发表机构
School of Physics, The University of New South Wales（新南威尔士大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出求解波矢非对角密度矩阵的量子动力学方程，以微观处理全轨道电流的外在散射贡献，并应用于狄拉克模型，发现外在修正与内在电流同阶且不可分离，为多带固体无序修正提供通用途径。
AI 中文摘要
轨道霍尔效应（OHE）支撑着新兴的轨道电子学领域。对通常的轨道电流算符进行完整的量子力学评估，必须保留位置算符的所有矩阵元，包括其能带对角微分部分；基于这种完整评估的内在计算，其结果可能与传统的截断方法相差数个数量级。已有关于无序效应对完整电流的弛豫时间估计，但由于位置算符需要波矢非对角密度矩阵元，外在散射的微观处理一直无法实现。在此，我们通过求解波矢非对角密度矩阵的量子动力学方程来发展这样的理论，在非交叉近似内包含了能带结构、场修正的侧跳和斜散射项。我们将该理论应用于大质量狄拉克锥以及具有粒子-空穴对称性破缺二次项的同一模型。无序产生的阶次为$\ au^0$的贡献在金属态区域通常与内在电流相当，且无法通过简单的无序强度标度与之分离。对于裸的大质量狄拉克锥，存留的非交叉外在修正抵消了传统的内在值，使总电流恰好为量子修正的两倍，而粒子-空穴不对称性则激活了具有非零三阶矩的无序的传统斜散射，该效应在足够干净的样品中占主导。波矢非对角构造独立于两带模型，为多带固体中位置依赖可观测量提供了一条通用的无序修正路径。
英文摘要
The orbital Hall effect (OHE) underpins the emerging field of orbitronics. A complete quantum-mechanical evaluation of the usual orbital-current operator must retain all matrix elements of the position operator, including its band-diagonal differential part; intrinsic calculations based on this full evaluation can differ by orders of magnitude from the conventional truncation. A relaxation-time estimate of disorder effects on the full current has been reported, but a microscopic treatment of extrinsic scattering has remained unavailable because the position operator requires wavevector-off-diagonal density-matrix elements. Here we develop such a theory by solving the quantum kinetic equation for the wavevector-off-diagonal density matrix, including band-structure, field-corrected side-jump, and skew-scattering terms within the non-crossing approximation. We apply the theory to a massive Dirac cone and to the same model with a particle-hole-symmetry-breaking quadratic term. Disorder-generated contributions of order $τ^0$ are generically comparable to the intrinsic current in the metallic regime and cannot be separated from it by simple disorder-strength scaling. For the bare massive Dirac cone the surviving non-crossing extrinsic correction cancels the conventional intrinsic value and leaves a total current exactly twice the quantum correction, whereas particle-hole asymmetry activates conventional skew scattering for disorder with a non-zero third moment, which dominates in sufficiently clean samples. The wavevector-off-diagonal construction is independent of the two-band model and provides a general route to disorder corrections for position-dependent observables in multiband solids.
