Collective modes, stability and superfluid transition of a quasi-two-dimensional dipolar Fermi gas

TL;DR

This paper studies the collective excitations, stability, and superfluid transition of a quasi-two-dimensional dipolar Fermi gas, revealing how interactions and tilting angles influence damping, instabilities, and the onset of superfluidity.

Contribution

It provides a comprehensive analysis of collective modes, stability criteria, and superfluid transition conditions in a dipolar Fermi gas using a conserving Hartree-Fock approach.

Findings

Exchange interactions cause strong damping of zero sound below a critical tilt angle.

Unstable modes can lead to collapse or density wave formation.

Superfluid transition occurs at weak interactions if the tilt angle exceeds a critical value.

Abstract

We examine collective modes, stability, and BCS pairing in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. By using the (conserving) Hartree-Fock approximation, which treats direct and exchange interactions on an equal footing, we obtain the spectrum of single-particle excitations and long wavelength collective modes (zero sound) in the normal phase. It appears that exchange interactions result in strong damping of zero sound when the tilting angle between the dipoles and the normal to the plane of confinement is below some critical value. In particular, zero sound cannot propagate if the dipoles are perpendicular to the plane of confinement. At intermediate coupling we find unstable modes that can lead either to collapse of the system or the formation of a density wave. The BCS transition to a superfluid phase, on the other hand, occurs at arbitrarily weak strengths of the dipole-dipole interaction, provided the tilting angle exceeds a critical value. We determine the critical temperature of the transition taking into account many-body effects as well as virtual transitions to higher excited states in the confining potential, and discuss prospects of experimental observations.