We study the Zeeman spin-splitting in hole quantum wires oriented along the [011] and [011] crystallographic axes of a high mobility undoped (100)-oriented AlGaAs/GaAs heterostructure. Our data shows that the spin-splitting can be switched 'on' (finite g * ) or 'off' (zero g * ) by rotating the field from a parallel to a perpendicular orientation with respect to the wire, and the properties of the wire are identical for the two orientations with respect to the crystallographic axes. We also find that the g-factor in the parallel orientation decreases as the wire is narrowed. This is in contrast to electron quantum wires, where the g-factor is enhanced by exchange effects as the wire is narrowed. This is evidence for a k-dependent Zeeman splitting that arises from the spin-3 2 nature of holes.

The out-of-plane g-factor g([perpendicular])(*) for quasi two-dimensional (2D) holes in a (100) GaAs heterostructure is studied using a variable width quantum wire. A direct measurement of the Zeeman splitting is performed in a magnetic field applied perpendicular to the 2D plane. We measure an out-of-plane g-factor up to g([perpendicular])(*) = 5, which is larger than previous optical studies of g([perpendicular])(*) and is approaching the long predicted but never experimentally verified out-of-plane g-factor of 7.2 for heavy holes.