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.

12 pages, 9 figures, submitted to Phys. Rev. Research

References in corpus (14)

• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• Thermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa${}_2$Cu${}_3$O${}_y$
• Two-Orbital Model Explains the Higher Transition Temperature of the Single-Layer Hg-Cuprate Superconductor Compared to That of the La-Cuprate Superconductor
• Orbital currents in extended Hubbard models of high-T${}_c$ cuprates
• Crossover between BCS Superconductor and Doped Mott Insulator of d-wave Pairing State in Two-Dimensional Hubbard Model
• Combined density-functional and dynamical cluster quantum Monte Carlo calculations for three-band Hubbard models for hole-doped cuprate superconductors
• Effective Hamiltonian for cuprate superconductors derived from multi-scale ab initio scheme with level renormalization
• Classification of multipole superconductivity in multi-orbital systems and its implications
• Hidden Mott transition and large-$U$ superconductivity in the two-dimensional Hubbard model
• Charge-density wave induced by combined electron-electron and electron-phonon interactions in 1$T$-TiSe${}_2$: A variational Monte Carlo study
• Development of a two-particle self-consistent method for multi-orbital systems and its application to unconventional superconductors
• Numerical analysis of three-band models for CuO planes as candidates for a spontaneous T violating orbital current phase
• Formulation of the augmented plane-wave and muffin-tin orbital method
• Pseudogap transition within the superconducting phase in the three-band Hubbard model