  We study the magnetic instability of gapless superconductors. The instability
arises due to the infrared divergence associated with the gapless modes of the
superconductor. When the Fermi-surface mismatch between pairing fermions is
close to the gap, the gapless modes have a quadratic energy dispersion relation
at low energy and open a secondary gap at the Fermi surface, which is only
power-suppressed by the coupling. On the other hand, for a large mismatch, we
find the gapless superconductor does not open a secondary gap, but instead
makes transition to a new phase by forming the condensate of supercurrents. We
calculate the condensate of supercurrents by minimizing the effective
potential. In the new phase, the Meissner mass is positive for the magnetic
fields orthogonal to the direction of the condensate but zero in the parallel
direction.
