Longitudinal spin decoherence in spin diffusion in semiconductors

We set up a set of many-body kinetic Bloch equations with spacial inhomogeneity. We reexamine the widely adopted quasi-independent electron model and show the inadequacy of this model in studying the spin transport. We further point out a new decoherence effect based on interference along the direction of diffusion in spin transport due to the so-called inhomogeneous broadening effect in the Bloch equations. We show that this inhomogeneous broadening can cause decoherence alone, even in the absence of the scattering and that the resulting decoherence is more important than the dephasing effect due to both the D'yakonov-Perel' term and the scattering.