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

Abstract

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 liquidcrystalline "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 vortexdislocation 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.

Fulde-Ferrell states and Berezinskii-Kosterlitz-Thouless phase transition in two-dimensional imbalanced Fermi gases

“…As was predicted by Nelson and Kosterlitz [68] in the isotropic case, the superfluid density jumps from ρ = 2T BKT /π to zero as T crosses T BKT from below. This has been observed experimentally in 2D 4 He films [74] and recently also in cold Bose gases [75]. We expect it is also true for the anisotropic FF state.…”

“…Another candidate for an inhomogeneous order parameter is the LO state, which does not have the problem of a vanishing transverse superfluid density [4]; however, it was also claimed to be unstable to a nematic phase at nonzero temperatures [33]. There has been one paper studying the BKT phase transition of the LO (stripe) state for an anisotropic 2D system composed of coupled 1D tubes [81], where several different BKT critical temperatures associated with different defects are discussed and found to be linearly dependent on the intertube coupling.…”

“…One may also consider the Larkin-Ovchinnikov (LO) state [3] with 0 cos(2Q · x), which can be taken as the superposition of two equal FF modes with opposite momenta [4]. More generally, the nonuniform order parameter can be expressed as a superposition of many possible FFLO vectors by Q 0Q e i2Q·x .…”

Holographic entanglement entropy in imbalanced superconductors

“…For this reasons the imbalanced systems has been studied vigorously -both theoretically and experimentally. Theoretical studies on imbalanced systems often focus on the possibility of exploring imbalanced superconducting states in different JHEP01 (2014)136 physical systems, for example, in population-imbalanced Ultracold atomic gases [38,[40][41][42], optical lattices [43], heavy-fermionic superconductor CeCoIn 5 [44], two-dimensional organic superconductors [37,39,45,46] and quark matter core of the neutron stars [47,48]. The experimental search is a topic of vigorous research till date as it is very hard to pinpoint this state in the phase diagram.…”

Cascade of Solitonic Excitations in a Superfluid Fermi gas: From Planar Solitons to Vortex Rings and Lines

“…A natural extension of our work is to approach a regime where the snake instability is inhibited, e.g., via a strong confining potential in the radial direction. Future prospects are a measurement of the soliton's current-phase relation in the BEC-BCS crossover [41,42], the detection and manipulation of Andreev bound states trapped inside the soliton [3,4], and the creation of soliton trains in the presence of spin imbalance, which would realize one limit of Fulde-Ferrell-Larkin-Ovchinnikov states [43][44][45].…”