Electron thermalization behavior in graphene using TDDFT

Thermalization behavior at extreme electronic temperatures is central to understanding how materials respond to high-intensity laser excitation. Because this is a highly non-linear regime, traditional perturbative approaches fail. In this work, we use real-time Time-Dependent Density Functional Theory (rt-TDDFT) to study how electronic states in monolayer graphene thermalize under ultrafast laser driving. Using the Octopus code, we track the time-dependent occupations by projecting time-evolved wavefunctions onto the ground-state basis, allowing us to reconstruct an effective electronic distribution at each timestep in the groundstate Kohn-Sham basis. We look at the nature of thermalization in TDDFT by comparing how close the distribution comes to resembling the Fermi-Dirac distribution over time. The distribution was also used to calculate thermodynamic properties like Entropy and Free energy. Results show that the single-orbital occupations oscillate at the laser carrier frequency, whereas the extracted thermodynamic quantities oscillate at a much lower beat frequency, consistent with a Rabi-like response in the driven electronic subspace. The results provide insights into the timescales and mechanisms governing thermalization in graphene, providing a more complete picture of how TDDFT encodes thermal behavior in driven quantum systems.