  Gapless superconductivity can arise when pairing occurs between fermion
species with different Fermi surface sizes, provided there is a sufficiently
large mismatch between Fermi surfaces and/or at sufficiently large coupling
constant. In gapless states, secondary Fermi surfaces appear where
quasiparticle excitation energy vanishes. This work focuses on homogeneous and
isotropic superfluids in the s-wave channel, with either zero (conventional
superconductor), one, or two spherical Fermi surfaces. The stability conditions
for these candidate phases are analyzed. It is found that gapless states with
one Fermi surface are stable in the BEC region, while gapless states with two
Fermi surfaces are unstable in all parameter space. The results can be applied
to ultracold fermionic atom systems.
