Temperature Effects in a Fermi Gas with Population Imbalance

TL;DR

This paper analyzes how temperature influences pairing and phase transitions in a population-imbalanced Fermi gas, deriving analytical expressions for critical temperatures and identifying stable and unstable solutions across coupling regimes.

Contribution

It provides analytical formulas for the transition temperature in imbalanced Fermi gases and clarifies the stability of solutions, including reentrant phenomena and tricritical points.

Findings

Existence of two solutions for $T_c$ indicating reentrant behavior.

Lower $T_c$ solutions are unstable.

Identification of tricritical points in phase diagram.

Abstract

We investigate temperature effects in a Fermi gas with imbalanced spin populations. From the general expression of the thermal gap equation we find, in {\it weak coupling limit}, an analytical expression for the transition temperature $T_c$ as a function of various possibilities of chemical potential and mass asymmetries between the two particle species. For a range of asymmetry between certain specific values, this equation always has two solutions for $T_c$ which has been interpreted as a reentrant phenomena or a pairing induced by temperature effect. We show that the lower $T_c$ is never related to a stable solution. The same results are obtained in {\it strong coupling limit}. The thermodynamical potential is carefully analyzed to avoid the consideration of the unstable solutions. We also obtain the tricritical points for the chemical potential and mass imbalanced cases, and beyond these points we properly minimize the thermodynamic potential to find the stable and metastable first order transition lines.