Abstract
Resonant inelastic X-ray scattering (RIXS) is used increasingly for characterizing low-energy collective excitations in materials. RIXS is a powerful probe, which often requires sophisticated theoretical descriptions to interpret the data. In particular, the need for accurate theories describing the influence of electron-phonon (e-p) coupling on RIXS spectra is becoming timely, as instrument resolution improves and this energy regime is rapidly becoming accessible. To date, only rather exploratory theoretical work has been carried out for such problems. We begin to bridge this gap by proposing a versatile variational approximation for calculating RIXS spectra in weakly doped materials, for a variety of models with diverse e-p couplings. Here, we illustrate some of its potential by studying the role of electron mobility, which is completely neglected in the widely used local approximation based on Lang-Firsov theory. Assuming that the e-p coupling is of the simplest, Holstein type, we discuss the regimes where the local approximation fails, and demonstrate that its improper use may grossly underestimate the e-p coupling strength.
Highlights
As we show in the following, this leads to a q dependence of the RIXS spectra that is entirely missed by the single-site approximation
The resonance peak is shifted in part by the polaron formation energy, which is already captured in the single-site Lang-Firsov calculation
We find that the RIXS intensity predicted by the Momentum Average (MA) approximation with p ≥ 1 depends on the transferred momentum q, even though we are studying a simple model where neither the phonon spectrum nor the electron-phonon coupling have any explicit momentum dependence
Summary
Resonant inelastic X-ray scattering [1] is being increasingly used to study electron-phonon (e-p) interactions in quantum materials [2,3,4,5,6,7,8,9,10,11,12,13]. Early efforts focused on extending the approach to small clusters using exact diagonalization (ED) [4, 8] While these models are only able to retain a limited subset of phonon modes, they do capture the effects of electron itineracy over a few unit cells, and produce results in qualitative agreement with the single-site model (no quantitative comparison of the intensities predicted by each model has been made). We demonstrate that electron mobility in the intermediate state produces a momentum dependence in the intensity of the phonon excitations, even when both the underlying e-p coupling, and the phonon dispersion, are momentum independent These results should be kept in mind when using the single-site model to do quantitative RIXS analysis. We include a short Appendix outlining the calculation of the non-interacting Green’s functions in the presence of the on-site core hole potential
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