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 (DSOI) 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. While a specific configuration exists where the DSOI is suppressed, many configurations allow for a strong DSOI on the order of meV. We extend our analysis of the DSOI-Hamiltonian to ki3 terms, focusing on couplings between the ground and first excited states, which become specially relevant for systems with strong spatial confinement. The inclusion of a similarly strong, gate-induced Rashba term, enables electrical control of the overall SOI. Our results can serve as a guideline for NW-based setups with applications that rely on SOI.