Superconductivity near phase separation in models of correlated electrons.

Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques , we have found strong indications that the two dimensional t − J model supercon-ducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera (Phys. Rev. Letters 70, 682 (1993)). At this density the dominant channel is d x 2 −y 2 , but a novel transition to s-wave superconduc-tivity is observed decreasing the electronic density. In addition, the one band t − U − V model has also been studied using the mean-field approximation that accurately described the spin density wave phase of the repulsive Hubbard model at half-filling. An interesting region of d x 2 −y 2 superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-Tc cuprates are briefly discussed. Finally, the two band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t − J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation , and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.