Thermodynamics of Attractive and Repulsive Fermi Gases in Two Dimensions

TL;DR

This paper investigates the thermodynamic properties of two-dimensional Fermi gases with attractive and repulsive interactions, analyzing stability, interaction energy, compressibility, and spin susceptibility across different interaction strengths, temperatures, and spin imbalances.

Contribution

It introduces a generalized $T$-matrix approach to study 2D Fermi gases with tunable interactions, providing new insights into their thermodynamics and stability criteria.

Findings

Identification of a critical interaction strength for the repulsive branch stability.

Calculation of interaction energy, compressibility, and spin susceptibility.

Dependence of critical interaction strength on temperature and spin imbalance.

Abstract

We study the attractive and repulsive two-component Fermi gas with spin imbalance in two dimensions. Using a generalized $T$-matrix approximation, we examine the thermodynamic properties of both attractive and repulsive contact interacting Fermi gases. The interaction strength, which is characterized by the bound state energy $E_b=\hbar^2/m a_{2d}^2$ in vacuum, can be adjusted through a Feshbach resonance. We calculate the interaction energy, compressibility and spin susceptibility of the two branches of the Fermi gas. For the repulsive branch, we also find a critical strength of interaction $a_{2d}^{(c)}$ above which this metastable thermodynamic state becomes unstable. This critical value depends on the temperature and the spin imbalance (the "magnetization") of the system.