Novel Fermi Liquid of 2D Polar Molecules

• Published in: arXiv.org 2011-11
• Main Authors: Zhen-Kai Lu, Shlyapnikov, G V
• Format: Article
• Language: English
• Subjects: Acoustic velocity; Chemical reactions; Dipole moments; Fermi liquids; Organic chemistry; Perturbation theory; Translational motion; Zero sound
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1111.7114

We study Fermi liquid properties of a weakly interacting 2D 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 \(k_Fr_*\), where \(k_F\) is the Fermi momentum, and \(r_*=md^2/\hbar^2\) 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 \(k_Fr_*\) and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, like 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.