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arXiv 2005.09694cond-mat.mes-hallphysics.flu-dyn
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强耦合电子-声子液体的输运性质

Transport properties of strongly coupled electron-phonon liquids

Alex Levchenko, Jörg Schmalian

摘要:

在这项工作中,我们考虑耦合的电子-声子流体的流体动力学行为,着重于电子输运的条件下的强声子阻力。当由于例如umklapp散射导致的声子平衡的速率比正常的电子-声子碰撞的速率慢得多时,发生这种状态。然后声子和电子形成耦合的非平衡态,其中电子-声子流体的总准动量守恒。一个联合流速出现作为一个集体的流体动力学变量。我们从微观动力学理论推导出这种流体的运动方程,并阐明其有效粘度和热导率。特别是,我们推导出的分布函数的任意谐波的衰减时间,并揭示其相应的费米表面上的超扩散弛豫。我们进一步考虑这一理论的几个应用程序的磁输运性质的霍尔酒吧和Corbino磁盘的几何形状,相关的实验。在我们的分析中,我们允许一般的边界条件,涵盖了从无滑移到无应力流动的交叉。我们的方法还涵盖了交叉从斯托克斯欧姆制度的条件下的Gurzhi效应。此外,我们考虑了表面阻抗和非平衡噪声的频率依赖性。对于后者,我们注意到,在扩散制度,福克-普朗克近似,适用于电子-声子碰撞积分的Eliashberg形式,减少了它的微分算子与Burgers非线性。结果,非平衡分布函数在能量域中具有冲击波结构。这种行为的噪声的Fano因子的后果进行了研究。最后,我们讨论了我们的结果的背景下,最近的电子-声子阻力测量狄拉克和外尔半金属的连接和局限性。

英文摘要:

In this work we consider the hydrodynamic behavior of a coupled electron-phonon fluid, focusing on electronic transport under the conditions of strong phonon drag. This regime occurs when the rate of phonon equilibration due to e.g. umklapp scattering is much slower than the rate of normal electron-phonon collisions. Then phonons and electrons form a coupled out-of-equilibrium state where the total quasi-momentum of the electron-phonon fluid is conserved. A joint flow-velocity emerges as a collective hydrodynamic variable. We derive the equation of motion for this fluid from the underlying microscopic kinetic theory and elucidate its effective viscosity and thermal conductivity. In particular, we derive decay times of arbitrary harmonics of the distribution function and reveal its corresponding super-diffusive relaxation on the Fermi surface. We further consider several applications of this theory to magneto-transport properties in the Hall-bar and Corbino-disk geometries, relevant to experiments. In our analysis we allow for general boundary conditions that cover the crossover from no-slip to no-stress flows. Our approach also covers a crossover from the Stokes to the Ohmic regime under the conditions of the Gurzhi effect. In addition, we consider the frequency dependence of the surface impedance and non-equilibrium noise. For the latter, we notice that in the diffusive regime, a Fokker-Planck approximation, applied to the electron-phonon collision integral in the Eliashberg form, reduces it to a differential operator with Burgers nonlinearity. As a result, the non-equilibrium distribution function has a shock-wave structure in the energy domain. The consequence of this behavior for the Fano factor of the noise is investigated. In conclusion we discuss connections and limitations of our results in the context of recent electron-phonon drag measurements in Dirac and Weyl semimetals.

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