论文标题
焦油加热不良金属和缓慢的金属
Joule heating in bad and slow metals
论文作者
论文摘要
提供给金属的热量被电子吸收，然后转移到晶格中。在传统的金属中，能量通过Lindhard Continuum发出的声子释放到晶格中。但是，在“不良”金属中，平均自由路径短，低能林哈德连续体被破坏。此外，在“慢速”金属中，费米速度小于声速，粒子孔对在运动学上是无法发出声子的。为了描述这些情况下的能量转移到晶格中，我们从电子密度光谱量$ \ text {im} \，g^r_ {nn}（ω_k，k）$上获得了能量放松率的一般公式。我们使用来自量子蒙特卡洛的最新数据和Ultracold Atoms中的实验来表征$ \ text {im} \，g^r_ {nnn}（ω_k，k，k）$，将久保公式应用于高温哈伯德模型。此外，我们还使用电子损失光谱的最新数据来估计库酸酯奇怪金属的能量弛豫率到高能光学声子。作为我们形式主义的第二个，独特的应用，我们认为“缓慢”的金属。这些被定义为具有小于声速的费米速度，因此粒子孔对在运动学上无法发射声子。我们从光导率方面获得了缓慢金属的能量松弛速率的表达。
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.
