具有宏观障碍物的二维电子系统中的流体动力学磁输运
Hydrodynamic magnetotransport in two-dimensional electron systems with macroscopic obstacles
AI总结：
本文理论上研究了含宏观障碍物样品中粘性电子流体的磁输运，采用流体动力学和准流体动力学两种方法，发现纵向磁阻率为强负值，理论与高质量GaAs量子阱实验数据吻合，证实了流体动力学输运区域的实现。
摘要：
在高质量导体中，电子输运的流体动力学区域最近已被实现。在这项工作中，我们从理论上研究了在含有电子不可穿透障碍物的样品中粘性电子流体的磁输运。我们使用两种方法来描述流体流动。第一种方法基于带电流体的流体动力学方程，该方程假设动理学方程考虑了电子分布函数的两个谐波。第二种方法基于考虑分布函数的三个谐波而得到的方程（“准流体动力学”）。在流体动力学方法中，我们考虑了圆盘粗糙边缘和光滑边缘的情况，电子在粗糙边缘上的散射是扩散的，在光滑边缘上的散射是镜面的。纵向磁阻率表现为强且为负，对于粗糙和光滑圆盘边缘在微小修正范围内是相同的。对于粗糙圆盘，霍尔电阻率等于其标准值。对于光滑圆盘，霍尔电阻率相对于标准值获得了一个与霍尔粘度成正比的小修正。在准流体动力学方法中，我们考虑了光滑圆盘和小磁场的情况。在流动与流体动力学流动显著不同的区域中，纵向电阻率不依赖于剪切应力弛豫时间（但依赖于第三角谐波的弛豫时间），而对标准霍尔电阻率的修正不依赖于这两个弛豫时间。我们将纵向电阻率的流体动力学计算结果与高质量GaAs量子阱中具有宏观缺陷的磁输运实验数据进行了比较。理论与实验的良好吻合证明了此类系统中流体动力学输运区域的实现。
英文摘要：
In high-quality conductors, the hydrodynamic regime of electron transport has been recently realized. In this work we theoretically investigate magnetotransport of a viscous electron fluid in samples with electron-impermeable obstacles. We use the two approaches to describe the fluid flow. The first one is based on the equations of hydrodynamics of a charged fluid, which assume that the kinetic equation takes into account the two harmonics of the electron distribution function. The second approach is based on the equations that are obtained by taking into account three harmonics of the distribution function (''quasi-hydrodynamics''). Within the hydrodynamic approach, we consider the cases of the rough and the smooth edges of the disks, on which the electron scattering is diffusive or specular, respectively. The longitudinal magnetoresistivity turns out to be strong and negative, the same for both rough and smooth discs edges to within small corrections. For rough discs, the Hall resistivity is equal to its standard value. For smooth discs the Hall resistance acquire a small correction to the standard value, proportional to the Hall viscosity. In the quasi-hydrodynamic approach, we considered the case of smooth discs and small magnetic fields. In the regime when the flow is substantially different from the hydrodynamic one, the longitudinal resistivity does not depend on the shear stress relaxation time (but depends on the relaxation time of the third angular harmonic), while the correction to the standard Hall resistivity does not depend on both relaxation times. We compare the results of the hydrodynamic calculation of the longitudinal resistance with the experimental data on magnetotransport in high-quality GaAs quantum wells with macroscopic defects. A good agreement of theory and experiment evidences in favor of the realization of the hydrodynamic transport regime in such systems.
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