Anisotropic Ginzburg-Landau and Lawrence-Doniach Models for Layered Ultracold Fermi Gases

TL;DR

This paper develops anisotropic Ginzburg-Landau and Lawrence-Doniach models for layered ultracold Fermi gases, analyzing their coefficients, anisotropy, and applicability near the unitary limit.

Contribution

It derives the anisotropic Ginzburg-Landau and Lawrence-Doniach models for layered ultracold Fermi gases, linking interlayer couplings with Ginzburg-Landau parameters and exploring anisotropy effects.

Findings

Effective anisotropy is reduced near the unitary limit.

Anisotropy parameter varies widely in realistic setups.

Lawrence-Doniach model is valid near the unitary limit.

Abstract

We study the anisotropic Ginzburg-Landau and Lawrence-Doniach models describing a layered superfluid ultracold Fermi gas in optical lattices. We derive the coefficients of the anisotropic Ginzburg-Landau and the mass tensor as a function of anisotropy, filling and interaction, showing that near the unitary limit the effective anisotropy of the masses is significantly reduced. The anisotropy parameter is shown to vary in realistic setups in a wide range of values. We also derive the Lawrence-Doniach model - often used to describe the 2D-3D dimensional crossover in layered superconductors - for a layered ultracold Fermi gas, obtaining a relation between the interlayer Josephson couplings and the Ginzburg-Landau masses. Comparing to the Ginzburg-Landau description, we find that the region of validity of the Lawrence-Doniach model is near the unitary limit.