The "W=0" Pairing Mechanism from Repulsive Interactions in Symmetric 2d Models

TL;DR

This paper explores a pairing mechanism in symmetric 2D models where repulsive interactions lead to electron pairing, using the concept of W=0 pairs, with analytical and numerical evidence supporting their role in superconductivity.

Contribution

It introduces the W=0 pairing mechanism in symmetric 2D Hubbard models and demonstrates its quantitative predictive power through analytical and numerical methods.

Findings

W=0 pairs form in symmetric clusters with no on-site repulsion.

Holes in W=0 pairs exhibit attraction and superconducting flux quantization.

The theory accurately predicts pairing behavior in 4x4 lattice models.

Abstract

In two-dimensional systems possessing a high degree of symmetry, the repulsive electron-electron interaction produces a pairing force; the mechanism would fail in the presence of strong distortions. We have studied this in the one-band and three-band Hubbard Model. From partially occupied orbitals one obtains pair eigenstates of the Hamiltonian with no on-site repulsion (the W=0 pairs). The concept of W=0 pairs allows to make qualitative and quantitative predictions about the behaviour of interacting many-body systems, a quite remarkable and unusual situation. Exact numerical solutions for clusters with ``magic'' hole numbers reveal attraction between the holes in W=0 pairs. The effect occurs in all fully symmetric clusters which are centered on a Cu site; then holes get paired in a wide, physically relevant parameter range and show superconducting quantization of the magnetic flux. A canonical transformation of the Hamiltonian, valid for clusters and for the full plane, leads to a Cooper-like equation for the W=0 pairs. We have evaluated the effective interaction and found that W=0 pairs are the bare quasiparticles which, once dressed, become two-hole bound states. We applied the above theory to the doped antiferromagnet, and found that the ground state at half filling is the singlet component of a determinantal state. We write down this determinant and the ground state wave function explicitly in terms of a many-body W=0 eigenstate. Our analytical results for the $4\times 4$ square lattice at half filling and with doped holes, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power.