Real-Time Dynamics of Electrons and Phonons from First Principles

Ultrafast laser excitation drives solids far from equilibrium, producing transient electronic and lattice states that cannot be described by equilibrium theories or phenomenological models such as the two-temperature model. This dissertation develops and applies a real-time, ab initio framework based on the time-dependent Boltzmann equation (TDBE) to investigate coupled electron–phonon dynamics in crystalline solids from femtosecond to picosecond timescales. The approach explicitly resolves the dynamics of momentum- and mode-dependent electron and phonon populations, where electron–phonon and phonon–phonon scatterings are explicitly computed from first principles without empirical parameters. The methodology is applied to photoexcited transition metal dichalcogenides, where the relaxation of these nonequilibrium states is shown to occur over hundreds of femtoseconds to several picoseconds through phonon–phonon scattering. Validation is achieved through direct comparison with ultrafast electron diffuse scattering experiments on bulk MoS2, revealing distinct stages of phonon thermalization and enabling identification of carrier-induced screening effects. In addition, a first-principles theory of coherent phonon damping is developed using many-body perturbation theory, demonstrating that phonon frequency renormalization and decay are governed by the phonon self-energy arising from electron–phonon and phonon–phonon interactions. Together, these results provide a unified microscopic description of ultrafast lattice dynamics in photoexcited materials.