Electrical control of the sign of the g factor in a GaAs hole quantum point contact

Zeeman splitting of one-dimensional hole subbands is investigated in quantum point contacts fabricated on a (311)-oriented GaAs-AlGaAs heterostructure. Transport measurements can determine the magnitude of the $g$ factor, but cannot usually determine the sign. Here we use a combination of tilted fields and a unique off-diagonal element in the hole $g$ tensor to directly detect the sign of ${g}^{*}$. We are able to tune not only the magnitude, but also the sign of the $g$ factor by electrical means, which is of interest for spintronics applications. Furthermore, we show theoretically that the resulting behavior of ${g}^{*}$ can be explained by the momentum dependence of the spin-orbit interaction.