Electron–electron scattering limits thermal conductivity of metals under extremely high electron temperatures

Abstract

We report on the thermal transport properties of noble metals (gold, silver and copper) under conditions
of extremely high electron temperatures (that are on the order of the Fermi energy). We perform parameterfree
density functional theory calculations of the electron temperature-dependent electron-phonon coupling,
electronic heat capacities, and thermal conductivities to elucidate the strong role played by the excitation of
the low lying d-bands on the transport properties of the noble metals. Our calculations show that, although
the three metals have similar electronic band structures, the changes in their electron-phonon coupling at
elevated electron temperatures are drastically different; while electron-phonon coupling decreases in gold,
it increases in copper and, it remains relatively unperturbed for silver with increasing electron temperatures
of up to ∼60,000 K (or 5 eV). We attribute this to the varying contributions from acoustic and longitudinal
phonon modes to the electron-phonon coupling in the three metals. Although their electron-phonon
coupling changes with electron temperature, the thermal conductivity trends with electron temperature are
similar for all three metals. For instance, the thermal conductivities for all three metals reach their maximum
values (on par with the room-temperature values of some of the most thermally conductive semiconductors)
at electron temperatures of ∼6,000 K, and thereafter monotonically decrease due to the enhanced effect of
electron-electron scattering for electronic states that are further away from the Fermi energy. As such, only
accounting for electron-phonon coupling and neglecting electron-electron scattering can lead to large overpredictions
of the thermal conductivities at extremely high electron temperatures. Our results shed light
on the microscopic understanding of the electronic scattering mechanisms and thermal transport in noble
metals under conditions of extremely high electron temperatures and, as such, are significant for a plethora
of applications such as in plasmonic devices that routinely leverage hot electron transport.