Charge Conjugation and Pairing in a model Cu$_{5}$O$_{4}$ Cluster

TL;DR

This paper investigates a symmetric Cu-O cluster using exact diagonalization, revealing bound electron pairs and flux quantization mechanisms that shed light on superconducting pairing phenomena.

Contribution

It demonstrates the existence of bound electron pairs with specific symmetries and elucidates the pairing mechanism involving charge and spin fluctuations in a Cu-O cluster.

Findings

Bound electron pairs of B2 symmetry are obtained at appropriate filling.

Flux quantization occurs similarly for electron and hole pairs.

Charge conjugation symmetry relates electron and hole pair states.

Abstract

Highly-symmetric three-band Hubbard Cu-O clusters have peculiar properties when the hole number is such that they admit W=0 hole pairs. These are two-hole eigenstates of the on-site Hubbard repulsion with eigenvalue 0, get bound by correlation effects when dressed by the interaction with the background, and cause superconducting flux quantization. We study the Cu$_{5}$O$_{4}$ cluster by exact diagonalization and show that bound electron pairs of $^{1}$% B$_{2}$ symmetry are obtained at an appropriate filling, and quantize flux like the hole pairs. The basic mechanism for pairing in this model is the second-order exchange diagram, and an approximate charge conjugation symmetry holds between electron and hole pairs. Further, the flux quantization property requires that the W=0 pairs of $d$ symmetry have $s$ symmetry couterparts, still with W=0; the former are due to a spin fluctuation, while the latter arise from a charge fluctuation mechanism. The simultaneous existence of both is an essential property of our model and is required for any model of superconducting $d$ pairs.