Exciton-exciton annihilation, in which two excitons interact to generate high-energy excitations, is an important nonradiative channel in light-induced excited-state relaxation. When efficient, this process offers an alternative route to exciton emission, potentially allowing extended energetically excited particle lifetime and coherence. These properties are significant in designing and understanding materials-based quantum devices, particularly for low-dimensional semiconductors. Here, we present a first-principles framework to compute exciton-exciton annihilation mechanisms and rates using many-body perturbation theory within the GW and Bethe-Salpeter equation formalism. Our method explicitly accounts for Coulomb-driven and phonon-assisted exciton-exciton scattering by explicitly evaluating the interaction channels between the constituent electrons and holes composing the Bethe-Salpeter equation excitons. We apply this framework to monolayer ${\mathrm{WSe}}_2$ and explore the $A$, $B$ excitation manifolds, finding picosecond-scale annihilation between bright and dark states, cross valleys, and cross peak manifolds. These channels become allowed due to scattering into free electron-hole pairs across the Brillouin zone. Our results supply new insights into nonradiative exciton relaxation mechanisms in two-dimensional materials, providing a predictive and general tool for modeling these interactions in excitonic materials.

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• Bethe-Salpeter equation
• Excitons
• Transition metal dichalcogenides
• GW method
• Many-body techniques