# Renormalization theory for the Fulde-Ferrell-Larkin-Ovchinnikov states at $T>0$

## TL;DR

This paper uses renormalization group analysis to investigate the stability of FFLO superfluid states at finite temperature, revealing their tendency to become uniform or normal due to thermal fluctuations in 2D and 3D systems.

## Contribution

It provides a renormalization group framework showing the instability of FFLO states towards uniform or normal phases at finite temperature in two and three dimensions.

## Key findings

- FFLO states are unstable at T>0 in 2D and 3D.
- Thermal fluctuations drive the ordering wave-vector towards zero.
- In 2D, the flow approaches Kosterlitz-Thouless or normal fixed points.

## Abstract

Within the renormalization group framework we study the stability of superfluid density wave states, known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with respect to thermal order-parameter fluctuations in two and three-dimensional ($d\in \{2,3\}$) systems. We analyze the renormalization-group flow of the relevant ordering wave-vector $\vec{Q_0}$. The calculation indicates an instability of the FFLO-type states towards either a uniform superfluid or the normal state in $d\in\{2,3\}$ and $T>0$. In $d=2$ this is signaled by $\vec{Q_0}$ being renormalized towards zero, corresponding to the flow being attracted either to the usual Kosterlitz-Thouless fixed-point or to the normal phase. We supplement a solution of the RG flow equations by a simple scaling argument, supporting the generality of the result. The tendency to reduce the magnitude of $\vec{Q_0}$ by thermal fluctuations persists in $d=3$, where the very presence of long-range order is immune to thermal fluctuations, but the effect of attracting $\vec{Q_0}$ towards zero by the flow remains observed at $T>0$.