-mat.mes-hall] 30 Apr 2018Appendix A: Plane wave expansion and numerical details
Semiconductor nanowires based on non-nitride III-V compounds can be synthesized under certain growth conditions to favor the appearance of wurtzite crystal phase. Despite the reports in literature of ab initio band structures for these wurtzite compounds, we still lack effective multiband models and parameter sets that can be simply used to investigate physical properties of such systems, for instance, under quantum confinement effects. In order to address this deficiency, in this study we calculate the ab initio band structure of bulk InAs and InP in wurtzite phase and develop an 8×8 k.p Hamiltonian to describe the energy bands around Γ point. We show that our k.p model is robust and can be fitted to describe the important features of the ab initio band structure. The correct description of the spin splitting effects that arise due to the lack of inversion symmetry in wurtzite crystals, is obtained with the k-dependent spin-orbit term in the Hamiltonian, often neglected in the literature. All the energy bands display a Rashba-like spin texture for the in-plane spin expectation value. We also provide the density of states and the carrier density as functions of the Fermi energy. Alternatively, we show an analytical description of the conduction band, valid close to Γ point. The same fitting procedure is applied to the 6×6 valence band Hamiltonian. However, we find that the most reliable approach is the 8×8 k.p Hamiltonian for both compounds. The k.p Hamiltonians and parameter sets that we develop in this paper provide a reliable theoretical framework that can be easily applied to investigate electronic, transport, optical, and spin properties of InAs-and InP-based nanostructures.
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