Anisotropic modification of the effective hole g factor by electrostatic confinement

We investigate effects of lateral confinement on spin splitting of energy levels in 2D hole gases grown on {[}311] GaAs. We found that lateral confinement enhances anisotropy of spin splitting relative to the 2D gas for both confining directions. Unexpectedly, the effective g factor does not depend on the 1D energy level number N for B parallel to{[}0 (1) over bar1] while it has strong N dependence for B parallel to{[}(2) over bar 33]. Apart from quantitative difference in the spin splitting of energy levels for the two orthogonal confinement directions, we also report qualitative differences in the appearance of spin-split plateaus, with nonquantized plateaus observed only for the confinement in the {[}0 (1) over bar1] direction. In our samples we can clearly associate the difference with anisotropy of spin-orbit interactions.