Wiedemann-Franz law and Fermi liquids
Wiedemann-Franz law and Fermi liquids
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DOI：
10.1103/physrevb.99.085104
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发表时间：
2019-02-04
影响因子：
3.7
通讯作者：
Das Sarma, Sankar
中科院分区：
文献类型：
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作者：
Lavasani, Ali;Bulmash, Daniel;Das Sarma, Sankar
我们深入考虑了Wiedemann-Franz （WF）定律的适用性，即电子热导率(K)与金属的绝对温度(T)和电导率(a)的乘积成正比，并具有比例常数，即所谓的洛伦兹数L-0，是符合费米液体（FL）模式的所有系统中与材料无关的通用常数。人们经常说，WF定律的有效性（无效）是FL[非费米液体（NFL）]的标志。我们考虑在二维（2D）和三维（3D）两个维度上，一个有限温度T下的传导电子系统与声子和淬火杂质相耦合，忽略电子-电子相互作用的影响。我们发现，只要声子散射强于杂质散射，WF定律就会被任意强烈地违反，有效洛伦兹数在低温下消失。对于T < T- bg，这在2D和3D中都发生，其中T- bg是系统的Bloch-Griineisen温度。然而，在没有声子散射的情况下（或等效地，当杂质散射比声子散射强得多时），即使杂质散射主要是小角度前向散射，在低温下也能恢复WF定律。因此，严格地在T = 0时，WF定律在存在无限小杂质散射的FL中总是有效的。对于强声子散射，WF定律恢复为T > T- bg（或德拜温度T- d，取较低者），就像在普通金属中一样。在非常高的温度下，费米表面的热涂布导致有效洛伦兹数低于L-0，表现出与WF定律的定量偏差。我们的论文明确地表明，将NFL行为与WF定律失效不加批判地联系在一起是不正确的。
We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity (K) is proportional to the product of the absolute temperature (T) and the electrical conductivity (a) in a metal with the constant of proportionality, the so-called Lorenz number L-0, being a materials-independent universal constant in all systems obeying the Fermi liquid (FL) paradigm. It has been often stated that the validity (invalidity) of the WF law is the hallmark of an FL [non-Fermi liquid (NFL)]. We consider, both in two (2D) and three (3D) dimensions, a system of conduction electrons at a finite temperature T coupled to a bath of acoustic phonons and quenched impurities, ignoring effects of electron-electron interactions. We find that the WF law is violated arbitrarily strongly with the effective Lorenz number vanishing at low temperatures as long as phonon scattering is stronger than impurity scattering. This happens both in 2D and in 3D for T < T-BG, where T-BG is the Bloch-Griineisen temperature of the system. In the absence of phonon scattering (or equivalently, when impurity scattering is much stronger than the phonon scattering), however, the WF law is restored at low temperatures even if the impurity scattering is mostly small angle forward scattering. Thus, strictly at T = 0 the WF law is always valid in a FL in the presence of infinitesimal impurity scattering. For strong phonon scattering, the WF law is restored for T > T-BG (or the Debye temperature T-D, whichever is lower) as in usual metals. At very high temperatures, thermal smearing of the Fermi surface causes the effective Lorenz number to go below L-0, manifesting a quantitative deviation from the WF law. Our paper establishes definitively that the uncritical association of an NFL behavior with the failure of the WF law is incorrect.