Phononic collective excitations in superfluid Fermi gases at nonzero temperatures

Abstract

We study the phononic collective modes of the pairing field ∆ in a superfluid Fermi gas at all temperatures below T c . We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a non-perturbative analytic continuation of the pairing field propagator. At low temperature, we recover the know exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of T c , and in the BCS regime, our calculations reveal two phononic branches; the first one has a velocity that tends to a finite non-zero value at T c , while the second one has a velocity that vanishes with a critical exponent of 1/2 (in contradiction with Ohashi et al., J. Phys. Soc. Jap. 66, 2437), and a quality factor that diverges logarithmically with T c − T . At temperatures close to T c , this results in a double peak structure in the response function of the phase of ∆, well resolved in the BCS regime. Away from T = 0 and T c , we develop a semi-numerical method to perform the analytic continuation. This confirms the existence of two branches, and allows us to follow the disappearance of the second branch as the temperature is lowered. Our results generalize to pure fermionic condensates the double peak structure observed by Carlson and Goldman in dirty superconductors (Phys. Rev. Lett. 31, 880).

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

“…The spectrum of collective excitations can be determined using the same method as for a one-band Fermi superfluid [19,20]. We solve the equation for the determinant of the inverse fluctuation propagator analytically continued from the set of Matsubara frequencies to the complex frequency plane…”

“…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.…”

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

“…Physically, ω b indicates the minimal threshold energy above which collective excitations become damped due to decay into fermion pairs. Within the analytic continuation method described above (see also for details [19,20]), the two pair-breaking edges determine, in general, three windowsfor the analytic continuation: the windowA for ω<ω b , the windowB for The chosen values of the scattering lengths in figure 1 are related to the BEC regime, where the chemical potentials for both bands are negative, even at zero detuning. Therefore there are no pair-breaking collective excitations in this regime [19].…”

“…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.…”