Propagation of first and second sound in a two-dimensional Fermi superfluid

TL;DR

This paper calculates and analyzes the velocities of first and second sound in a two-dimensional ultracold Fermi superfluid across the BCS-BEC crossover, revealing their behavior and excitation modes near the superfluid transition.

Contribution

It provides a comprehensive calculation of sound velocities throughout the BCS-BEC crossover and clarifies the excitation mechanisms of first and second sound in 2D Fermi superfluids.

Findings

First sound velocity matches recent experimental measurements.

Second sound vanishes at the BKT transition, indicating superfluid depletion.

Mode mixing occurs only in the finite-temperature BEC regime.

Abstract

Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover and we analyze the system response to an external perturbation. In the low-temperature regime we reproduce the recent measurements [Phys Rev. Lett. {\bf 124}, 240403 (2020)] of the first sound velocity, which, due to the decoupling of density and entropy fluctuations, is the sole mode excited by a density probe. Conversely, a heat perturbation excites only the second sound, which, being sensitive to the superfluid depletion, vanishes in the deep BCS regime, and jumps discontinuously to zero at the Berezinskii-Kosterlitz-Thouless superfluid transition. A mixing between the modes occurs only in the finite-temperature BEC regime, where our theory converges to the purely bosonic results.