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 the stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. On general grounds, we argue that the mean-field phase diagram hosting a Lifshitz point cannot be stable to fluctuations for isotropic, continuum systems, 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.