Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene

TL;DR

This paper explains the unusual quantum Hall states in monolayer graphene under strong magnetic fields as resulting from interaction-driven chiral symmetry-breaking, supported by self-consistent calculations matching experimental data.

Contribution

It introduces a novel interaction-based explanation for quantum Hall states in graphene, emphasizing chiral symmetry-breaking orders and their magnetic field dependence.

Findings

Chiral symmetry-breaking explains $ u=0$ and $ u= ext{±}1$ states.

Self-consistent calculations match experimental activation gaps.

Implications for fractional quantum Hall states are discussed.

Abstract

Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $\nu = 0$ and $\nu = \pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from interaction-induced chiral symmetry-breaking orders. We argue that when the chemical potential is at the Dirac point, weak on-site repulsion supports an easy-plane antiferromagnet state, which simultaneously gives rise to ferromagnetism oriented parallel to the magnetic field direction, whereas for $|\nu|=1$ easy-axis antiferromagnet and charge-density-wave orders coexist. We perform self-consistent calculations of the magnetic field dependence of the activation gap for the $\nu = 0$ and $|\nu| = 1$ states and obtain excellent agreement with recent experimental results. Implications of our study for fractional Hall states in monolayer graphene are highlighted.