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Joule heating in bad and slow metals

by Paolo Glorioso, Sean A. Hartnoll

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Submission summary

Authors (as registered SciPost users): Paolo Glorioso · Sean Hartnoll
Submission information
Preprint Link: https://arxiv.org/abs/2202.00689v3  (pdf)
Date accepted: 2022-09-05
Date submitted: 2022-09-01 07:52
Submitted by: Glorioso, Paolo
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

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 $\text{Im} \, G^R_{nn}(\omega_k,k)$ evaluated on the phonon dispersion $\omega_k$. 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 $\text{Im} \, G^R_{nn}(\omega_k,k)$. 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.

Published as SciPost Phys. 13, 095 (2022)


Reports on this Submission

Report #2 by Anonymous (Referee 4) on 2022-9-1 (Invited Report)

Report

The authors have addressed all points raised in the previous round of review. I recommend the manuscript for publication.

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Report #1 by Anonymous (Referee 3) on 2022-9-1 (Invited Report)

Report

This is easy -- as I expressed in my first report, this paper is conceptually interesting and valuable. My report was intended to alert the authors that they should not overstate the quantitative significance of their findings. This is well understood by the authors the various tweaks in the resubmitted version do effectively mitigate this issue. This present version is more balanced and should be published in Scipost physics.

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