Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points

TL;DR

This paper analyzes the stability of FFLO superfluid states under fluctuations, showing they are unstable in isotropic systems but can exist in layered anisotropic systems, and introduces a method to compute critical exponents at Lifshitz points.

Contribution

It demonstrates the instability of FFLO states in isotropic systems at finite temperature and develops a nonperturbative RG method to analyze Lifshitz critical behavior.

Findings

FFLO states are unstable in isotropic systems for d<4 at T>0.

Layered systems can host FFLO order in d=3 but not in d=2.

A nonperturbative RG approach computes critical exponents at Lifshitz points.

Abstract

We revisit the question concerning stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. Invoking the properties of the putative phase diagram of two-component Fermi mixtures, on general grounds we argue, that for isotropic, continuum systems the phase diagram hosting a long-range-ordered FFLO-type phase envisaged by the mean-field theory cannot be stable to fluctuations at any temperature $T>0$ in any dimensionality $d<4$. In contrast, in layered unidirectional systems the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at $T>0$ is $d=5/2$. In consequence, its occurrence is excluded in $d=2$, but not in $d=3$. We propose a relatively simple method, based on nonperturbative renormalization group to compute the critical exponents of the thermal $m$-axial Lifshitz point continuously varying $m$, spatial dimensionality $d$ and the number of order parameter components $N$. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.