Joule heating in bad and slow metals
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 destro...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2022-10-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.13.4.095 |
| _version_ | 1798020632658575360 |
|---|---|
| author | Paolo Glorioso, Sean A. Hartnoll |
| author_facet | Paolo Glorioso, Sean A. Hartnoll |
| author_sort | Paolo Glorioso, Sean A. Hartnoll |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T17:00:39Z |
| format | Article |
| id | doaj.art-e491c485f6cd482d8144d5a4a63ee110 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-11T17:00:39Z |
| publishDate | 2022-10-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-e491c485f6cd482d8144d5a4a63ee1102022-12-22T04:13:10ZengSciPostSciPost Physics2542-46532022-10-0113409510.21468/SciPostPhys.13.4.095Joule heating in bad and slow metalsPaolo Glorioso, Sean A. HartnollHeat 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.https://scipost.org/SciPostPhys.13.4.095 |
| spellingShingle | Paolo Glorioso, Sean A. Hartnoll Joule heating in bad and slow metals SciPost Physics |
| title | Joule heating in bad and slow metals |
| title_full | Joule heating in bad and slow metals |
| title_fullStr | Joule heating in bad and slow metals |
| title_full_unstemmed | Joule heating in bad and slow metals |
| title_short | Joule heating in bad and slow metals |
| title_sort | joule heating in bad and slow metals |
| url | https://scipost.org/SciPostPhys.13.4.095 |
| work_keys_str_mv | AT paologloriososeanahartnoll jouleheatinginbadandslowmetals |