论文标题
洛伦兹比率的奇怪金属性标准
A Criterion for Strange Metallicity in the Lorenz Ratio
论文作者
论文摘要
The Wiedemann-Franz (WF) law, stating that the Lorenz ratio $L = κ/(Tσ)$ between the thermal and electrical conductivities in a metal approaches a universal constant $L_0=π^2 k_B^2/ (3 e^2)$ at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles.相比之下，我们表明，各种弱小的非Fermi液体的模型也遵守$ t \至0 $的WF法律。取而代之的是，我们建议对WF法律使用领先的低温校正，$ L（t）-l_0 $（与非弹性散射率成正比），以区分不同类型的奇怪金属。例如，我们证明在边缘费米液体的可解决模型中，$ l（t）-l_0 \ propto -t $。使用量子玻尔兹曼方程（QBE）方法，我们在一类具有弱动量依赖性的非弹性散射的边缘和非弗米液体中发现了类似行为。相比之下，在费米液体中，$ l（t）-l_0 $与$ -t^2 $成正比。即使在电阻率随$ t $线性增长时，由于$ t- $线性准弹性散射（如在debye频率上方的温度下的电子 - phonon散射的情况下）。最后，通过利用QBE方法，我们证明了横向Lorenz的比率，$ l_ {xy} =κ_{xy}/（tσ_{xy}）$表现出相同的行为。
The Wiedemann-Franz (WF) law, stating that the Lorenz ratio $L = κ/(Tσ)$ between the thermal and electrical conductivities in a metal approaches a universal constant $L_0=π^2 k_B^2/ (3 e^2)$ at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at $T \to 0$. Instead, we propose using the leading low-temperature correction to the WF law, $L(T)-L_0$ (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi liquid, $L(T)-L_0\propto -T$. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi liquid, $L(T)-L_0$ is proportional to $-T^2$. This holds even when the resistivity grows linearly with $T$, due to $T-$linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, $L_{xy} = κ_{xy}/(Tσ_{xy})$, exhibits the same behavior.
