Spin relaxation of "upstream" electrons: beyond the drift diffusion model

TL;DR

This paper demonstrates that the classical drift diffusion model inadequately describes upstream spin transport in quantum wires, revealing complex, non-monotonic spin dynamics influenced by subband structure and energy quantization.

Contribution

The study introduces a semi-classical simulation approach that incorporates subband effects, showing the limitations of the drift diffusion model for upstream spin transport.

Findings

Upstream spin transport exhibits non-exponential, complex dynamics.

The drift diffusion model fails to predict qualitative behavior.

Electrons show population inversion due to energy-dependent density of states.

Abstract

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 non-trivial influence of subband structure on spin relaxation. Here we highlight this influence by simulating upstream spin transport in a multi-subband quantum wire, in the presence of D'yakonov-Perel' spin relaxation, using a semi-classical 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.