Theory of dispersive optical phonons in resonant inelastic x-ray scattering experiments

TL;DR

This paper investigates how phonon and electron dispersion affect RIXS spectra in solids, revealing significant momentum-dependent effects and challenges in data interpretation, extending beyond previous models that assumed dispersionless phonons.

Contribution

It introduces a new theoretical approach incorporating phonon and electron dispersion in RIXS analysis, providing deeper insight into the electron-phonon interaction in materials.

Findings

Dispersion significantly affects RIXS intensity and line shapes.

Mutual interplay of electron and phonon dispersion introduces momentum variations.

Results challenge simplified models assuming dispersionless phonons.

Abstract

The community currently lacks a complete understanding of how resonant inelastic x-ray scattering (RIXS) experiments probe the electron-phonon ($e$-ph) interaction in solids. For example, most theoretical models of this process have focused on dispersionless Einstein phonons. Using a recently developed momentum average (MA) variational approximation for computing RIXS spectra of band insulators, we examine the influence of both electron and phonon dispersion in the intermediate state of the scattering process. We find that the inclusion of either, and their mutual interplay, introduces significant momentum variations in the RIXS intensity, even for momentum-independent electron-phonon coupling. The phonon dispersion also induces nontrivial changes in the excitation line shapes, which can have a quantitative impact on the data analysis. These results highlight the considerable challenges of interpreting RIXS data in actual materials.