Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals
Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals
复制标题
电子流体动力学以及相互作用金属中维德曼-弗朗茨定律和莫特定律的失效
作者：
A. Lucas;S. Sarma
我们提出了具有长寿命准粒子的金属中的热电输运理论，仔细解决了电子-电子散射以及电子-杂质散射的相互作用，但忽略了电子-声子散射。在具有大费米表面和弱电子杂质散射的费米液体中，我们为弹道-流体动力交叉过程中的热电导率行为提供了通用且简单的公式。在这种情况下，电导率相对不受流体动力效应的影响。相反，热导率在参数上可能小于维德曼-弗朗兹定律预测的参数。出现了对莫特定律不太严重的违反。我们定量比较了由于（i）碰撞积分中动量守恒的电子-电子散射，（ii）电子-杂质散射率的流体动力学修改，以及（iii）费米表面的热展宽而引起的违反维德曼-弗朗茨定律的情况，并表明（i）通常是最大的影响。我们提出了跨越弹道到流体动力学极限的电导率和热导率的简单公式，以及热电导率的更复杂的公式。在有限磁场中，洛伦兹数可能小于或大于维德曼-弗朗茨定律的预测，这些行为之间的交叉是对实验的明确预测。我们的工作中发现的对维德曼-弗朗兹定律的任意强烈违反完全源于费米液体范式内的电子-电子相互作用效应，并不意味着任何非费米液体行为。我们预测高迁移率二维 GaAs 半导体结构中体流体动力学的清晰实验特征，其中维德曼-弗朗茨定律的惊人失败应该在高质量和低密度样品中持续到非常低的温度。
We present the theory of thermoelectric transport in metals with long-lived quasiparticles, carefully addressing the interplay of electron-electron scattering as well as electron-impurity scattering, but neglecting electron-phonon scattering. In Fermi liquids with a large Fermi surface and weak electron-impurity scattering, we provide universal and simple formulas for the behavior of the thermoelectric conductivities across the ballistic-to-hydrodynamic crossover. In this regime, the electrical conductivity is relatively unchanged by hydrodynamic effects. In contrast, the thermal conductivity can be parametrically smaller than predicted by the Wiedemann-Franz law. A less severe violation of the Mott law arises. We quantitatively compare the violations of the Wiedemann-Franz law arising from (i) momentum-conserving electron-electron scattering in the collision integral, (ii) hydrodynamic modifications of the electron-impurity scattering rate, and (iii) thermal broadening of the Fermi surface, and show that (i) is generally the largest effect. We present simple formulas for electrical and thermal magnetoconductivity across the ballistic-to-hydrodynamic limit, along with a more complicated formula for the thermoelectric magnetoconductivity. In a finite magnetic field, the Lorenz number may be smaller or larger than predicted by the Wiedemann-Franz law, and the crossover between these behaviors is a clear prediction for experiments. The arbitrarily strong violation of the Wiedemann-Franz law found in our work arises entirely from electron-electron interaction effects within the Fermi-liquid paradigm, and does not imply any non-Fermi-liquid behavior. We predict clear experimental signatures of bulk hydrodynamics in high-mobility two-dimensional GaAs semiconductor structures, where a spectacular failure of the Wiedemann-Franz law should persist down to very low temperatures in high-quality and low-density samples.
影响因子：
64.8
作者：
H. Pfau;S. Hartmann;U. Stockert;P. Sun;S. Lausberg;M. Brando;S. Friedemann;C. Krellner;C. Geibel-C.-G
通讯作者：
H. Pfau;S. Hartmann;U. Stockert;P. Sun;S. Lausberg;M. Brando;S. Friedemann;C. Krellner;C. Geibel-C.-G