Electron-phonon coupling and energy flow in a simple metal beyond the two-temperature approximation

Abstract

The electron-phonon coupling and the corresponding energy exchange are investigated experimentally and by ab initio theory in nonequilibrium states of the free-electron metal aluminium. The temporal evolution of the atomic mean-squared displacement in laser-excited thin freestanding films is monitored by femtosecond electron diffraction. The electron-phonon coupling strength is obtained for a range of electronic and lattice temperatures from density functional theory molecular dynamics simulations. The electron-phonon coupling parameter extracted from the experimental data in the framework of a twotemperature model (TTM) deviates significantly from the ab initio values. We introduce a nonthermal lattice model (NLM) for describing nonthermal phonon distributions as a sum of thermal distributions of the three phonon branches. The contributions of individual phonon branches to the electron-phonon coupling are considered independently and found to be dominated by longitudinal acoustic phonons. Using all material parameters from first-principles calculations except the phonon-phonon coupling strength, the prediction of the energy transfer from electrons to phonons by the NLM is in excellent agreement with time-resolved diffraction data. Our results suggest that the TTM is insufficient for describing the microscopic energy flow even for simple metals like aluminium and that the determination of the electronphonon coupling constant from time-resolved experiments by means of the TTM leads to incorrect values. In contrast, the NLM describing transient phonon populations by three parameters appears to be a sufficient model for quantitatively describing electron-lattice equilibration in aluminium. We discuss the general applicability of the NLM and provide a criterion for the suitability of the two-temperature approximation for other metals.