Rashba and Dresselhaus spin-orbit interaction strength in GaAs/GaAlAs heterojunctions

Using a recently developed variational theory for the spin split subbands, we investigate the relative strength of the Rashba and Dresselhaus spin orbit terms in GaAs/GaAlAs heterojunctions. The envelope function formalism is employed using the 8-band k· p Kane model for the bulk, and the Rashba split subbands are obtained with spin-dependent trial functions. The total spin splitting is then calculated analytically by including also the bulk Dresselhaus contribution via quasi-degenerate first order perturbation theory. The total spin-orbit splitting at the Fermi energy of the two dimensional electron gas (2DEG) is calculated as a function of the direction of the Fermi wave-vector. The obtained total spin-orbit splittings along [11] and [1ø1] in-plane directions are shown to be in good agreement with recent experiments. The well known ratio α/β between the Rashba and Dresselhaus contributions is a fundamental parameter in dierent proposals for new semiconductor spintronic devices. Due to barrier penetration and the corresponding spin dependent boundary conditions, the total spin-orbit anisotropy calculated here is shown to be in general determined by more then one parameter, and thus the above ratio should not be estimated using the common α and β =<γk2> z expressions.