Abstract:
Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with
different chemical potentials, can lead to quasiparticle excitation energies that vanish at either
zero, one, or two spheres in momentum space. With no zeroes, we have
a conventional BCS superconductor. The other two cases, ``gapless'' superconductors,
appear in mean field theory
for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria
for those candidate phases.
Positivity of number susceptibility appears to provide the most powerful constraint, and renders
all the two-zero states that we have examined mechanically unstable.
Our results should apply directly to ultracold fermionic atom systems.