Electrical control of the spin-orbit coupling in GaAs from single to double and triple wells

We consider a realistic GaAs/Al0.3Ga0.7As well, inside which there are either one or two additional AlxGa1-xAs barriers embedded, with two occupied electron subbands nu = 1, 2. By varying the Al content x in the AlxGa1-xAs layer, we investigate the electrical control of the spin-orbit (SO) interaction, i.e., intrasubband Rashba (Dresselhaus) alpha(nu) (beta(nu)) and intersubband Rashba (Dresselhaus) eta (Gamma), in the course of the transition of our system from single to double and triple wells. At x = 0 (single well), the scenario of SO terms is usual, e.g., alpha(1) and alpha(2) have the same sign and both change almost linearly as functions of an external gate voltage V-g. In contrast, when x away from zero and only one AlxGa1-xAs barrier embedded (double well), alpha(1) and alpha(2) tend to have opposite signs, and alpha(2) first increases with V-g, while peaks at some point depending on x. For a larger value of x, alpha(2) increases with V-g more abruptly till it peaks. As opposed to alpha(1) and alpha(2), the intrasubband Dresselhaus terms beta(nu) have a relatively weak dependence on V-g, and beta(1) and beta(2) become close as x increases. As for the intersubband SO terms, at x = 0, the Rashba coupling eta remains essentially constant, while the Dresselhaus Gamma changes almost linearly with V-g. When x is nonzero, on the one hand, both eta and Gamma have a sensitive dependence on V-g near the symmetric configuration; on the other hand, right at the symmetric configuration eta exhibits the highest while Gamma vanishes. In the case of our system having two additional AlxGa1-xAs barriers (triple well), we find that the gate dependence of SO terms becomes more smooth and beta(nu) becomes more stronger. The persistent-spin-helix symmetry of the two subbands is also discussed. These results are expected to be important for a broad control of the SO interaction in semiconductor nanostructures. (C) 2015 Elsevier Ltd. All rights reserved.