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

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.

Fermi liquid of two-dimensional polar molecules

“…This corresponds to omitting the terms β 2¯ j /2 in Eqs. (97)- (99) and is consistent with numerical calculations [24]. Only the manybody corrections to the interaction function of quasiparticles, given by Eqs.…”

“…This is shown in Sec. IV of our paper, whereas mean-field calculations do not find undamped zero sound [24]. Both collisionless and hydrodynamic regimes are achievable in ongoing experiments.…”

“…Various aspects have been discussed regarding this system in literature, in particular, the emergence and beyond mean-field description of the topological p x + ip y phase for microwave-dressed polar molecules [12,19], interlayer superfluids in bilayer and multilayer systems [13,15,20,33], and the emergence of density-wave phases for tilted dipoles [17,18,[21][22][23][24]. The case of superfluid pairing for tilted dipoles in the quasi-2D geometry beyond the simple BCS approach has been discussed in Ref.…”

“…The case of superfluid pairing for tilted dipoles in the quasi-2D geometry beyond the simple BCS approach has been discussed in Ref. [24]. The Fermi-liquid behavior of this system has been addressed by using the Fourier transform of the dipole-dipole interaction potential [11,18,24,[34][35][36][37] and then employing various types of mean-field approaches, such as the Hartree-Fock approximation [18] or variational approaches [11,36].…”

“…[24]. The Fermi-liquid behavior of this system has been addressed by using the Fourier transform of the dipole-dipole interaction potential [11,18,24,[34][35][36][37] and then employing various types of mean-field approaches, such as the Hartree-Fock approximation [18] or variational approaches [11,36]. It should be noted, however, that the short-range physics can become important for the interaction between such polar molecules, since in combination with the long-range behavior it introduces a peculiar momentum dependence of the scattering amplitude [19].…”