Electron interactions in graphene in a strong magnetic field

TL;DR

This paper investigates how electron interactions and symmetry-breaking effects influence the quantum Hall states in graphene, highlighting differences between Landau levels and the role of lattice effects and pseudopotentials.

Contribution

It provides a detailed analysis of symmetry-breaking terms in graphene's Landau levels, especially contrasting the n=0 level with others, using a lattice-based approach and continuum limit.

Findings

Leading symmetry-breaking terms differ in origin between n=0 and other Landau levels.

The ratio of lattice constant to magnetic length acts as a small control parameter.

The study evaluates the easy-plane anisotropy of the graphene ferromagnet.

Abstract

Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.