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

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.