d_x²-y² superconductivity in a model of correlated fermions

A two-dimensional fermionic model with attractive interactions is discussed. Its form is motivated by the phenomenology of the underdoped high-T_c cuprates, as discussed in previous literature. The exact solution to the two-particle problem leads to a bound state in the d_x²-y² subspace. Numerical techniques show that the model has strong d_x²-y² pairing correlations in the ground state at low fermionic density. Within a self-consistent random phase approximation diagrammatic study, the model has a d-wave superconducting (SC) phase. 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, is actually not useful as a toy model for d-wave SC for a variety of reasons.