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Comprehending nonequilibrium electron-phonon dynamics at the microscopiclevel and at the short time scales is one of the main goals in condensed matterphysics. Effective temperature models and time-dependent Boltzmann equationsare standard techniques for exploring and understanding nonequilibrium stateand the corresponding scattering channels. However, these methods consider onlythe time evolution of carrier occupation function, while the self-consistentphonon dressing in each time instant coming from the nonequilibrium populationis ignored, which makes them less suitable for studying ultrafast phenomenawhere softening of the phonon modes plays an active role. Here, we combineab-initio time-dependent Boltzmann equations and many-body phonon self-energycalculations to investigate the full momentum- and mode-resolved nonadiabaticphonon renormalization picture in the MoS$_2$ monolayer under nonequilibriumconditions. Our results show that the nonequilibrium state of photoexcitedMoS$_2$ is governed by multi-valley topology of valence and conduction bandsthat brings about characteristic anisotropic electron-phonon thermalizationpaths and the corresponding phonon renormalization of strongly-coupled modesaround high-symmetry points of the Brillouin zone. As the carrier population isthermalized towards its equilibrium state, we track in time the evolution ofthe remarkable phonon anomalies induced by nonequilibrium and the overallenhancement of the phonon relaxation rates. This work shows potentialguidelines to tailor the electron-phonon relaxation channels and control thephonon dynamics under extreme photoexcited conditions.

Ultrafast nonadiabatic phonon renormalization in photoexcited single-layer MoS$_2$