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.
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