Commensurability condition and hierarchy of fillings for FQHE in higher Landau levels in conventional 2DEG systems and in graphene—monolayer and bilayer

Abstract

The structure of the filling rate hierarchy referred to as the fractional quantum Hall effect is studied in higher Landau levels using the commensurability condition. The hierarchy of fillings that are derived in this manner is consistent with the experimental observations of the first three Landau levels in conventional semiconductor Hall systems. The relative poverty of the fractional structure in higher Landau levels compared with the lowest Landau level is explained using commensurability topological arguments. The commensurability criterion for correlated states for higher Landau levels (with ) including the paired states at half fillings of the spin-subbands of these levels is formulated. The commensurability condition is applied to determine the hierarchy of the fractional fillings of Landau levels in the monolayer and bilayer graphene. Good agreement with current experimental observations of fractional quantum Hall effect in the graphene monolayer and bilayer is achieved. The presence of even denominator rates in the hierarchy for fractional quantum Hall effect in the bilayer graphene is also explained.