Mean field exact solutions showing charge density wave crossover at low fillings in the fractional quantum Hall regime

摘要

A general analytical framework for the determination of the mean field statesat arbitrary rational filling factors for the 2DEG in FQHE regime is given. Itsuse allows to obtain analytic expressions for the solutions at filling factorsof the form $\nu=1/q$ for arbitrary odd $q$. The analysis can be performed fortwo general classes of states characterized by $\gamma=1$ or $\gamma={1/2}$particles per unit cell. Instead of the periodic peaks of the Wigner solidsolution, the new states show electron densities forming percolating ridgesthat may favor an energy decrease through correlated ring of exchangecontributions. Therefore, we estimate that they can realize mean field versionsof the so called Hall Crystal (HC) states. The obtained analytic HC solutionshows the same crystalline symmetry that the corresponding WC state in itsclass $\gamma=1$, but a qualitatively different charge density distribution.The energy dependence of the corresponding HC and WC states on the fillingfactor is also evaluated here for the class $\gamma=1/2$. The results show acrossover between HC state and the Wigner crystal, close to filling 1/7.Therefore, transitions may occur from one to the other as the electron densityis varied. This result is consistent with recent experimental findings.