Phonon-induced long-lasting nonequilibrium in the electron system of a laser-excited solid

Abstract

Electron-electron thermalization and electron-phonon relaxation processes in laser-excited solids are often assumed to occur on different timescales. This is true for the majority of the conduction band electrons in a metal. However, electron-phonon interactions can influence the thermalization process of the excited electrons. We study the interplay of the underlying scattering mechanisms for the case of a noble metal with help of a set of complete Boltzmann collision integrals. We trace the transient electron distribution in copper and its deviations from a Fermi-Dirac distribution due to the excitation with an ultrashort laser pulse. We investigate the different stages of electronic nonequilibrium after an excitation with an ultrashort laser-pulse of 800 nm wavelength and 10 fs pulse duration. Our calculations show a strong nonequilibrium during and directly after the end of the laser pulse. Subsequently, we find a fast thermalization of most electrons. Surprisingly, we observe a long-lasting nonequilibrium, which can be attributed to the electron-phonon scattering. This nonequilibrium establishes at energies around peaks in the density of states of the electrons and persists on the timescale of electron-phonon energy relaxation. It influences in turn the electron phonon coupling strength. * weber@physik.uni-kl.de 1 A. Vogel and V. Venugopalan, Chemical Reviews 103, 577

Energy Relaxation and Electron–Phonon Coupling in Laser-Excited Metals

“…If the initial state is a solid, the lattice is heated due to electron–phonon energy transfer to a new thermal equilibrium over several (tens to hundreds of) picoseconds. During this evolution, many interesting effects such as the ultrafast electron and non-equilibrium phonon dynamics [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], changes in lattice stability [ 20 , 21 , 22 , 23 , 24 ], phase transitions [ 25 , 26 , 27 , 28 , 29 , 30 ], and non-equilibrium electron–phonon interactions [ 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 ] take place. It should be pointed out that these various physical processes are all driven by electronic excitations.…”

Nonequilibrium Band Occupation and Optical Response of Gold After Ultrafast XUV Excitation

“…Such behaviour has also been observed for the very different case of ultrafast magnetisation of itinerant ferromagnets 40 . It proves that signatures of electronic nonequilibrium can be present on much longer time scales than suggested by the relaxation time 29,41 . Of course, this effect is more prominent for the case with stronger electron-phonon coupling.…”

“…Here, we have chosen τ relax = 200 fs. This time scale is within existing bounds: it should be considerably longer than the fully kinetic phase that establishes Fermi-like distributions in each band and takes a few femtoseconds 29,36,37 and it must be shorter than the time resolution of previous measurements (540 fs) that could be described by equilibrium densities 9,50 . The value we have taken here is thus near the upper limit to yield estimates for the minimum time resolution an experiment must have to investigate these effects.…”

“…Both lattice heating and strong changes in the electronic structure can trigger phase transitions 13,14,25 . Despite the consensus on the general behaviour, the time scales of the different stages and the importance of specific processes are highly debated 4,[26][27][28][29] .…”

Effect of Nonequilibrium Transient Electronic Structures on Lattice Stability in Metals: Density Functional Theory Calculations

“…The electron excitation can be considered as nonthermal process, and the electronic subsystem reaches local equilibrium by electron-electron collisions, described by Fermi-Dirac distribution [40]. In the next step, the crystalline structure will be rearranged after laser excitation, and the energy will be transferred from the excited electrons to the lattice by electron-phonon coupling [41][42][43].The whole system is in a nonequilibrium state until the electron-phonon equilibration is reached [40,44,45]. During this period, the lattice temperature is lower than the electron temperature.…”