Stability conditions and phase diagrams for two component Fermi gases with population imbalance

TL;DR

This paper clarifies stability conditions for polarized superfluid phases in two-component Fermi gases across the BCS-BEC crossover, analyzing their implications for phase diagrams and the effects of temperature and pseudogap phenomena.

Contribution

It establishes the equivalence of thermodynamic stability criteria and particle susceptibility positivity, providing a systematic analysis of phase stability in polarized Fermi gases.

Findings

Stability conditions are linked to positive second derivatives of thermodynamic potential.

Positivity of the particle number susceptibility matrix is crucial for stability.

Finite temperature and pseudogap effects significantly influence phase diagrams.

Abstract

Superfluidity in atomic Fermi gases with population imbalance has recently become an exciting research focus. There is considerable disagreement in the literature about the appropriate stability conditions for states in the phase diagram throughout the BCS to Bose-Einstein condensation (BEC) crossover. Here we discuss these stability conditions for homogeneous polarized superfluid phases, and compare with recent alternative proposals. The requirement of a positive second order partial derivative of the thermodynamic potential with respect to the fermionic excitation gap $\Delta$ (at fixed chemical potentials) is demonstrated to be equivalent to the positive definiteness of the particle number susceptibility matrix. In addition, we show the positivity of the effective pair mass constitutes another nontrivial stability condition. These conditions determine the stability of the system towards phase separation of one form or another. We also study systematically the effects of finite temperature and the related pseudogap on the phase diagrams defined by our stability conditions.