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.
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