  We study theoretically the spin-orbit interaction of low-energy electrons in
semiconducting nanowires with a zinc-blende lattice. The effective Dresselhaus
term is derived for various growth directions, including <11(-2)>-oriented
nanowires. While a specific configuration exists where the Dresselhaus
spin-orbit coupling is suppressed even at confinement potentials of low
symmetry, many configurations allow for a strong Dresselhaus coupling. In
particular, we discuss qualitative and quantitative results for nanowire
cross-sections modeled after sectors of rings or circles. The parameter
dependence is analyzed in detail, enabling predictions for a large variety of
setups. For example, we gain insight into the spin-orbit coupling in recently
fabricated GaAs-InAs nanomembrane-nanowire structures. By combining the
effective Dresselhaus and Rashba terms, we find that such structures are
promising platforms for applications where an electrically controllable
spin-orbit interaction is needed. If the nanowire cross-section is scaled down
and InAs replaced by InSb, remarkably high Dresselhaus-based spin-orbit
energies of the order of millielectronvolt are expected. A Rashba term that is
similar to the effective Dresselhaus term can be induced via electric gates,
providing means to switch the spin-orbit interaction on and off. By varying the
central angle of the circular sector, we find, among other things, that
particularly strong Dresselhaus couplings are possible when nanowire
cross-sections resemble half-disks.
