<i>Ab initio</i> theory of coherent phonon damping in semimetals

Phonon decoherence determines the characteristic timescales over which coherent lattice vibrations decay, making it a crucial process for understanding the nonequilibrium dynamics of crystal lattices after excitation by a pump pulse. Here, we report a theoretical and computational investigation of the origin of phonon decoherence within a first-principles many-body framework. We derive quantum kinetic equations for the dynamics of coherent phonons by explicitly accounting for dissipation processes induced by electron-phonon and phonon-phonon interactions. The decoherence rate and frequency renormalization are formulated in terms of the nonequilibrium phonon self-energy, providing a framework amenable for calculations. To validate this approach, we conduct a first-principles study of phonon decoherence for the elemental semimetals antimony and bismuth. The robust agreement with available temperature- and fluence-dependent experimental data confirms the accuracy of our theoretical and computational framework. More generally, our findings reveal that either electron-phonon or phonon-phonon coupling can prevail in determining the decoherence time, depending on the temperature and driving conditions. Overall, this work fills a critical gap in the theoretical understanding of phonon decoherence, providing a predictive framework for determining the timescales of light-induced structural dynamics in driven solids.