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

The dynamics of the band-gap renormalization and gain build-up in monolayer MoTe$_2$ is investigated by solving the non-equilibrium Dirac-Bloch equations where the incoherent carrier-carrier and carrier-phonon scattering is treated via quantum-Boltzmann type scattering equations. The pump-pulse generation of excited charge carriers induces a large band-gap renormalization during the time-scale of the pulse. Efficient phonon coupling leads to a subsequent carrier thermalization which defines the time scale for the optical gain build-up energetically close to the low-density exciton resonance.