Spin-splitting in GaAs two-dimensional holes

We present quantitative measurements and calculations of the spin-orbit-induced zero-magnetic-field spin splitting in two-dimensional (2D) hole systems in modulation-doped GaAs (3 1 1)A quantum wells. The results show that the splitting is large and tunable. In particular, via a combination of back- and front-gate biases, we can tune the splitting while keeping the 2D hole density constant. The data also reveal a surprising result regarding the magnetoresistance (Shubnikov-de Haas) oscillations in a 2D system with spin-split energy bands: the frequencies of the oscillations are not simply related to the population of the spin-subbands. Next we concentrate on the metallic-like behavior observed in these 2D holes and its relation to spin-splitting. The data indicate that the metallic behavior is more pronounced when two spin-subbands with unequal populations are occupied. Our measurements of the magnetoresistance of these 2D hole systems with an in-plane magnetic field corroborate this conclusion: while the system is metallic at zero magnetic field, it turns insulating when one of the spin subbands is depopulated at high magnetic field.