Polarised Fermi condensates with equal and unequal masses

We consider a two-spin atomic Fermi gas, where both the mass and population of each component are unequal. We show that the finite temperature phase diagram contains a region of phase separation between the superfluid and normal states that touches the boundary of second-order superfluid transitions at a tricritical point, reminiscent of the phase diagram of $^3$He-$^4$He mixtures. We discuss the implications of our findings for a trapped gas at finite temperature and the different topologies of phase separation by changing the mass ratio. Finally we find that the interior gap state is always unstable to phase separation, while the breached pair state with one Fermi surface for the excess fermions exhibits differences in its DoSs and pair correlation functions depending on which side of the resonance it lies.