Abstract:

In this work we present the self-consistent determination of the spin-orbit coupling constant in heterostructure with two subbands.As recently proposed, the effective hamiltonian for the conduction band in the effective mass approximation contains an inter-subband spin-orbit coupling which is non-zero even for symmetric heterostructures. We present the theoretical derivation which leads to this proposal and show a selfconsistent determination of the coupling constant. We also compare the magnitude of the new coupling constant with the usual Rashba coupling. Starting with a discussion of the k.p method and the Envelope Function Approximation (EFA) we show the derivation of the 8x8 Kane model for semiconductors with zincblende structure. We then apply the 'folding down' method, isolating the conduction band sector of the EFA hamiltonian. By projecting this hamiltonian in the first two states of the orbital part, we find an effective 4x4 hamiltonian that contains an inter-subband spin orbit coupling. The eingenvalues and eigenvectors of this hamiltonian are shown and, specializing the model for single and double quantum wells, we self-consistently determine the inter-subband and Rashba coupling constants in the Hartree approximation. The results indicate the possibility of electrical control of the coupling constant and show an effective mass renormalization effect that can be up to 5% in some cases.