Superconductivity near Pomeranchuk instabilities in the spin channel

We study the competition between a Pomeranchuk instability in the spin channel with angular momentum $\ell=1$ and an attractive interaction, favoring Cooper-pair formation. We found that the superconducting gap strongly suppresses the phase space for the Pomeranchuk instability. We computed a mean-field phase diagram displaying a first order transition between two superconductor phases with different symmetries: p-wave (with spontaneously generated spin-orbit interaction) and s-wave for greater values of the coupling constant. Moreover, we have looked for a possible modulated superconducting phase. We have found that this phase appears only as a meta-stable state in the strong coupling regime.