LOFF Pairing vs. Breached Pairing in Asymmetric Fermion Superfluids
  A general analysis for the competition between breached pairing (BP) and LOFF pairing mechanisms in asymmetric fermion superfluids is presented in the frame of a four fermion interaction model. Two physical conditions which can induce mismatched Fermi surfaces are considered: (1) fixed chemical potential asymmetry $\delta\mu$ and (2) fixed fermion number asymmetry $\alpha$. In case (1), the BP state is ruled out because of Sarma instability and LOFF state is thermodynamically stable in a narrow window of $\delta\mu$. In case (2), while the Sarma instability can be avoided and both the BP and LOFF states can survive provided $\alpha$ is less than the corresponding critical value, the BP state suffers magnetic instability and the LOFF state is always thermodynamically stable. While the LOFF window in case (2) is much larger than the one in the conventional case (1), for small $\alpha$ the longitudinal superfluid density of the LOFF state is negative and it suffers also magnetic instability. 
Lianyi He, Meng Jin and Pengfei Zhuang