Holelike analytic mean-field solutions in the fractional quantum Hall regime

We show that besides the Wigner crystal, the lowest Landau level supports a state with the same unit cell but a qualitatively different charge density distribution. Instead of periodic peaks, the new state forms percolating ridges that may favor an energy decrease through correlated ring exchange contributions. It is found after developing a general framework for the determination of the mean-field states at arbitrary filling factor p∕q, q odd. For fillings 1∕q, the eigenstate is given in complete analytical form. In the case for which the unit cell contains one half electron, a crossover is found close to filling 1∕7 between this state and the periodic peak solid, suggesting that it may compete with the Wigner solid after correlations are included.