Spin-orbit interaction in GaAs wells: From one to two subbands

We investigate the Rashba and Dresselhaus spin-orbit (SO) couplings in GaAs quantum wells in the range of well widths w allowing for a transition of the electron occupancy from one to two subbands. By performing a detailed Poisson-Schrodinger self-consistent calculation, we determine all the intra-and intersubband Rashba ( alpha sub(1), alpha sub(2), [eta]) and Dresselhaus ( beta sub(1), beta sub(2), [Gamma]) coupling strengths. For relatively narrow wells with only one subband occupied, our results are consistent with the data of Koralek et al. [Nature (London) 458, 610 (2009) (http://dx.doi.org/10.1038/nature07871)], i.e., the Rashba coupling alpha sub(1) is essentially independent of w in contrast to the decreasing linear Dresselhaus coefficient beta sub(1). When we widen the well so that the second subband can also be populated, we observe that alpha sub(2) decreases and alpha sub(1) increases, both almost linearly with w. Interestingly, we find that in the parameter range studied (i.e., very asymmetric wells), alpha sub(2) can attain zero and change its sign, while alpha sub(1) is always positive. In this double-occupancy regime of w's, beta sub(1) is mostly constant and beta sub(2) decreases with w (similarly to beta sub(1) for the single-occupancy regime). On the other hand, the intersubband Rashba coupling strength [eta] decreases with w, while the intersubband Dresselhaus [Gamma] remains almost constant. We also determine the persistent-spin-helix symmetry points, at which the Rashba and the renormalized (due to cubic corrections) linear Dresselhaus couplings in each subband are equal, as a function of the well width and doping asymmetry. Our results should stimulate experiments probing SO couplings in multisubband wells.