Precise ${dd}$ excitations and commensurate intersite Coulomb interactions in the dissimilar cuprates YBa 2 Cu 3 O 7–y and La 2–x Sr x CuO 4
Using high-resolution extreme ultraviolet resonant inelastic X-ray scattering (EUVRIXS) spectroscopy at Cu M-edge, we observed the doping dependent spectral shifts of inter-orbital (${dd}$) excitations of YBa 2 Cu 3 O 7-y and La 2-x Sr x CuO 4 . With increasing hole doping level from undoped to optimally doped superconducting compositions, the leading edge of ${dd}$ excitations is found to shift towards lower energy loss in a roughly linear trend that is irrespective to the cuprate species. The magnitude of energy shift can be explained by including a 0.15 eV Coulomb attraction between Cu 3d(x 2 -y 2 ) electrons and the doped holes on the surrounding oxygens in the atomic multiplet calculations. Finally, the consistent energy shift between distinct cuprate families suggests that this inter-site Coulomb interaction energy scale is relatively material-independent, and provides an important reference point for understanding charge density wave phenomena in the cuprate phase diagram.