# Saturation of Strong Electron-Electron Umklapp Scattering at High Temperature

## TL;DR

This paper demonstrates that in clean three-dimensional metals at high temperatures, the electron-electron umklapp scattering rate saturates and becomes independent of temperature and inelastic scattering rate, explaining resistivity saturation.

## Contribution

It reveals a saturation phenomenon of umklapp scattering rate in 3D metals at high temperature, challenging the conventional understanding of its temperature dependence.

## Key findings

- Umklapp scattering rate saturates at high T.
- Saturation occurs when inelastic rate exceeds band splitting.
- Resistivity saturation is explained by this scattering behavior.

## Abstract

We consider clean metals, at finite temperature, in which the inelastic rate, $\hbar/ \tau_{ee}$, can become of the order of, or larger, than the band splitting energy. We show that in suchsystems, contrary to the common knowledge, the umklapp scattering rate becomes independent of both $\tau_{ee}$ and the temperature $T,$ in three dimensional systems. We discuss the relation of this phenomenon to the saturation of resistivity at high temperature.