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

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