Theoretical investigation of momentum-dependent carrier-carrier scattering from crystal-strong laser interaction

Ultrafast electron-electron scattering is widely believed to dominate coherence loss in strongly driven solids, yet its microscopic, momentum-resolved description under intense laser excitation remains lacking. In current solid-state high-harmonic generation (HHG) modeling, the dephasing time T₂ is typically introduced phenomenologically, without a field-dependent many-body derivation. Here we develop a first-principles microscopic theory of carrier-carrier scattering in strongly field-driven crystalline solids. Starting from a Born-Markov quantum master equation in the Houston-Floquet basis, we derive a field-dressed Fermi's golden rule for the momentum-resolved dephasing rate Γ(k), in which the driving laser field explicitly modifies scattering matrix elements, occupation factors, screening, and energy conservation. We demonstrate that the rapid formation of a nonequilibrium carrier plasma under mid-infrared excitation dramatically enhances electron-electron scattering through phase-space expansion and Floquet-dressed Coulomb interactions, rendering it the dominant dephasing channel while electron-phonon scattering remains comparatively weak. This microscopic framework quantitatively explains the few-femtosecond coherence times universally extracted from HHG experiments. Finally, we show that the full momentum-dependent decoherence kernel, Γ(k), can be reconstructed from measured HHG spectra, thereby establishing solid-state HHG as a nonlinear spectroscopy of ultrafast many-body scattering in solids.