Two-electron bound state formation in the t-J-U model for exchange-coupled planes

TL;DR

This paper investigates the formation of two-electron bound states in a simplified anisotropic t-J-U model representing exchange-coupled planes in high-temperature superconductors, revealing that even minimal interplanar exchange can induce pairing.

Contribution

It demonstrates that in a model of exchange-coupled planes, infinitesimal interplanar exchange suffices for bound state formation, contrasting with the higher threshold in isotropic 3D systems.

Findings

Bound states form with Jc=0 in exchange-coupled planes.

Higher Jc/t ratio needed for 3D isotropic systems.

Weak interplanar exchange influences electron pairing.

Abstract

An anisotropic t-J-U model Hamiltonian is used to model electron behaviour in quasi-2d materials in the dilute limit, and as a highly simplified representation of the weakly coupled CuO2 planes of the high-Tc cuprates we model the very poor out-of-plane conductivity via the complete suppression of interplanar hopping. However, we do include the very weak interplanar superexchange, and are thus considering a model of exchange-coupled planes. For an isotropic three-dimensional system in the dilute limit, we find that the formation of two-particle bound states requires Jc/t ~ 5.9. Also, it is known that Jc/t = 2 for a 2d square lattice. However, for our model of exchange-coupled planes any infinitesimal interplanar exchange (Jc = 0) is adequate to form bound states.