Fulde-Ferrell-Larkin-Ovchinnikov state of two-dimensional imbalanced Fermi gases

The ground-state phase diagram of attractively interacting Fermi gases in two dimensions with a population imbalance is investigated. We find the regime of stability for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, in which pairing occurs at a finite wave vector, and determine the magnitude of the pairing amplitude Delta and FFLO wave vector q in the ordered phase, finding that Delta can be of the order of the two-body binding energy. Our results rely on a careful analysis of the zero-temperature gap equation for the FFLO state, which possesses nonanalyticities as a function of Delta and q, invalidating a Ginzburg-Landau expansion in small Delta.