Fluctuations and phase transitions in Larkin-Ovchinnikov liquid-crystal states of a population-imbalanced resonant Fermi gas

Motivated by a realization of imbalanced Feshbach-resonant atomic Fermi gases, we formulate a low-energy theory of the Fulde-Ferrell and the Larkin-Ovchinnikov (LO) states and use it to analyze fluctuations, stability, and phase transitions in these enigmatic finite momentum-paired superfluids. Focusing on the unidirectional LO pair-density-wave state, which spontaneously breaks the continuous rotational and translational symmetries, we show that it is characterized by two Goldstone modes, corresponding to a superfluid phase and a smectic phonon. Because of the liquid-crystalline softness of the latter, at finite temperature the three-dimensional state is characterized by a vanishing LO order parameter, quasi-Bragg peaks in the structure and momentum distribution functions, and a charge-4, paired-Cooper-pairs, off-diagonal long-range order, with a superfluid-stiffness anisotropy that diverges near a transition into a nonsuperfluid state. In addition to conventional integer vortices and dislocations, the LO superfluid smectic exhibits composite half-integer vortex-dislocation defects. A proliferation of defects leads to a rich variety of descendant states, such as the charge-4 superfluid and Fermi-liquid nematics and topologically ordered nonsuperfluid states, that generically intervene between the LO state and the conventional superfluid and the polarized Fermi liquid at low and high imbalance, respectively. The fermionic sector of the LO gapless superconductor is also quite unique, exhibiting a Fermi surface of Bogoliubov quasiparticles associated with the Andreev band of states, localized on the array of the LO domain walls.