Fermi liquid of two-dimensional polar molecules

Abstract

We study Fermi-liquid properties of a weakly interacting two-dimensional gas of single-component fermionic polar molecules with dipole moments d oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean-field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r 3 at large distances r, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter k F r * , where k F is the Fermi momentum and r * = md 2 /h 2 is the dipole-dipole length, with m being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in k F r * and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, as it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.

Wigner crystallization in two dimensions: Evolution from long- to short-ranged forces

“…Hence, we expect the system to support zero sound modes. A detailed calculation likely renormalizes the zero sound velocity, but does not alter the qualitative physical phenomenon; see, for example, the analysis performed in the context of polarized dipole gases [21][22][23][24] . The speed of the zero sound diverges when ξ → ∞, since the power expansion in q/ω q breaks down in this limit.…”

“…Positive and negative charges accumulate at opposite ends of the electrolyte. Finally, recent progress in cooling techniques have allowed the study of degenerate dipolar gases [14][15][16][17][18][19][20][21][22] including Wigner crystallization of dipoles with 1/r 3 potentials 20 and collective modes [21][22][23][24] . Such objects interact as 1/r 3 at large separations.…”

Zero sound in a two-dimensional dipolar Fermi gas

“…The many-body theory relying on the Abrikosov-Khalatnikov approach has been developed in Ref. [28] for 2D fermionic single-component dipoles perpendicular to the plane of their translational motion (θ 0 = 0). This theory accounts for the short-range physics in the scattering properties and represents thermodynamic quantities as a series of expansion in the small parameter p F r * up to the second order.…”

“…The many-body theory (beyond mean field) describing Fermi liquid properties of a weakly interacting 2D gas of identical fermionic dipoles with dipole moments d oriented perpendicularly to the plane of their translational motion, has been developed in Ref. [28]. The theory relies on the presence of a small parameter p F r * , where p F is the Fermi momentum, and r * = md 2 /h 2 is the dipole-dipole length, with m being the molecule mass.…”

“…In some sense, the 2D gas of identical fermionic dipoles perpendicular to the plane of their translational motion, constitutes a novel Fermi liquid because the existence of zero sound in this system is provided only by many-body effects [28]. Zero sound modes represent collective oscillations related to deformations of the Fermi surface and are important characteristics of Fermi liquids and gases in the collisionless regime [41,42].…”