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The rate of energy transfer between electrons and phonons is investigated bya first principles framework for electron temperatures up to $T_e=50000$ Kwhile considering the lattice at ground state. Two typical but differentlycomplex metals are investigated, namely Aluminium and Copper. In order toreasonably take the electronic excitation effect into account, we adopt finitetemperature density functional theory and linear response to determine theelectron-temperature-dependent Eliashberg function and electron density ofstates. Of the three branch-dependent electron-phonon coupling strengths, thelongitudinal acoustic mode plays a dominant role in the electron-phononcoupling for Aluminium for all temperatures considered here, but for Copper itonly dominates above an electron temperature of $T_e=40000$ K. The secondmoment of the Eliashberg function and the electron phonon coupling constant atroom temperature $T_e=315$ K show good agreement with other results. Forincreasing electron temperatures, we show the limits of the $T=0$ approximationfor the Eliashberg function. Our present work provides a rich perspective onthe phonon dynamics and this will help to improve insight into the underlyingmechanism of energy flow in ultra-fast laser-metal interaction.

Energy relaxation and electron-phonon coupling in laser-excited metals