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The dynamics of band-gap renormalization and gain build-up in monolayerMoTe$_2$ is investigated by evaluating the non-equilibrium Dirac-Blochequations with the incoherent carrier-carrier and carrier-phonon scatteringtreated via quantum-Boltzmann type scattering equations. For the case where anapproximately $300$ fs-long high intensity optical pulse generatescharge-carrier densities in the gain regime, the strong Coulomb coupling leadsto a relaxation of excited carriers on a few fs time scale. The pump-pulsegeneration of excited carriers induces a large band-gap renormalization duringthe time scale of the pulse. Efficient phonon coupling leads to a subsequentcarrier thermalization within a few ps, which defines the time scale for theoptical gain build-up energetically close to the low-density exciton resonance.

Ultrafast band-gap renormalization and build-up of optical gain in monolayer MoTe$_2$