Cascade of two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov phases with anisotropy

For an isotropic two-dimensional system, when the temperature is lowered toward T=0, it has been found recently that, for the transition from the normal to the superfluid state in the paramagnetic limit, the order parameter describing the Fulde-Ferrell-Larkin-Ovchinnikov phase has an increasingly complex structure with contributions from an increasing number of wavevectors. This cascade of phase transitions is directly linked to the fact that, due to the rotational invariance, all the wavevectors directions which can enter the order parameter are degenerate. We study how this cascade of phase transitions is modified when one takes into account the anisotropy arising in a real solid state compound. For a simple model of anisotropy with elliptical dispersion relation, we find surprisingly that the cascade of phase transitions is not modified and the degeneracy with respect to the wavevector direction is still present. When we take into account a deviation with respect to this elliptical model, which is treated to first order in perturbation, we find that the degeneracy is lifted and that, basically, a single wavevector is favored right at the transition. However when one enters the superfluid phase, additional wavevectors come in the order parameter and the cascade of transitions is still present, though in a modified form.