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 six superfluid can arise from melting a hexagonal vortex-anitvortex lattice FFLO/PDW phase. The charge six 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 two) 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.