Beyond the single-site approximation modeling of electron-phonon coupling effects on resonant inelastic X-ray scattering spectra

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.

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

“…( 2) captures the core-hole's influence on the system in the intermediate state via a local core-hole potential. We note that although the bare U Q potential is purely local, the effective potential can extend over the entire lattice (albeit decaying very fast away from the core hole) [16,19,20] once dressed by the e-ph interaction.…”

“…In order to focus on the effects of the electron and phonon dispersions, we have omitted the geometric prefactors associated with the dipole matrix elements. The specific elemental edge does not matter at our level of modeling [16].…”

“…Our choice for U Q is smaller than the U Q ∼ 4-6 eV typically adopted in the literature [4,12,[24][25][26], so as to partially account for the interaction between the core hole and the lattice. As discussed previously [16], the core-hole-lattice coupling, which is neglected in Eq. ( 1), can frustrate polaron formation in the valence band.…”

“…Recently, we introduced an efficient variational method for computing RIXS spectra for band insulators [16]. Our method is built on the Momentum Average (MA) class of variational approximations [17,18] and allows us to treat situations wherein the intermediate state of the RIXS process, a core electron is excited into an empty band and is allowed to interact with the lattice.…”

“…Additional technical details can be found in the Supplementary Material, as well as Refs. [16][17][18].…”