Zhang-Rice singlets dominate critical temperature evolution of cuprate superconductivity

We show that formation of Zhang-Rice singlets (ZRS) naturally explains the empirical superconducting dome by random distribution of holes in copper-oxygen plane of cuprates. A general relation T_c/T_cmax=25(c-0.04), where c is the concentration of the ZRS and T_cmax is the maximum of critical temperature T_c, is obtained and reproduces the doping-dependent critical temperature evolution in the whole superconducting dome. The relation has been applied to estimate the effects of impurities substituting copper in the copper-oxygen plane. Our relation successfully predicts the suppression of superconductivity due to the substitution of Cu by the impurities. We demonstrate that T_c decreases linearly with the increase of the impurity concentration and the scattering range plays a key role in the suppression of the superconductivity. These results agree well with the experimental observations of the substitutions by Zinc and Nickel. Our relation is universal for all families of cuprates and explains the formation of the superconducting dome in the phase diagram.