AI 中文总结
本研究发展半经典玻尔兹曼框架，保留散射核的角与带依赖，求解拓扑绝缘体带隙表面态的二阶非本征自旋电流，揭示高阶角谐量和等能轮廓间散射对非线性自旋输运的关键作用。
AI 中文摘要
我们发展了一种半经典玻尔兹曼框架，用于研究存在偏斜散射时的二阶非本征自旋输运。常规的弛豫时间近似将完整的碰撞积分简化为单一的唯象时间尺度，从而忽略了杂质散射的角结构。尽管输运弛豫时间主要表征非平衡分布的主导角谐量，但非线性响应对其高阶角谐量敏感，这些高阶角谐量由碰撞算子的不同分量决定。因此，我们保留散射核的角依赖和带依赖，并将碰撞积分和分布函数都分解为傅里叶谐量。所得的耦合代数方程允许按电场阶次递归求解分布函数的对称修正项和偏斜散射修正项。我们将该形式主义应用于具有自旋依赖杂质散射的拓扑绝缘体的带隙表面态，并评估相应的二阶非本征自旋电流响应。结果表明，非平衡分布的高阶角谐量以及不同等能轮廓之间的散射，在超越单弛豫时间近似的非本征非线性自旋输运中起着关键作用。
英文摘要
We develop a semiclassical Boltzmann framework for second-order extrinsic spin transport in the presence of skew scattering. The conventional relaxation-time approximation reduces the full collision integral to a single phenomenological timescale and thereby neglects the angular structure of impurity scattering. While the transport relaxation time primarily characterizes the leading angular harmonic of the nonequilibrium distribution, nonlinear response is sensitive to its higher angular harmonics, which are governed by distinct components of the collision operator. We therefore retain the angular and band dependence of the scattering kernel and decompose both the collision integral and the distribution function into Fourier harmonics. The resulting coupled algebraic equations allow the symmetric and skew-scattering corrections to the distribution function to be obtained recursively order by order in the electric field. We apply this formalism to the gapped surface states of a topological insulator with spin-dependent impurity scattering and evaluate the corresponding second-order extrinsic spin-current response. Our results show that higher angular harmonics of the nonequilibrium distribution and scattering between distinct constant-energy contours play an essential role in extrinsic nonlinear spin transport beyond the single-relaxation-time approximation.
Comments14 pages, 4 figures
