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

Understand

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, that 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 3d 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.