  We have studied the Zeeman splitting in ballistic hole quantum wires formed
in a (311)A quantum well by surface gate confinement. Transport measurements
clearly show lifting of the spin degeneracy and crossings of the subbands when
an in-plane magnetic field B is applied parallel to the wire. When B is
oriented perpendicular to the wire, no spin-splitting is discernible up to B =
8.8 T. The observed large Zeeman splitting anisotropy in our hole quantum wires
demonstrates the importance of quantum-confinement for spin-splitting in
nanostructures with strong spin-orbit coupling.
