Unified description of cuprate superconductors using a four-band d − p model

In the 35 years since the discovery of cuprate superconductors, we have not yet reached a unified understanding of their properties, including their material dependence of the superconducting transition temperature T_{c}. The preceding theoretical and experimental studies have provided an overall picture of the phase diagram, and some important parameters for the T_{c}, such as the contribution of the Cu d_{z^{2}} orbital to the Fermi surface and the site-energy difference Δ_{dp} between the Cu d_{x^{2}−y^{2}} and O p orbitals. However, they are somewhat empirical and limited in scope, always including exceptions, and do not provide a comprehensive view of the series of cuprates. Here we propose a four-band d-p model as a minimal model to study material dependence in cuprates. Using the variational Monte Carlo method, we theoretically investigate the phase diagram for the La_{2}CuO_{4} and HgBa_{2}CuO_{4} systems and the correlation between the key parameters and the superconductivity. Our results comprehensively account for the empirical correlation between T_{c} and model parameters, and thus can provide a guideline for new material design. We also show that the effect of the nearest-neighbor d-d Coulomb interaction V_{dd} is actually quite important for the stability of superconductivity and phase competition.