Conduction Band Structure and Ultrafast Dynamics of Ferroelectric $\alpha$-GeTe(111)

$\alpha$-GeTe(111) is a non-centrosymmetric ferroelectric (FE) material for which a significative lattice distortion combined with a strong spin-orbit interaction gives rise to giant Rashba split states in the bulk and at the surface, which have been intensively probed in the occupied valence states using static angle-resolved photoemission spectroscopy (ARPES). Nevertheless, its unoccupied conduction band structure remains unexplored, in particular the experimental determination of its electronic band gap across momentum space. Using time-resolved ARPES based on high-repetition rate and extreme ultraviolet femtosecond (fs) laser, we unveil the band structure of $\alpha$-GeTe(111) in the full Brillouin zone, both in the valence and conduction states, as well as the exploration of its out-of-equilibrium dynamics. Our work confirms the semiconducting nature of $\alpha$-GeTe(111) with a 0.85 eV indirect band gap, which provides an upper limit for comparison to density functional theory calculations. We finally reveal the dominant scattering mechanisms of photoexcited carriers during the out-of-equilibrium dynamics under fs light pulses.