Phonon RIXS theory for a mobile electron*

Electron-phonon coupling lies at the heart of conventional superconductivity and, it is hoped, its better understanding in high temperature superconductors might help elucidate some of the mysteries still surrounding those materials. RIXS is a novel, emerging spectroscopic technique, that only recently started approaching the resolving power needed for phononic features. Thus, theoretical predictions concerning phonon RIXS are becoming timely in this rapidly developing field. We apply the Momentum Average (MA) Green's function technique to the problem of phonon RIXS calculations, in order to improve on the widely utilized treatment derived from a localised electron theory, while avoiding the finite size issues inherent in exact diagonalization. We show that the role of electron mobility is important, especially for a strongly screened core hole, resulting in significant departures from the predictions of the localised theory. This points to MA as a promising and flexible alternative to existing approaches to theoretical treatment of RIXS.