Enhanced Dresselhaus spin-orbit interaction in low-symmetry nanowires*

Semiconducting nanowires (NWs) are promising building blocks for solid-state quantum computers, since they allow for conventional spin and charge qubits as well as for topological quantum computing schemes. Such systems often rely on spin-orbit interaction (SOI), which is a crucial mechanism in modern fields of condensed matter physics.
We study theoretically the Dresselhaus SOI of electrons in zinc-blende NWs of various growth directions. We present qualitative and quantitative results for low-symmetry NW cross-sections modeled after sectors of rings or circles. Our analysis enables predictions for a variety of NW cross-sections, such as those of recently fabricated GaAs-InAs nanomembrane-NW structures (Friedl et al., Nano Lett. 18, 2666, 2018). While a specific configuration exists where the Dresselhaus SOI is suppressed, many configurations allow for a strong Dresselhaus coupling on the order of meV. By introducing dimensionless and material-independent functions, it is straightforward to recalculate the spin-orbit length and energy. The inclusion of a similarly strong, gate-induced Rashba term, enables electrical control of the overall SOI.
Our results (arXiv:1910.00562) can serve as a guideline for NW-based setups with applications that rely on SOI.