Thermal conductivity of metals with hot electrons

Abstract

The action of an ultrashort laser pulse transforms a metal into a two-temperature (2T) state with different temperatures of the electron and ion subsystems (Te ≫ Ti). The metal stays in this state in a rather long time interval (from several to several tens of picoseconds depending on the metal). The 2T stage is very important since it includes 2T relaxation, in which laser energy is transferred to ions, and the formation of a heated layer, which plays a key role in the subsequent dynamics. The kinetic coefficients of a condensed medium with hot electrons are poorly known: researchers use phenomenological dependences consisting of asymptotics at low and high temperatures Te. However, it is impossible to perform a numerical simulation of the interaction of laser radiation with a substance without these coefficients. In this work, the thermal conductivity is calculated using a kinetic equation for the first time. This calculation is valid at low (Te ≪ TF = EF/kB, where EF is the Fermi energy and kB is the Boltzmann constant) and moderate (Te < TF) temperatures. The earlier kinetic calculations are related to the case of Te < TF, where the calculations of, e.g., the electron-electron collision frequency are significantly simplified due to the reduction of multiple integration to integration in a small neighborhood of the Fermi sphere. In our case, integration at moderate temperatures should be performed over the entire volume of momentum space.