AI 中文总结
本文建立含任意粗糙度边缘的低缺陷二维电子样品的流体动力学磁输运理论，发现霍尔电阻随磁场的极小值特性可用于识别电子输运的流体动力学 regime 并确定边缘粗糙度等参数。
AI 中文摘要
在超洁净导体中，粒子间的快速碰撞可形成粘性电子流体，实现流体动力学输运 regime。本文针对缺陷密度低、边缘粗糙度任意的样品，建立二维（2D）电子的流体动力学磁输运理论。模型中，边缘粗糙度由边界条件中一个具有速度量纲的单一参数描述，计算了长样品中的电子流体流动分布及对应的纵向电阻与霍尔电阻。与弛豫过程相关的霍尔电阻贡献，在高磁场极限下呈现饱和，且当边缘足够粗糙时，霍尔电阻随磁场变化会出现一个极小值；该极小值会随边缘粗糙度降低、样品宽度增大或缺陷的体散射增强而消失。霍尔电阻的这些特性可作为实验中识别电子输运流体动力学 regime 的标志，用于确定其参数，特别是边缘粗糙度程度。
英文摘要
In ultra-clean conductors, fast inter-particle collisions can lead to the formation of a viscous electron fluid and realization of the hydrodynamic transport regime. Here we develop a theory of hydrodynamic magnetotransport of two-dimensional (2D) electrons in samples with low densities of defects and edges of arbitrary roughness. Within our model the roughness is described by a single parameter with the dimension of speed in the boundary conditions on sample edges. The electron-fluid flow profiles in long samples, as well as the corresponding longitudinal and Hall resistances, are calculated. The contribution to the Hall resistance associated with the relaxation processes exhibits a saturation in the limit of high magnetic field and a minimum as a function of the magnetic field for sufficiently rough edges. The minimum disappears as the edge roughness decreases or the sample width and bulk scattering by defects increase. These properties of the Hall resistance can serve as the signs to identify the hydrodynamic regime of electron transport in experiments and can be used to determine its parameters, in particular, the degree of edge roughness.
Comments8 pages, 3 figures
