Unified description of cuprate superconductors using 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 $T_{\text{c}}$. 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.

arXiv comment12 pages, 9 figures, submitted to Phys. Rev. Research

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• Optimizing superconductivity: from cuprates via nickelates to palladates
• Altermagnetism and superconductivity in a multiorbital t-J model
• Strongly-overdoped La${}_{2-x}$Sr${}_x$CuO${}_4$: Evidence for Josephson-coupled grains of strongly-correlated superconductor
• Superconductivity studied by solving ab initio low-energy effective Hamiltonians for carrier doped CaCuO${}_2$, Bi${}_2$Sr${}_2$CuO${}_6$, Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$, and HgBa${}_2$CuO${}_4$
• Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens
• Superconductivity in bilayer $t$-$t^{\prime }$ Hubbard models
• Monte Carlo study of cuprate superconductors in a four-band $d$-$p$ model: Role of orbital degrees of freedom
• Possibility of BCS-BEC crossover in $\kappa$-type organic superconductors