Fermion Cooper Pairing with Unequal Masses: Standard Field Theory Approach

The fermion Cooper pairing with unequal masses is investigated in a standard field theory approach. We derived the superfluid density and Meissner mass squared of the U(1) gauge field in a general two species model and found that the often used proportional relation between the two quantities is broken down when the fermion masses are unequal. In weak coupling region, the superfluid density is always negative but the Meissner mass squared becomes mostly positive when the mass ratio between the pairing fermions is large enough. We established a proper momentum configuration of the LOFF pairing with unequal masses and showed that the LOFF state is energetically favored due to the negative superfluid density. The single plane wave LOFF state is physically equivalent to an anisotropic state with a spontaneously generated superflow. The extension to finite range interaction is briefly discussed.