# Instability of Fulde-Ferrell-Larkin-Ovchinnikov states in three and two dimensions

## TL;DR

This paper demonstrates that FFLO superfluid states are intrinsically unstable in two and three dimensions, explaining their absence in experiments across condensed matter and ultracold atomic systems.

## Contribution

The study provides a theoretical analysis showing the fundamental instability of FFLO states due to pairing fluctuations in 2D and 3D, clarifying experimental non-observations.

## Key findings

- FFLO states are intrinsically unstable in 2D and 3D.
- Pairing fluctuations prevent the formation of stable FFLO superfluids.
- This instability accounts for the lack of experimental evidence in various systems.

## Abstract

The exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states have been actively searched for experimentally since the mean-field based FFLO theories were put forward half a century ago. Here we investigate the stability of FFLO states against unavoidable pairing fluctuations, and conclude that FFLO superfluids cannot exist due to their intrinsic instability in three and two dimensions. This explains their absence in experimental observations in both condensed matter systems and the most recent, more promising ultracold atomic Fermi gases with a population imbalance.