Comment on "Superfluid stability in the BEC-BCS crossover"

TL;DR

This paper critiques a recent study on superfluid stability in polarized Fermi gases, identifying an error in their stability criteria that invalidates their proposed phase diagram for certain interaction regimes.

Contribution

It highlights a critical mistake in the stability analysis of polarized Fermi gases, correcting the criteria used to determine the ground state and phase diagram.

Findings

Identifies an incorrect stability condition used in prior work.

Shows the proposed phase diagram is invalid for some detunings.

Emphasizes the importance of proper stability criteria in Fermi gas studies.

Abstract

We point out an error in recent work by Pao, Wu, and Yip [Phys. Rev.B {\bf 73}, 132506 (2006)], that stems from their use of a necessary but not sufficient condition [positive compressibility (magnetic susceptibility) and superfluid stiffness] for the stability of the ground state of a polarized Fermi gas. As a result, for a range of detunings their proposed ground-state solution is a local maximum rather than a minimum of the ground state energy, which thereby invalidates their proposed phase diagram for resonantly interacting fermions under an imposed population difference.