Stable gapless superconductivity at strong coupling

We study cross-flavor Cooper pairing in a relativistic system of two fermion species with mismatched Fermi surfaces. We find that there exist gapless phases which are characterized by either one or two gapless nodes in the energy spectra of their quasiparticles. An analysis of the current-current correlator reveals that, at strong coupling, both of these gapless phases can be free of magnetic instabilities. This is in contrast to the weak-coupling case where there are always two gapless nodes and the phase becomes magnetically unstable.