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Time- and angle-resolved photoemission spectroscopy (TR-ARPES) accesses theelectronic structure of solids under optical excitation, and is a powerfultechnique for studying the coupling between electrons and collective modes. Oneapproach to infer electron-boson coupling is through the relaxation dynamics ofoptically-excited electrons, and the characteristic timescales of energyredistribution. A common description of electron relaxation dynamics is throughthe effective electronic temperature. Such a description requires thatthermodynamic quantities are well-defined, an assumption that is generallyviolated at early delays. Additionally, precise estimation of the non-thermalwindow -- within which effective temperature models may not be applied -- ischallenging. We perform TR-ARPES on graphite and show that Boltzmann rateequations can be used to calculate the time-dependent electronic occupationfunction, and reproduce experimental features given by non-thermal electronoccupation. Using this model, we define a quantitative measure of non-thermalelectron occupation and use it to define distinct phases of electron relaxationin the fluence-delay phase space. More generally, this approach can be used toinform the non-thermal-to-thermal crossover in pump-probe experiments.

Establishing non-thermal regimes in pump-probe electron-relaxation dynamics