  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.
