Time- and angle-resolved photoemission spectroscopy (tr-ARPES) constitutes a powerful tool to inspect the dynamics and thermalization of hot carriers. The identification of the processes that drive the dynamics, however, is challenging even for the simplest systems owing to the coexistence of several relaxation mechanisms. Here, we devise a Greens function formalism for predicting the tr-ARPES spectral function and establish the origin of carrier thermalization entirely from first principles. The predictive power of this approach is demonstrated by an excellent agreement with experiments for graphene over time scales ranging from a few tens of femtoseconds up to several picoseconds. Our work provides compelling evidence of a non-equilibrium dynamics dominated by the establishment of a hot-phonon regime.
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