Thermalization in simple metals: Role of electron-phonon and phonon-phonon scattering

We study the electron and phonon thermalization in simple metals excited by a laser pulse. The thermalization is investigated numerically by solving the Boltzmann equation taking into account the relevant scattering mechanism: electron-electron, electron-phonon (e-ph), phonon-electron (ph-e), and phonon-phonon (ph-ph) scattering. In the initial stage of the relaxation, most of the excitation energy is transferred from the electrons to phonons through the e-ph scattering. This creates hot high-frequency phonons due to the ph-e scattering, followed by an energy redistribution between phonon subsystems through the ph-ph scattering. This yields an overshoot of the total longitudinal-acoustic phonon energy at a time, across which a crossover occurs from a nonequilibrium state, where the e-ph and ph-e scattering frequently occur, to a state, where the ph-ph scattering occurs to reach a thermal equilibrium. This picture is quite different from the scenario of the well-known two-temperature model (2TM). The behavior of the relaxation dynamics is compared with those calculated by several models, including the 2TM, the four-temperature model, and nonequilibrium electron or phonon models. The relationship between the relaxation time and the initial distribution function is also discussed.