Ultrafast band-gap renormalization and build-up of optical gain in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>MoTe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

The dynamics of band-gap renormalization and gain build-up in monolayer ${\mathrm{MoTe}}_{2}$-H is investigated by evaluating the nonequilibrium Dirac-Bloch equations with the incoherent carrier-carrier and carrier-phonon scattering treated via quantum-Boltzmann type scattering equations. For the case where an approximately 300-fs-long high-intensity optical pulse generates charge-carrier densities in the gain regime, the strong Coulomb coupling leads to a relaxation of excited carriers on a few-femtosecond timescale. The pump-pulse generation of excited carriers induces a large band-gap renormalization during the timescale of the pulse. Efficient phonon coupling leads to a subsequent carrier thermalization within a few picoseconds, which defines the timescale for the optical gain build-up energetically close to the low-density exciton resonance.