BCS-BEC crossover and effects of density fluctuations in a two-component Fermi gas loaded on an optical lattice

TL;DR

This paper studies the superfluid transition in a two-component Fermi gas on an optical lattice, highlighting how density fluctuations influence the transition temperature across the BCS-BEC crossover.

Contribution

It introduces a self-consistent theoretical approach that includes both superfluid and density fluctuations, respecting particle-hole symmetry throughout the crossover.

Findings

Charge density fluctuations suppress Tc near half-filling.

Maximum Tc occurs away from half-filling due to competing fluctuations.

Lattice effects and Fermi surface nesting significantly impact superfluidity.

Abstract

We investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature Tc, including both superfluid and (spin and charge) density fluctuations within the self-consistent t-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS-BEC crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of Tc. As a result, the maximum Tc is obtained away the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.