Strongly correlated Fermi superfluid near an orbital Feshbach resonance: Stability, equation of state and Leggett mode

We theoretically study the superfluid phase of a strongly correlated $^{173}$Yb Fermi gas near its orbital Feshbach resonance, by developing a quantitative pair-fluctuation theory within a two-band model. We examine the density excitation spectrum of the system and determine a stability phase diagram. We find that the $^{173}$Yb Fermi gas is intrinsically metastable and has a peculiar equation of state, due to the small but positive singlet scattering length. The massive Leggett mode, arising from the fluctuation of the relative phase of two order parameters, is severely damped. We discuss the parameter space where an undamped Leggett mode may exist.