First-principles description of pumped inelastic x-ray scattering: Example of K-edge RIXS in graphite

We present an ab initio framework for predicting resonant inelastic x-ray scattering (RIXS) in optically pumped materials. Our methodology is based on the Kramers-Heisenberg formula for the double-differential cross section formulated using the results of the Bethe-Salpeter equation from many-body perturbation theory. To extend this approach to the time domain, we incorporate non-equilibrium charge-carrier distributions obtained from real-time, time-dependent density-functional theory. Generalizing the RIXS implementation with respect to arbitrary polarizations allows us to consider different orientations of incoming and outgoing light. We demonstrate our method's capabilities by studying RIXS at the K-edge of graphite for various non-equilibrium charge-carrier distributions, representing different delay times after optical pumping. Our results reveal angular dependencies in π- and σ-orbital-derived spectral regions, in good agreement with the experiment.