Kinetic theory of spin transport in n-typed semiconductor quantum wells

We set up a set of many-body kinetic Bloch equations with spacial inhomogeneity. We reexamine the widely adopted quasi-independent electron model (QIEM) and show the inadequacy of this model in studying the spin transport. We further point out a new decoherence effect based on interference effect of electrons/spins with different momentum ${\bf k}$ along the direction of the diffusion, which is referred as ``inhomogeneous broadening effect'' in our paper. We show that this inhomogeneous broadening can cause spin decoherence alone even in the absence of the scattering and that the resulting decoherence can be more important than the dephasing effect due to the D'yakonov-Perel' (DP) term together with the scattering. Our theory takes all the inhomogeneous broadening effect, the spin diffusion due to the spacial inhomogeneity and the spin dephasing into account and gets the results self-consistently. We further study the spin diffusion/transport of an $n$-typed GaAs quantum well (QW) in the steady state under different conditions, such as at different temperatures; in the presence of impurities; in the presence of external electric fields along the diffusion direction and/or the QW growth direction; and with magnetic fields in the Voigt configuration. We also demonstrate a time evolution of a spin package calculated from our many-body theory. Different features predicted from our many-body theory are highlighted in the paper.