考虑自旋轨道相互作用的二维电子气的量子漂移扩散方程
Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interaction
摘要：
本文导出了具有Rashba型自旋轨道相互作用的二维电子气的量子漂移扩散方程。形式化的推导是Wigner变换、Moyal乘积展开和Chapman-Enskog展开等常用数学工具的非标准应用。其主要特点在于，在查普曼-恩斯科格展开式中的首阶项已经携带了一个非零电流。据我们所知，这是第一个涉及全自旋矢量的量子漂移扩散方程的例子。事实上，以前的模型要么是量子双极（只涉及给定轴上的自旋投影），要么是全自旋但半经典的。
英文摘要：
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.
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