Hierarchy of fillings for FQHE in monolayer and in bilayer graphene: Explanation of $\nu=-\frac{1}{2}$ fractional quantum Hall state in bilayer graphene

TL;DR

This paper applies the commensurability condition to determine the hierarchy of fractional quantum Hall states in monolayer and bilayer graphene, explaining observed filling fractions including even denominators, with good experimental agreement.

Contribution

It introduces a hierarchy model based on commensurability conditions to explain FQHE in graphene, including the $ u=-rac{1}{2}$ state in bilayer graphene.

Findings

Hierarchy of fractional fillings derived for graphene

Good agreement with experimental data

Explanation of even denominator filling fractions

Abstract

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and bilayer graphene. The filling rates for FQHE in graphene are found and illustrated in the first three Landau levels. The good agreement with the experimental data is achieved. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained.