Eur. Phys. J. B 44, 189-202 (2005)
https://doi.org/10.1140/epjb/e2005-00114-7

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

Laboratoire de Physique Statistique, École Normale Supérieure (Associated to the CNRS and Paris 6 and Paris 7 Universities) , 24 rue Lhomond, 75231 Paris Cedex 05, France

Corresponding author: ^a combesco@lps.ens.fr

Received: 17 November 2004
Revised: 13 January 2005
Published online: 20 April 2005

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.