Theory of resonant inelastic x-ray scattering at the K edge in La$_2$CuO$_4$ - Multiple scattering effects -

TL;DR

This paper develops an improved theoretical model for RIXS at the K edge in La$_2$CuO$_4$, incorporating multiple scattering effects and realistic band structures, revealing shifts in absorption peaks and minor spectral shape modifications.

Contribution

The authors extend previous RIXS theory by including multiple scattering effects and realistic $4p$ density of states, enhancing the accuracy of spectral predictions for La$_2$CuO$_4$.

Findings

Multiple scattering shifts the K-edge peak to lower energy.

The two-peak structure in RIXS spectra remains largely unchanged.

Multiple scattering effects can be approximated by core-level energy renormalization.

Abstract

We develop a theory of resonant inelastic x-ray scattering (RIXS) at the $K$ edge in La$_2$CuO$_4$ on the basis of the Keldysh Green's function formalism. In our previous analysis (Phys. Rev. B 71, 035110 (2005)), the scattering by the core-hole potential was treated within the Born approximation, and a crude-model density of states was used for the $4p$ band. We improve the analysis by taking account of the multiple scattering in Cu3d-O$2p$ bands and by using a realistic $4p$ DOS obtained from a band calculation. The multiple scattering effect is evaluated with the use of the time representation developed by Nozi\`eres and De Dominicis. It is found that the multiple scattering effect makes the $K$-edge peak in the absorption coefficient shift to the lower energy region as a function of photon energy, that is, the photon energy required to excite the $1s$ electron to the $K$-edge peak reduces. It is also found that the multiple-scattering effect does not change the two-peak structure in the RIXS spectra but modifies slightly the shape as a function of energy loss. These findings suggests that the multiple scattering effect could mainly be included into a renormalization of the core-level energy and partly justify the Born approximation, leading to a future application to the RIXS in three-dimensional systems.