Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases

Abstract

We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors, as suggested by Littlewood and Varma in 1982. We analytically continue the RPA equation on the collective mode energy through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. For ∆/µ > 1.210 (very close to unitarity in a superfluid Fermi gas), where ∆ is the order parameter and µ the chemical potential, the real part of the branch is wholly within the band gap [0, 2∆]. In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically. This contradicts the result of Littlewood and Varma that prevailed so far.

Leggett collective excitations in a two-band Fermi superfluid at finite temperatures

“…) in accordance with (19). In general, the spectral function f r w ( )contains several non-analytic points which determine several windowsfor the analytic continuation.…”

“…In general, the spectral function f r w ( )contains several non-analytic points which determine several windowsfor the analytic continuation. Within the interpretation of [19,20], eigenfrequencies which lie in different windowsdescribe peaks of the pair response function in the corresponding frequency intervals.…”

“…In a two-band superfluid, there exist hybrid phononic branches with sound velocities described by EFT [18], and two pair-breaking branches [19] with frequencies strongly pinned to the two pair-breaking continuum edges 2Δ j . In the present treatment, we focus on Leggett collective modes.…”

“…), as in [19,20]. Because fluctuations lead to scaling of parameters of state, the dimensionless ratios T T T , ,…”

“…In the present work, we consider Leggett collective modes in a two-band Fermi superfluid using the GPF effective action for a two-band system derived in [18] within the path integral formalism. The frequencies and the damping factors for Leggett modes are determined through complex poles of the fluctuation propagator, similarly to [19,20], where this method has been applied to pair-breaking and phononic collective excitations in ultracold Fermi gases. In the literature, the damping factor of collective excitations is frequently determined through a second-order perturbation expression with a real eigenfrequency.…”