Theory of the electron relaxation in metals excited by an ultrashort optical pump

TL;DR

This paper develops a detailed theoretical model for electron relaxation in metals after ultrashort optical excitation, revealing a two-stage energy relaxation process involving phonon emission and electron-phonon thermalization.

Contribution

The theory incorporates both electron-electron and electron-phonon collisions, extending beyond the two temperature model to explain the relaxation dynamics.

Findings

90% of energy is emitted via phonons before electron thermalization.

The second relaxation stage involves small energy transfer, explaining the absence of divergence at low temperatures.

The two temperature model is a limiting case of the developed theory.

Abstract

The theory of the electron relaxation in metals excited by an ultrashort optical pump is developed on the basis of the solution of the linearized kinetic equation. The kinetic equation includes both the electron-electron and the electron-phonon collision integrals. The widely used two temperature model follows from the theory as the limiting case, when the thermalization due to the electronelectron collisions is fast with respect to the electron-phonon relaxation. It is demonstrated that the energy relaxation has two consecutive processes. The first and most important step describes the emission of phonons by the photo-excited electrons. It leads to the relaxation of 90% of the energy before the electrons become thermalized among themselves. The second step describes electronphonon thermalization and may be described by the two temperature model. The second stage is difficult to observe experimentally because it involves the transfer of only a small amount of energy from electrons. Thus the theory explains why the divergence of the relaxation time at low temperatures was never observed experimentally.