Intervalley scattering in MoS$_2$ imaged by two-photon photoemission with a high-harmonic probe

We report on the direct mapping of electron transfer in the momentum space of bulk MoS$_2$ by means of time- and angle-resolved two-photon photoemission with a high-harmonic probe. For this purpose, we have combined a high-repetition rate high-harmonic source with tunable femtosecond pump pulses and a 3D ($k_x, k_y, E$) electron spectrometer. We show that optical excitation slightly above the A exciton resonance results in an immediate occupation of the conduction band at $\overline{K}$ followed by an ultrafast transfer ($< 50$~fs) to the conduction band minimum at $\overline{\Sigma}$. Both signals, at $\overline{K}$ and $\overline{\Sigma}$, do not vanish over the observed period of 400~fs. The technique described here enables direct access to the charge transfer dynamics in $k$-space and allows the study of decay times and decay channels in various systems with dependence on the excess energy or helicity of the excitation.