Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points

Abstract

We revisit the question concerning stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. Invoking the properties of the putative phase diagram of two-component Fermi mixtures, on general grounds we argue, that for isotropic, continuum systems the phase diagram hosting a long-range-ordered FFLO-type phase envisaged by the mean-field theory cannot be stable to fluctuations at any temperature T > 0 in any dimensionality d < 4. In contrast, in layered unidirectional systems the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at T > 0 is d = 5/2. In consequence, its occurrence is excluded in d = 2, but not in d = 3. We propose a relatively simple method, based on nonperturbative renormalization group to compute the critical exponents of the thermal m-axial Lifshitz point continuously varying m, spatial dimensionality d and the number of order parameter components N. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.