title: Unconventional fractional quantum Hall effect in monolayer and bilayer graphene.
abstract: The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition.
authors.affiliation: Institute of Physics, Wrocław University of Technology , Wyb. Wyspiańskiego 27, 50-370, Wrocław , Poland .
authors.forename: Janusz
authors.initials: J
authors.lastname: Jacak
authors.affiliation: Institute of Physics, Wrocław University of Technology , Wyb. Wyspiańskiego 27, 50-370, Wrocław , Poland .
authors.forename: Lucjan
authors.initials: L
authors.lastname: Jacak
keywords: 104 Carbon and related materials; 105 Low-Dimension(1D/2D) materials; 40 Optical, magnetic and electronic devicematerials; FQHE; Monolayer graphene; bilayer graphene; hierarchy of filling fractions