Enhanced g factors of a one-dimensional hole gas with quantized conductance

We have measured the transport properties of quasi-one-dimensional ballistic constrictions defined on a high-mobility two-dimensional hole gas. The conductance quantization of the constrictions is changed from even to odd multiples of ${\mathrm{e}}^2$/h as a function of the magnetic field in the plane of the heterojunction, as spin splitting causes the subbands of the one-dimensional (1D) channel to cross. We calculate the in-plane g factors of the 1D subbands using the magnetic fields at which crossing occurs and find that they increase as the number of occupied 1D subbands decreases. We attribute this enhancement of the g factor to Coulomb interactions.