Abstract
Recently, in certain flat band lattice systems at commensurate fillings, fractional quantum Hall states have been found -- which have anyonic excitations. We study such systems away from commensuration, i.e. the ground state of an anyon gas in such a system. The presence of the underlying lattice allows access to an entirely new regime where the anyon kinetic energy can be larger than their interaction energy. Within the flux-attachment approach, using mean-field then adding fluctuations, we find several possible superfluid states. Two have intrinsic topological order, i.e. fractionalized quasiparticles with a fusion structure of (Z_2)^4 and (Z_8)^2 respectively, and a third has no fractionalized excitations similar to a BCS-type state. This represents a mechanism for superconductivity driven purely by strong repulsion and complex hopping of electrons.
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