We have fabricated and characterized a single hole transistor in an undoped AlGaAs-GaAs heterostructure. Our device consists of a p-type quantum dot, populated using an electric field rather than modulation doping. Low temperature transport measureme
nts reveal periodic conductance oscillations due to Coulomb blockade. We find that the low frequency charge noise is comparable to that in modulation-doped GaAs single electron transistors (SETs), and almost an order of magnitude better than in silicon SETs.
We study the Zeeman spin-splitting in hole quantum wires oriented along the $[011]$ and $[01bar{1}]$ 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.
