Joule heating in bad and slow metals

Journal Article · Wed Oct 12 00:00:00 EDT 2022 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.13.4.095· OSTI ID:1891939

Glorioso, Paolo ^[1]; Hartnoll, Sean ^[2]

---

1. Stanford University
2. University of Cambridge

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. 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{lm} \, G^R_{nn}(\omega_{k},k) $\text{lm}{G}_{nn}^R({\omega }_k,k)$ evaluated on the phonon dispersion \omega_k ${\omega }_k$ . 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{lm} \, G^R_{nn}(\omega_{k},k) $\text{lm}{G}_{nn}^R({\omega }_k,k)$ . 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0019380
• OSTI ID: 1891939
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Vol. 13 Journal Issue: 4; ISSN 2542-4653
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English