Fractional Quantum Hall Effect in n=0 Landau Band of Graphene with Chern Number Matrix

TL;DR

This paper investigates fractional quantum Hall states in graphene's n=0 Landau band, emphasizing the role of lattice structure, chirality, and Chern number matrices, revealing a quantum phase transition linked to chirality ferromagnetism.

Contribution

It introduces a novel approach by incorporating lattice effects and chirality into the analysis of fractional quantum Hall states in graphene, defining and evaluating Chern number matrices.

Findings

Identification of a quantum phase transition related to interaction range changes.

Ground state consistent with Halperin 331 state in bilayer quantum Hall system.

Demonstration of chirality ferromagnetism in the system.

Abstract

Fully taking into account of the honeycomb lattice structure, fractional quantum Hall states of graphene are considered by a pseudopotential projected into the n = 0 Landau band. By using a chirality as an internal degree of freedom, the Chern number matrices are defined and evaluated numerically. Quantum phase transition induced by changing a range of the interaction is demonstrated which is associated with chirality ferromagnetism. The chirality-unpolarized ground state is consistent with the Halperin 331 state of the bilayer quantum Hall system.