Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interaction
Mathematical Physics
2020-08-03 v1 math.MP
Abstract
Quantum drift-diffusion equations are derived for a two-dimensional electron gas with spin-orbit interaction of Rashba type. The (formal) derivation turns out to be a non-standard application of the usual mathematical tools, such as Wigner transform, Moyal product expansion and Chapman-Enskog expansion. The main peculiarity consists in the fact that a non-vanishing current is already carried by the leading-order term in the Chapman-Enskog expansion. To our knowledge, this is the first example of quantum drift-diffusion equations involving the full spin vector. Indeed, previous models were either quantum bipolar (involving only the spin projection on a given axis) or full spin but semiclassical.
Cite
@article{arxiv.2007.15947,
title = {Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interaction},
author = {Luigi Barletti and Philipp Holzinger and Ansgar Jüngel},
journal= {arXiv preprint arXiv:2007.15947},
year = {2020}
}