We study two-dimensional (2D) electron systems in the hydrodynamic regime. We show that a geometrical Berry curvature modifies the effective Navier-Stokes equation for viscous electron flow in topological materials. For small electric fields, the Hall current becomes negligible compared to the viscous longitudinal current. In this regime, we highlight an unconventional Poiseuille flow with an asymmetric profile and a deviation of the maximum of the current from the center of the system. In a 2D infinite geometry, the Berry curvature leads to current whirlpools and an asymmetry of the potential profile. This phenomenon can be probed by measuring the asymmetric nonlocal resistance profile.

中文翻译：

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二维霍尔材料的电子流体动力学

我们研究流体力学领域中的二维（2D）电子系统。我们显示几何Berry曲率修改了拓扑材料中粘性电子流的有效Navier-Stokes方程。对于小电场，与粘性纵向电流相比，霍尔电流可以忽略不计。在这种情况下，我们突出显示了非常规的Poiseuille流动，该流动具有不对称的轮廓，并且最大电流与系统中心之间存在偏差。在2D无限几何中，贝里曲率会导致电流涡旋和电势轮廓的不对称性。可以通过测量不对称的非局部电阻曲线来探究这种现象。