Determination of the Coulomb interaction strength on copper sites of cuprates using electron distribution in the Emery model

We study the Emery model of high-temperature superconductors, specifically for three materials: LCO, YBCO and NCCO. We compare the hole distribution on oxygen and copper orbitals with experimental data obtained from NMR in hope of identifying the best Coulomb interaction strength U_d for these materials. We use cluster dynamical mean field theory (CDMFT) with an exact diagonalization impurity solver, which allows us to study the covalent parameter regime of cuprates. We find that for LCO and YBCO, U_d should be around U_d=14.0 and U_d=9.5 (in units of t_pp) respectively. For NCCO, the value of U_d found does not allow for superconductivity on the electron-doped region, leading us to believe that our method slightly underestimates the value of U_d. Our results are in agreement with the predictions that stronger correlations lead to a greater concentration of doped holes on oxygens orbitals and that the strength of superconductivity is inversely related to the size of the charge transfer gap (CTG). We observe a shift between an itinerant and insulating antiferromagnetic solution for NCCO at around U_d=8.97, concomitant with the opening of the CTG. We also observe a jump in the derivative of the n_d (copper occupation) vs n_p (oxygen occupation) curve at half-filling (n_d+n_p=5), jump that stops as the CTG closes.