Incident-energy-dependent spectral weight of resonant inelastic x-ray scattering in doped cuprates

We theoretically investigate the incident-photon energy ${\ensuremath{\omega}}_{\mathrm{i}}$ dependence of resonant inelastic x-ray scattering (RIXS) tuned for the Cu $L$ edge in cuprate superconductors by using the exact diagonalization technique for a single-band Hubbard model. Depending on the value of core-hole Coulomb interaction in the intermediate state, RIXS for non-spin-flip channel shows either a ${\ensuremath{\omega}}_{\mathrm{i}}$-dependent fluorescencelike or ${\ensuremath{\omega}}_{\mathrm{i}}$-independent Raman-like behavior for hole doping. An analysis of x-ray absorption suggests that the core-hole Coulomb interaction is larger than on-site Coulomb interaction in the Hubbard model, resulting in a fluorescencelike behavior in RIXS consistent with recent RIXS experiments. A shift on the high-energy side of the center of spectral distribution is also predicted for electron-doped systems though spectral weight is small. Main structures in the spin-flip channel exhibit a Raman-like behavior as expected, accompanied with a fluorescencelike behavior with small intensity.