Zero-field spin splitting in GaAs/AlGaAs 2D holes

From Fourier analysis of the low-magnetic-field Shubnikov-de Haas oscillations, we quantitatively determine the spin splitting, in the limit of zero magnetic field, for high-mobility two-dimensional hole systems confined to GaAs/AlGaAs heterostructures. The spin-splitting can be tuned continuously from large values to nearly zero in a square quantum well whose charge distribution can be controlled from being asymmetric to symmetric via the application of a front-gate bias. In a triangular well with an asymmetric potential, we always observe substantial spin splitting. In the latter system, our measured commensurability oscillations, induced by a one-dimensional periodic potential, reveal two frequencies, providing clear evidence for spin-resolved ballistic transport.