Excitation Pathways in Resonant Inelastic X-ray Scattering of Solids

Resonant inelastic x-ray scattering (RIXS) is a powerful spectroscopic technique that offers an elemental- and orbital-selective probe of the electronic excitations over a huge energy range. In this talk, we present a novel many-body approach to determine RIXS spectra in solids, yielding an intuitive expression for the RIXS cross section in terms of pathways between intermediate many-body states containing a core hole, and final many-body states containing a valence hole. Explicit excited many-body states are obtained from the diagonalization of the Bethe-Salpeter equation in an all-electron framework. For the paradigmatic examples of the fluorine K edge of LiF and the carbon K edge in diamond, we show how the excitation pathways determine the spectral shape of the emission, and demonstrate the nontrivial role of electron-hole correlation in the RIXS spectra. Finally, we discuss for the example of Ga₂O₃ how RIXS can be employed to determine the nature of bound valence excitons and probes the valence hole distribution of the bound excitons in this material.