The coupled nonequilibrium dynamics of electrons and phonons in monolayer MoS2 is investigated by combining first-principles calculations of the electron-phonon and phonon-phonon interaction with the time-dependent Boltzmann equation. Strict phase-space constraints in the electron-phonon scattering are found to influence profoundly the decay path of excited electrons and holes, restricting the emission of phonons to crystal momenta close to few high-symmetry points in the Brillouin zone. As a result of momentum selectivity in the phonon emission, the nonequilibrium lattice dynamics is characterized by the emergence of a highly-anisotropic population of phonons in reciprocal space, which persists for up to 10 ps until thermal equilibrium is restored by phonon-phonon scattering. Achieving control of the nonequilibrium dynamics of the lattice may provide unexplored opportunities to selectively enhance the phonon population of two-dimensional crystals and, thereby, transiently tailor electron-phonon interactions over sub-picosecond time scales.
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