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

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 parameter-free 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 lyingd-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 ∼6000 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 over-predictions 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.