Effect of the inter-subband spin-orbit interaction on the spin transistor operation

We consider the electron transport in the Datta-Das spin transistor within the two-subband model taking into account the intra- and inter-subband spin-orbit (SO) interaction and study the influence of the inter-subband SO coupling on the spin-transistor operation. Starting from the model, in which the SO coupling constants are treated as parameters, we show that the inter-subband SO interaction strongly affects the ordinary conductance oscillations predicted for the transistor with the single occupancy. Interestingly, we find that even in the absence of the intra-subband SO interaction, the conductance oscillates as a function of the inter-subband SO coupling constant. This phenomenon is explained as resulting from the inter-subband transition with spin-flip. Next, we consider the realistic spin transistor model based on the gated Al$_{0.48}$In$_{0.52}$As/Ga$_{0.47}$In$_{0.53}$As double quantum well, for which the SO coupling constants are determined by the Schr\"{o}dinger-Poisson approach. We show that the SO coupling constants rapidly change around $V_g=0$, which is desirable for the spin transistor operation. We demonstrate that for high electron densities the inter-subband SO interaction starts to play the dominant role. The strong evidence of this interaction is the reduction of the conductance for gate voltage $V_g=0$, which leads to the reduction of the on/off conductance ratio.