A Model of Correlated Fermions with $d_{x^2-y^2}$ Superconductivity

Motivated by the phenomenology of the high-Tc cuprates, a two dimensional fermionic model with attractive interactions is here discussed. The exact solution to the two particle problem leads to a bound state in the $d_{x^2 - y^2}$ subspace. Numerical techniques suggest that the model has $d_{x^2 - y^2}$ superconductivity (SC) in the ground state at low fermionic density. Within a self-consistent RPA diagrammatic study, the density dependence of the critical temperature is calculated. We argue that in the context of d-wave SC this model fulfills the role that the attractive on-site Hubbard model has played for s-wave SC. We also show that another candidate, the attractive ``t-U-V'' model, which has d-wave SC at the mean-field level is actually not useful as a realization of this family of condensates for a variety of reasons.