Asymmetric Fermi Superfluid With Two Types Of Pairings

Inspired by ultracold atomic physics, nuclear physics and color superconductivity, the fermion pairing between different species with mismatched Fermi surfaces prompted great interest1,2,3,4,5,6,7,8,9,10,11,12,13 in recent experimental and theoretical studies. In conventional fermion superfluid the ground state is well described by the BCS theory, while for asymmetric fermion superfluid with double-species pairing the phase structure is much more rich and the pairing mechanism is not yet very clear. Various exotic phases have been suggested in the literatures, such as the Sarma phase14,15,16, the Fulde-Ferrel-Larkin-Ovchinnikov(FFLO) phase17, the phase with deformed Fermi surfaces18,19, and the phase separation20,21 in coordinate space. For asymmetric fermion superfluid, one of the most surprising phenomena is the magnetic instability, i.e., when the asymmetry characterized by the chemical potential mismatch is larger than the condensate of Cooper pair, the BCS superfluid is unstable under the perturbation of an external magnetic field. This instability leads to the ground state to be a FFLO phase. For color superconductivity, a similar but more complicated phenomenon is also found, namely the chromomagnetic instability15. One of the mechanisms to cure the magnetic instability is to introduce another pairing channel. In this paper, we propose a simple model including both doubleand single-species pairings and investigate how the single-species pairing influences the FFLO state. Our model can be used to describe a general fermion superfluid system where fermions from the same species can form Cooper pairs. In ultracold atom gas like Li and K, there exist pairings between different elements and between different states of the same element22. In color superconductivity phase of dense quark matter23, the quarks of different flavors can form total spin zero Cooper pairs and the quarks