Charge-flux density waves: anyons in a periodic potential

We show that the lattice periodicity which causes a modulation of the charge density by a wave vector q also leads to a modulation of the flux density if the charged particles are anyons. Within mean field theory, we obtain a Charge and Flux Density Wave (CFDW) where the degenerate Landau levels of a constant magnetic field split into bands. For a weak periodic flux superimposed on a strong constant flux, anyon superconductivity at integer filling of Landau levels (corresponding to a statistics parameter of θ = π(1 − 1/ν) with ν = n = integer) is not affected. However, at statistics corresponding to non-integer filling of Landau levels, for certain commensurability conditions between the lattice length (a), the magnetic length (l) and the filling fraction (ν), gaps open up at the Fermi level and convert an anyon metal into an anyon insulator