Intermediate-Energy Charge-Transfer Excitations in the Cuprate Superconductors and the Photon Energy Dependence of the RIXS process

We present a study of the charge-transfer excitations of the structurally simple high-Tc superconductor HgBa$_2$CuO$_4+\delta$ and of the Mott insulator La$_2$CuO$_4$ using the burgeoning experimental technique of resonant inelastic X-ray scattering (RIXS). Our measurements address the 1-7 eV spectral range and place particular emphasis on the incident photon energy dependence of the cross section. Our results reveal clear evidence for a group of weakly-dispersing excitations \footnote{ L. Lu et al., \textit{Phys. Rev. Lett.} \textbf{95}, 217003 (2005).} \footnote{J. N. Hancock et al., unpublished.}. Collectively, these results call for the use of a multi-band theoretical approach for the description of the charge dynamics of high-Tc cuprate superconductors in this intermediate-energy regime.