  We study theoretically the low-energy hole states in Si, Ge, and Ge/Si
core/shell nanowires (NWs). The NW core in our model has a rectangular cross
section, the results for a square cross section are presented in detail. In the
case of Ge and Ge/Si core/shell NWs, we obtain very good agreement with
previous theoretical results for cylindrically symmetric NWs. In particular,
the NWs allow for an unusually strong and electrically controllable spin-orbit
interaction (SOI) of Rashba type. We find that the dominant contribution to the
SOI is the "direct Rashba spin-orbit interaction" (DRSOI), which is an
important mechanism for systems with heavy-hole-light-hole mixing. Our results
for Si NWs depend significantly on the orientation of the crystallographic
axes. The numerically observed dependence on the growth direction is consistent
with analytical results from a simple model, and we identify a setup where the
DRSOI enables spin-orbit energies of the order of millielectronvolts in Si NWs.
Furthermore, we analyze the dependence of the SOI on the electric field and the
cross section of the Ge or Si core. A helical gap in the spectrum can be opened
with a magnetic field. We obtain the largest g factors with magnetic fields
applied perpendicularly to the NWs.
