Spin relaxation of upstream electrons in quantum wires: Failure of the drift diffusion model

The classical drift diffusion (DD) model of spin transport treats spin relaxation via an empirical parameter known as the spin diffusion length. According to this model, the ensemble averaged spin of electrons drifting and diffusing in a solid decays exponentially with distance due to spin dephasing interactions. The characteristic length scale associated with this decay is the spin diffusion length. The DD model also predicts that this length is different for upstream electrons traveling in a decelerating electric field than for downstream electrons traveling in an accelerating field. However, this picture ignores energy quantization in confined systems (e.g., quantum wires) and therefore fails to capture the nontrivial influence of subband structure on spin relaxation. Here we highlight this influence by simulating upstream spin transport in a multisubband quantum wire, in the presence of D'yakonov-Perel' spin relaxation, using a semiclassical model that accounts for the subband structure rigorously. We find that upstream spin transport has a complex dynamics that defies the simplistic definition of a spin diffusion length. In fact, spin does not decay exponentially or even monotonically with distance, and the drift diffusion picture fails to explain the qualitative behavior, let alone predict quantitative features accurately. Unrelated to spin transport, we also find that upstream electrons undergo a population inversion as a consequence of the energy dependence of the density of states in a quasi-one-dimensional structure.