Cumulant Green’s function approach for phonon satellites in resonant inelastic X-ray scattering

Resonant inelastic X-ray scattering (RIXS) probes various excitations in materials, including plasmons, magnons and phonons. Calculating RIXS spectra is challenging since it is a second-order process involving the coupling of core-excited states to bosonic collective modes, and requires summation over virtual intermediate states. Using a cumulant expansion [1], we develop a tractable excitonic Green’s function formulation of the RIXS cross section. We demonstrate our methodology by reproducing the phonon contribution to the RIXS spectrum of acetone [2].
The relative intensities of multiple phonon satellites are used to quantify the electron-phonon coupling strength. First, we show that RIXS actually probes exciton-phonon coupling, which can differ significantly from electron-phonon coupling. Second, we extend our numerical demonstration on acetone to the more challenging cases of quasi-1D Li₂CuO₂ and 3D SrTiO₃. This requires generalizing concepts of density functional perturbation theory to generate exciton-phonon coupling constants throughout the Brillouin zone. Comparison to experiment is made, resolving apparent anomalies in the spectra of Li₂CuO₂.

[1] Langreth, Phys Rev B 1, 471 (1970)
[2] Geondzhian and Gilmore, submitted