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

The electron-phonon coupling and the corresponding energy exchange was investigated experimentally and by ab initio theory in non-equilibrium states of the free-electron metal aluminium. The temporal evolution of the atomic mean squared displacement in laser-excited thin free-standing films was monitored by femtosecond electron diffraction. The electron-phonon coupling strength was obtained for a range of electronic and lattice temperatures from density functional theory molecular dynamics (DFT-MD) simulations. The electron-phonon coupling parameter extracted from the experimental data in the framework of a two-temperature model (TTM) deviates significantly from the ab initio values. We introduce a non-thermal lattice model (NLM) for describing non-thermal 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-principle calculations besides 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 electron-phonon 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.