Hot electron relaxation in metals within the G\"otze-W\"olfle memory function formalism

TL;DR

This paper extends the memory function formalism to analyze non-equilibrium hot electron relaxation in metals, deriving analytical scattering rates and revealing temperature difference independence at high regimes.

Contribution

It introduces a generalized formalism for hot-electron relaxation, providing analytical expressions for scattering rates across various regimes, and highlights new temperature-independent behaviors.

Findings

High-temperature dc scattering rate is independent of electron-phonon temperature difference.

High-frequency optical scattering rate remains unaffected by temperature difference.

The formalism aligns with previous studies in limiting cases.

Abstract

We consider non-equilibrium relaxation of electrons due to their coupling with phonons in a simple metal. In our model electrons are living at a higher temperature than that of the phonon bath, mimicking a non-equilibrium steady state situation. We study the relaxation of such hot electrons proposing a suitable generalization of the memory function formalism formulated by G\"otze and W\"olfle[Phys. Rev. B 6, 1226 (1972)]. We derive analytical expressions for both dc and optical scattering rates in various temperature and frequency regimes. Limiting cases are in accord with the previous studies. An interesting feature, that the dc scattering rate at high temperatures and optical scattering rate at high frequencies, are independent of the temperature difference between the electrons and the phonons is found in this study. The present formalism forms a basis which can also be extended to study hot-electron relaxation in more complex situations