We present a three-band Hubbard Hamiltonian and the associated Cu $K$-edge resonant inelastic x-ray scattering (RIXS) spectra for electron- and hole-doped cuprates over a wide range of energy and momentum transfers. By comparing computed spectra for the unfilled case with the corresponding results for 15% electron or hole doping at two different values of the effective Hubbard parameter $U$, generic signatures of the collapse of the magnetic gap and the characteristic momentum dependencies and evolution of the spectra with doping are identified. Available RIXS data support the gap collapse scenario for electron-doped cuprates, but the situation in hole-doped systems is found to be less clear.

• Received 20 June 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.107005