Systematics of the strength of superconductivity of the d-p model in relation to cuprates

Cuprate high-Tc superconductors are known to have several relationships between Tc and features of electronic structure. In the firstly found one, Tc is correlated with the Madelung potential difference between planar Cu and O sites. Another one relates Tc to the relative ratio of hole densities at the Cu and O sites. In this work we analyze the dependences of the strength of superconductivity (SC) on the model parameters of the d-p model. We first transform the d-p model into a Hubbard model that proves to have k-dependent Coulomb interaction. To this model we apply a kind of mean-field theory, i. e., Kondo's theory of the d-wave SC gap in cuprates. The obtained so-called SC strength parameter increases with increase of |ep - ed| on both positive and negative sides of ep - ed due to increase of effective on-site Coulomb interaction U. ep and ed are hole energy levels of O2p and Cu3d orbitals referenced to the d9 configuration. The above-mentioned two relationships are shown to be understandable in terms of the d-wave SC, if ep - ed < 0.