Anisotropic Fermi liquid theory of the ultra cold fermionic polar molecules: Landau parameters and collective modes

TL;DR

This paper investigates the anisotropic Fermi liquid behavior of ultracold dipolar fermionic molecules, analyzing Landau parameters and collective excitations, revealing anisotropic Fermi surface distortions and direction-dependent collective modes.

Contribution

It provides a detailed perturbative analysis of anisotropic Fermi liquid properties, including Landau parameters and collective modes, in dipolar fermionic gases, highlighting the effects of dipolar anisotropy.

Findings

Fermi surfaces exhibit anisotropic distortions due to dipolar interactions.

Landau interaction matrices become tri-diagonal in dipolar Fermi liquids.

Large dipolar interactions can collapse the Fermi surface perpendicular to dipole orientation.

Abstract

We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the $d_{r^2-3z^2}$-type in three dimensions and of the $d_{x^2-y^2}$-type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tri-diagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal p-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multi-component dipolar systems.