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

TL;DR

This paper introduces a four-band $d$-$p$ model to unify understanding of cuprate superconductors, explaining material dependence of $T_c$ and guiding new material design through variational Monte Carlo analysis.

Contribution

The study develops a minimal four-band $d$-$p$ model and demonstrates its effectiveness in explaining cuprate superconductivity and material dependence of $T_c$.

Findings

The model accounts for empirical $T_c$ correlations with key parameters.

Nearest-neighbor $d$-$d$ Coulomb interaction $V_{dd}$ significantly influences superconductivity.

Results provide guidelines for designing new high-$T_c$ cuprate materials.

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 $T_{\text{c}}$. The preceding theoretical and experimental studies have provided an overall picture of the phase diagram, and some important parameters for the $T_{\text{c}}$, such as the contribution of the Cu $d_{z^2}$ orbital to the Fermi surface and the site-energy difference $\Delta_{dp}$ 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 $T_{\text{c}}$ 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.