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

摘要

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 bythe core-hole potential was treated within the Born approximation, and acrude-model density of states was used for the $4p$ band. We improve theanalysis by taking account of the multiple scattering in Cu3d-O$2p$ bands andby using a realistic $4p$ DOS obtained from a band calculation. The multiplescattering effect is evaluated with the use of the time representationdeveloped by Nozi\`eres and De Dominicis. It is found that the multiplescattering effect makes the $K$-edge peak in the absorption coefficient shiftto the lower energy region as a function of photon energy, that is, the photonenergy required to excite the $1s$ electron to the $K$-edge peak reduces. It isalso found that the multiple-scattering effect does not change the two-peakstructure in the RIXS spectra but modifies slightly the shape as a function ofenergy loss. These findings suggests that the multiple scattering effect couldmainly be included into a renormalization of the core-level energy and partlyjustify the Born approximation, leading to a future application to the RIXS inthree-dimensional systems.