Control of the Rashba spin-orbit coupling in semiconductor two-dimensional electron gases ͑2DEGs͒ is of fundamental interest to the rapidly evolving semiconductor spintronics and depends on the detailed knowledge of the controversial interface and barrier penetration effects. Based on the 8 ϫ 8 k · p Kane model for the bulk, we propose a spin-dependent variational solution for the conduction subbands of III-V heterojuctions, which reveals analytically the different contributions to the Rashba splitting and its dependency on heterostructure and band parameters as the band offset and effective masses. Perturbation expansions are used to derive renormalized parameters for an effective, simple, and yet accurate one band model. Spin-dependent modified Fang-Howard trial functions, which satisfy the spin-dependent boundary conditions, are then introduced. The subband splitting is given as a function of the variational parameter which is obtained minimizing the total energy of the 2DEG. Our calculations applied to InAlAs/InGaAs heterojunctions, where a near 20% increase in the splitting is observed due to the barrier penetration, are in good agreement with both experiment and exact numerical calculations. Well-known expressions in the limit of a perfect insulating barrier are exactly reproduced. The desired control of the spin-orbit splitting for twodimensional ͑2D͒ electron gases ͑2DEGs͒ in III-V semiconductor heterojunctions, as in the Datta and Das spin transistor, has not been achieved yet. The quantitative agreement between theory and experiment is far from complete. Among different studies, there are in particular long-standing controversies concerning the barrier and boundary effects, 1,2 as well as regarding the splitting dependence on the electron density and the consistency among the different experimental methods. [3][4][5] In view of the spintronics, semiconductor heterojunctions form a special class of Rashba split 2DEGs. The electrons are confined by a triangular potential and the strength of the Rashba coupling as well as the electron density ͑n s ͒ can be varied with the gate voltage. Different experiments have been quantitatively interpreted with a simple model for the 2DEGs, 6 i.e., H c = ប 2 ͑k x 2 + k y 2 ͒ / 2m ء + ␣ ء · k ϫ e z , where the Rashba coupling parameter derived from Kane model in the infinite barrier approximation 7 is given byHere the band parameters are those of the well material and E is the confining electric field seen by the 2DEG near the interface. The spin splitting at the Fermi level is then given by ␦ =2␣ ء k F . However, this model has some limitations because it does not include nonparabolicity, barrier penetration, and spin-dependent boundary conditions known to lead to sizable corrections. 2,[8][9][10][11][12][13] There is, however, no simple or consensus way to include or calculate these effects which are usually included through numerical integration of multiband models. 2,[8][9][10][11][12] The problems with such numerical calculations are the spurious solutions, ...
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