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Finite-Temperature Behavior of an Inter-species Fermionic Superfluid with Population Imbalance

We determine the superfluid transition temperature $T_c$ and related finite temperature phase diagrams for the entire BCS-Bose Einstein condensation crossover in a homogeneous mixture of $^{6}$Li and $^{40}$K atoms with population imbalance. Our work is motivated by the recent observation of an inter-species Feshbach resonance. Pairing fluctuation effects, which significantly reduce $T_c$ from the onset temperature for pairing ($T^*$), provide reasonable estimates of $T_c$ and indicate that the inter-species superfluid phase should be accessible in future experiments. Although a generalized-Sarma phase is not stable in the ground state near unitarity, our phase diagrams show that it appears as an intermediate-temperature superfluid.