不良和慢金属中的焦耳加热
Joule heating in bad and slow metals
摘要：
提供给金属的热量被电子吸收，然后传递到晶格。在传统的金属中，能量通过从林哈德连续谱发射的声子释放到晶格中。然而，在平均自由程短的“坏”金属中，低能林哈德连续谱被破坏。此外，在费米速度小于声速的“慢”金属中，粒子-空穴对在运动学上不能发射声子。为了描述能量转移到晶格在这些情况下，我们得到一个一般的Kubo公式的能量弛豫速率的电子密度谱权重$\text{Im} \, G^R_{nn}(ω_k,k)$评价声子色散$ω_k$。我们将我们的久保公式应用到高温哈伯德模型中，利用量子蒙特卡罗和超冷原子实验的最新数据来表征$\text{Im} \, G^R_{nn}(ω_k,k)$。此外，我们使用最近的数据从电子能量损失谱估计的能量弛豫速率的铜酸盐奇怪的金属的高能光学声子。作为我们的形式主义的第二个不同的应用，我们考虑“慢”金属。它们被定义为费米速度小于声速，这样粒子-空穴对在运动学上就不能发射声子。我们得到了慢金属的能量弛豫速率的表达式的光学电导率。
英文摘要：
Heat supplied to a metal is absorbed by the electrons and then transferred to the lattice. In conventional metals energy is released to the lattice by phonons emitted from the Lindhard continuum. However in a `bad' metal, with short mean free path, the low energy Lindhard continuum is destroyed. Furthermore in a `slow' metal, with Fermi velocity less than the sound velocity, particle-hole pairs are kinematically unable to emit phonons. To describe energy transfer to the lattice in these cases we obtain a general Kubo formula for the energy relaxation rate in terms of the electronic density spectral weight $\text{Im} \, G^R_{nn}(ω_k,k)$ evaluated on the phonon dispersion $ω_k$. We apply our Kubo formula to the high temperature Hubbard model, using recent data from quantum Monte Carlo and experiments in ultracold atoms to characterize $\text{Im} \, G^R_{nn}(ω_k,k)$. We furthermore use recent data from electron energy-loss spectroscopy to estimate the energy relaxation rate of the cuprate strange metal to a high energy optical phonon. As a second, distinct, application of our formalism we consider `slow' metals. These are defined to have Fermi velocity less than the sound velocity, so that particle-hole pairs are kinematically unable to emit phonons. We obtain an expression for the energy relaxation rate of a slow metal in terms of the optical conductivity.
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