Transitions to the Fulde-Ferrell-Larkin-Ovchinnikov phases at low temperature in two dimensions

TL;DR

This paper investigates the transition to Fulde-Ferrell-Larkin-Ovchinnikov superfluid phases in two-dimensional systems at low temperatures, revealing a cascade of increasingly complex order parameters and a singular behavior as temperature approaches zero.

Contribution

It applies the Larkin-Ovchinnikov approach to analyze the transition, uncovering a sequence of transitions with complex order parameters in two dimensions at low temperatures.

Findings

Cascade of transitions with complex order parameters

Order parameter as superposition of cosines with equal weights

Spacing of wavevector directions approaches zero at zero temperature

Abstract

We explore the nature of the transition to the Fulde-Ferrell-Larkin- Ovchinnikov superfluid phases in the low temperature range in two dimensions, for the simplest isotropic BCS model. This is done by applying the Larkin-Ovchinnikov approach to this second order transition. We show that there is a succession of transitions toward ever more complex order parameters when the temperature goes to zero. This gives rise to a cascade with, in principle, an infinite number of transitions. Except for one case, the order parameter at the transition is a real superposition of cosines with equal weights. The directions of these wavevectors are equally spaced angularly, with a spacing which goes to zero when the temperature goes to zero. This singular behaviour in this $ T = 0$ limit is deeply linked to the two-dimensional nature of the problem.