A Unified First-Principles Description of Ultrafast Electron-Lattice Dynamics in Photoexcited Crystals

Ultrafast nonequilibrium spectroscopy has become a central tool in condensed matter physics, providing direct access to the coupled dynamics of electrons and lattice vibrations on their intrinsic timescales and opening new routes to the control of materials. A major open challenge in this context is the lack of a unified first-principles framework able to describe photoexcited solids while treating carrier--carrier, carrier--phonon, and phonon--phonon interactions on the same footing. This thesis addresses this problem by developing a first-principles real-time microscopic approach. The formalism combines density-matrix and nonequilibrium Green's function techniques to derive equations of motion for electronic occupations and microscopic polarisations together with mode-resolved phonon populations, allowing coherent renormalisation, dissipative scattering, hot-phonon dynamics, and coherent lattice motion to be described within a unified scheme. The framework is integrated into a practical computational workflow interfaced with standard first-principles electronic-structure codes, enabling material-specific real-time simulations on dense Brillouin-zone meshes. Its predictive capabilities are demonstrated through applications to representative systems. In monolayer MoS$_2$ and h-BN, the calculations clarify the hierarchy of ultrafast processes, the competition between scattering channels, and the role of photocarrier-induced screening in reshaping electronic, optical, and vibrational properties. In 1T-TiSe$_2$, a reduced first-principles description reproduces the time-dependent modulations observed in time-resolved ARPES and shows that they originate from anharmonic coherent motion along the photoexcited potential-energy landscape. In SnSe, the framework is used both to interpret time-resolved Se $K$-edge X-ray absorption measurements and to show that photoexcitation can drive the system along a nonthermal pathway towards transient and metastable structural phases, including the rocksalt topological crystalline insulating phase. Overall, the thesis shows that a unified first-principles treatment of coupled electron and lattice dynamics can provide both microscopic interpretation and predictive insight into ultrafast phenomena in solids.