Instability of superfluid across Feshbach resonances C.-H. Paoa , Shin-Tza Wua , and Sungkit Yipb a b Department of Physics, National Chung Cheng University, Chiayi 621, Taiwan Institute of Physics, Academia Sinica, Nankang, Taipei 115, Taiwan We consider a dilute atomic gas with two species of Fermions with unequal concentrations. We study at zero temperature the atom-molecule mixture with inter-species low-energy scatterings induced by a Feshbach resonance. To examine the stability of this superfluid, we calculate the chemical potential and the superfluid density for fixed individual concentrations. We find that the system can have distinct properties compared to the ordinary Bose-Fermi mixture due to the unbound fermions. Sorting category: Aa Quantum gases, fluids and solids Keywords: superfluidity, BEC-BCS crossover, Bose-Fermi mixture LT1398