  We investigate fermionic superconductivity with mismatched Fermi surfaces in
a general two-band system. The exchange interaction between the two bands
changes significantly the stability structure of the pairing states. The Sarma
state with two gapless Fermi surfaces which is always unstable in single-band
systems, can be the stable ground state in two-band systems. To realize a
visible mismatch window for the stable Sarma state, two conditions should be
satisfied: a nonzero inter-band exchange interaction and a large asymmetry
between the two bands.
