We demonstrate the feasibility of the time-linear scaling formulation of the $GW$ method [Phys. Rev. Lett. 124, 076601 (2020)] for ab initio simulations of optically driven two-dimensional materials. The time-dependent $GW$ equations are derived and solved numerically in the basis of Bloch states. We address carrier multiplication and relaxation in photoexcited graphene and find deviations from the typical exponential behavior predicted by the Markovian Boltzmann approach. For a resonantly pumped semiconductor we discover a self-sustained screening cascade leading to the Mott transition of coherent excitons. Our results draw attention to the importance of non-Markovian and dynamical screening effects in out-of-equilibrium phenomena.

• Received 30 September 2021
• Accepted 18 November 2021

DOI:https://doi.org/10.1103/PhysRevLett.128.016801