Population and mass imbalance in atomic Fermi gases

We develop an accurate theory of resonantly interacting Fermi mixtures with both spin and mass imbalance. We consider Fermi mixtures with arbitrary mass imbalances but focus, in particular, on the experimentally available Li-6-K-40 mixture. We determine the phase diagram of the mixture for different interactions strengths that lie on the BCS side of the Feshbach resonance. We also determine the universal phase diagram at unitarity. We find, for the mixtures with a sufficiently large mass imbalance, which includes the Li-6-K-40 mixture, a Lifshitz point in the universal phase diagram that signals an instability toward a supersolid phase.