  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.
