Theoretical Aspects of the Fractional Quantum Hall Effect in Graphene

TL;DR

This paper reviews the theoretical understanding of strong correlation effects in graphene's Landau levels, focusing on quantum Hall ferromagnetism and fractional quantum Hall states within an SU(4) symmetry framework, and compares theory with experiments.

Contribution

It provides a comprehensive theoretical analysis of fractional quantum Hall effects in graphene, emphasizing the SU(4) symmetry and strong correlation limit, and relates findings to experimental data.

Findings

Identification of SU(4) symmetry in graphene Landau levels

Explanation of quantum Hall ferromagnetism in graphene

Analysis of fractional quantum Hall states in strong correlation regime

Abstract

We review the theoretical basis and understanding of electronic interactions in graphene Landau levels, in the limit of strong correlations. This limit occurs when inter-Landau-level excitations may be omitted because they belong to a high-energy sector, whereas the low-energy excitations only involve the same level, such that the kinetic energy (of the Landau level) is an unimportant constant. Two prominent effects emerge in this limit of strong electronic correlations: generalised quantum Hall ferromagnetic states that profit from the approximate four-fold spin-valley degeneracy of graphene's Landau levels and the fractional quantum Hall effect. Here, we discuss these effects in the framework of an SU(4)-symmetric theory, in comparison with available experimental observations.