Department of Physics, Stanford University, Stanford, CA 94305
Proc Natl Acad Sci U S A. 2017 Oct 24;114(43):11344-11349. doi: 10.1073/pnas.1711414114. Epub 2017 Oct 10.
We obtain a rigorous upper bound on the resistivity [Formula: see text] of an electron fluid whose electronic mean free path is short compared with the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a nonthermal diffusion process-such as an imbalance mode between different bands-we show that the resistivity bound becomes [Formula: see text] The coefficient [Formula: see text] is independent of temperature and inhomogeneity lengthscale, and [Formula: see text] is a microscopic momentum-preserving scattering rate. In this way, we obtain a unified mechanism-without umklapp-for [Formula: see text] in a Fermi liquid and the crossover to [Formula: see text] in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides, and heavy fermion compounds and has presented a long-standing challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.
我们得到了一个严格的上界[公式：见文本]对于电子流体的电阻率，其电子平均自由程与空间非均匀性的尺度相比很短。当这样的流体支持非热扩散过程——例如不同能带之间的不平衡模式——我们表明，电阻率的上界变为[公式：见文本]其中系数[公式：见文本]独立于温度和非均匀性长度尺度，并且[公式：见文本]是微观的动量守恒散射率。通过这种方式，我们得到了一个统一的机制——没有 umklapp——用于费米液体中的[公式：见文本]以及量子临界区的[公式：见文本]的交叉。这种行为在过渡金属氧化物、有机金属、磷化物和重费米化合物中广泛存在，对输运理论提出了长期挑战。我们的流体力学边界允许声子对扩散常数的贡献，包括热扩散，直接影响电导率。
