Collective excitation and stability of flowing gapless fermi superfluids

We study the collective excitation and stability of superfluid Fermi gases flowing with a constant velocity in threedimensional free space. In particular, we investigate a possible gapless superfluid state induced by the superflow using the mean-field theory and the generalized random-phase approximation (GRPA). For weak attractive interactions, we find that the mean-field superfluid order parameter takes a nonzero value even after the superflow velocity exceeds the threshold for the onset of Bogoliubov quasiparticle excitations. Since the Cooper pairs are only partially broken by the quasiparticle excitations, a gapless superfluid state can be formed over a certain range of superflow velocity above the pair-breaking onset. The GRPA excitation spectrum of the gapless superfluid state has a quasiparticle-quasihole continuum in addition to the usual quasiparticle-pair continuum and the Anderson-Bogoliubov collective mode. Moreover, the dynamic structure factor exhibits a characteristic peak structure in a long-wavelength and low-energy region of the quasiparticle-quasihole continuum. We find that the long-wavelength excitations eventually cause dynamical instability of the system when the superflow velocity further increases. As a result, the formation of a (dynamically stable) flowing gapless superfluid state is limited in a very narrow range of superflow velocity.