Real-Time Relaxation Dynamics of Dark Excitons in Mirror-Symmetric Monolayers

Symmetry governs which exciton-phonon (exc-ph) scattering channels can exist, but not which a relaxing exciton actually uses. Combining group theory with ab initio many-body perturbation theory, we derive the mirror parity σ h, of finite-momentum excitons in planar D 3h monolayers, and form exact exc-ph selection rules that hold across the whole Brillouin zone. The parity of the lowest exciton band changes across a closed contour. The even phonons connect states of the same parity, while odd phonons connect states of opposite parity. We use these rules to compute exciton linewidths and we solve the real-time Boltzmann transport equation for monolayer GaN as the test case and benchmark it against monolayer hBN.