Conventional and charge-six superfluids from melting hexagonal Fulde-Ferrell-Larkin-Ovchinnikov phases in two dimensions

We consider defect-mediated melting of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and pair density wave (PDW) phases in two dimensions. Examining mean-field ground states in which the spatial oscillations of the FFLO/PDW superfluid order parameter exhibit hexagonal lattice symmetry, we find that thermal melting leads to a variety of novel phases. We find that a spatially homogeneous charge 6 superfluid can arise from melting a hexagonal vortex-antivortex lattice FFLO/PDW phase. The charge 6 superfluid has an order parameter corresponding to a bound state of six fermions. We further find that a hexagonal vortex-free FFLO/PDW phase can melt to yield a conventional (charge 2) homogeneous superfluid. A key role is played by topological defects that combine fractional vortices of the superfluid order and fractional dislocations of the lattice order.

Figure 1

Directions of ${\mathbf{Q}}_i$ used in the text.

Figure 2

Hexagonal FFLO/PDW states considered in detail in this paper. Filled (red) circles depict maxima in the magnitude of the superfluid density, and plus(minus) signs depict vortices of positive(negative) phase winding. Both states are stable 2D FFLO states in weak-coupling theories with cylindrical symmetry.

Figure 3

Phase diagrams for ${\Psi }_{▵}$ and ${\Psi }_{\text{v-av}}$. Phase boundaries are given by solid lines. The shaded triangles are discussed in the text. The new phases that arise from melting the FFLO/PDW phases are the density wave, superfluid, orbital antiferromagnet, and homogeneous charge six superfluid (${\Psi }_{6e}$) phases. The density wave phase has no superfluid order and breaks translational symmetry through the formation of a hexagonal lattice. The superfluid phase is a homogenous conventional paired superfluid. The orbital antiferromagnet phase has no superfluid order and hexagonal orbital current antiferromagnetic order. The ${\Psi }_{6e}$ phase is a spatially homogenous superfluid phase of bound states of six fermions