Superconductivity with antiferromagnetic background in a d = ∞ Hubbard model

We show that in an infinite dimensional (d = infinity) Hubbard model a superconducting phase exists in the vicinity of the Mott transition. Analyzing the antiferromagnetic (AF) phase using a Gutzwiller-type variational wave function, we show that the compressibility takes negative (kappa (n) < 0), which, in a naive interpretation, would lead to phase separation. However, this instability should be taken as a Cooper instability due to the strong attractive interactions between the quasiparticles. We construct a phenomenological theory of the AF Fermi liquid and determine the corresponding Landau parameters using a microscopic approach. These results indicate the existence of spin waves whose dispersion is given by a linear spectrum <omega>(k) = ck, which is absent in a Brinkman-Rice Fermi liquid. In addition. one of the Landau parameters becomes negative, indicating that the true ground-state is superconducting. As a result, the compressibility restores a positive value (kappa (s) > 0), and the phase separation in a normal phase turns out to be an artifact.