Ultrafast thermalization pathways of excited bulk and surface statesin the ferroelectric Rashba semiconductor GeTe

In ferroelectric Rashba semiconductors, the study of nonequilibrium properties is particularly attractive. In this work we use time-resolved ARPES to access ultrafast dynamics of bulk and surface Rashba bands after fs optical excitation of GeTe. We observe a complex thermalisation pathway with three distinguishable timescales: intraband thermalisation, interband equilibration and electronic cooling due to electron-phonon coupling. The last two timescales show an intriguing temperature dependence. While electronic cooling speeds up with increasing sample temperature, the opposite happens for interband equilibration. To explain such counterintuitive effect we use our novel numerical solver [1,2,3] for the full, non-linearised, time-dependent Boltzmann scattering equation and compute temperature-dependent momentum-resolved lifetimes, for 21 electron-electron and 9 electron-phonon scatterings. All electron-phonon scatterings strengthen with increasing temperature. But counterintuitively, the electron-electron scatterings with largest phase-space get weaker with increasing temperature. We also find these features to survive the removal of spin-dependent selection rules in the scattering, showing that they are an effect of the Rashba splitting rather than of the wavefunction overlap.