Pairing in the Hubbard model: the Cu_{5}O_{4} Cluster versus the Cu-O plane

TL;DR

This paper investigates electron pairing mechanisms in the Cu_{5}O_{4} cluster using a three-band Hubbard model, demonstrating the formation of bound pairs and flux quantization, which extend to larger systems.

Contribution

It introduces a canonical transformation approach to pairing in the Hubbard model, highlighting W=0 pairs with different symmetries in a cluster context.

Findings

Bound electron/hole pairs form at specific fillings.

Flux quantization relates to symmetry properties.

W=0 pairs exhibit d and s symmetries due to fluctuations.

Abstract

We study the Cu_{5}O_{4} cluster by exact diagonalization of a three-band Hubbard model and show that bound electron or hole pairs are obtained at appropriate fillings, and produce superconducting flux quantisation. The results extend earlier cluster studies and illustrate a canonical transformation approach to pairing that we have developed recently for the full plane. The quasiparticles that in the many-body problem behave like Cooper pairs are W=0 pairs, that is, two-hole eigenstates of the Hubbard Hamiltonian with vanishing on-site repulsion. The cluster allows W=0 pairs of d symmetry, due to a spin fluctuation, and s symmetry, due to a charge fluctuation. Flux quantisation is shown to be a manifestation of symmetry properties that hold for clusters of arbitrary size.