Pairing in the Three-Band Hubbard Model of the Cu-O Plane

TL;DR

This paper derives an effective Hamiltonian for two-hole propagation in the Cu-O plane of the three-band Hubbard model, revealing potential pairing mechanisms and estimating binding energies relevant to high-temperature superconductivity.

Contribution

It introduces an analytical effective Hamiltonian for hole pairs in the three-band Hubbard model, extending previous cluster results and allowing inclusion of additional interactions like phonons.

Findings

Effective interaction between dressed holes is derived analytically.

Numerical estimates suggest binding energies of tens of meV.

The Fermi liquid state is shown to be unstable under these conditions.

Abstract

By a canonical transformation of the three-band Hubbard model, we introduce an effective Hamiltonian for the propagation of two holes doped into the ground state of the Cu-O plane. When the pair belongs to the $^{1}B_{2}$ or $% ^{1}A_{2}$ Irreducible Representations of the C$_{4v}$ Group, the bare holes do not interact by the on-site repulsion; the effective interaction between the dressed holes is obtained analytically in terms of renormalized matrix elements, and generalizes earlier findings from cluster calculations. The Fermi liquid is unstable and numerical estimates with reasonable parameters of the binding energy of the pair are in the range of tens of meV. Our scheme naturally lends itself to embody phonon-mediated and other interactions which cannot occur in the Hubbard model but may give important contributions.