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

Abstract

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 Tc. The preceding theoretical and experimental studies have provided an overall picture of the phase diagram, and some important parameters for the Tc, such as the contribution of the Cu dz2 orbital to the Fermi surface and the site-energy difference Δdp between the Cu dx2-y2 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 La2CuO4 and HgBa2CuO4 systems and the correlation between the key parameters and the superconductivity. Our results comprehensively account for the empirical correlation between Tc 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 Vdd is actually quite important for the stability of superconductivity and phase competition.