Phononic collective excitations in superfluid Fermi gases at nonzero temperatures

Abstract

We study the phononic collective modes of the pairing field $\Delta$ and their corresponding signature in both the order-parameter and density response functions for a superfluid Fermi gas at all temperatures below $T_c$ in the collisionless regime. The spectra of collective modes are calculated within the Gaussian Pair Fluctuation approximation. 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 known exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of $T_c$, we find analytically a weakly-damped collective mode whose velocity vanishes with a critical exponent of $1/2$, and whose quality factor diverges logarithmically with $T_c-T$, thereby clarifying an existing debate in the literature (Andrianov et al. Th. Math. Phys. 28, 829, Ohashi et al. J. Phys. Jap. 66, 2437). A transition between these two phononic branches is visible at intermediary temperatures, particularly in the BCS limit where the phase-phase response function displays two maxima.

31 pages, 15 figures

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• Following the Higgs mode across the BCS-BEC crossover in two dimensions
• Collective excitation branch in the continuum of pair-condensed Fermi gases : analytical study and scaling laws
• Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures
• Collective excitations of superfluid Fermi gases near the transition temperature
• Beyond mean-field corrections to the quasiparticle spectrum of superfluid Fermi gases
• Dispersion of plasmons in three-dimensional superconductors
• Collective excitations of a charged Fermi superfluid in the BCS-BEC crossover
• Linear response of a superfluid Fermi gas inside its pair-breaking continuum
• Low-Lying Collective Excitations of Superconductors and Charged Superfluids
• Quasiparticle disintegration in fermionic superfluids
• BCS-BEC crossover in a quasi-two-dimensional Fermi superfluid