Electronic Properties of Graphene in a Strong Magnetic Field

TL;DR

This paper reviews the electronic properties of graphene under strong magnetic fields, focusing on relativistic quantum Hall effects, electron interactions, and related phenomena, linking theoretical models with experimental observations.

Contribution

It provides a comprehensive theoretical overview of electron behavior in graphene in high magnetic fields, including Landau quantization and interaction effects, with relevance to recent experimental findings.

Findings

Observation of relativistic quantum Hall effect in graphene

Analysis of electron-electron interactions in Landau levels

Discussion of exotic quantum phases and fractional quantum Hall states

Abstract

We review the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field. One of its most salient features is the relativistic quantum Hall effect the observation of which has been the experimental breakthrough in identifying pseudo-relativistic massless charge carriers as the low-energy excitations in graphene. The effect may be understood in terms of Landau quantization for massless Dirac fermions, which is also the theoretical basis for the understanding of more involved phenomena due to electronic interactions. We present the role of electron-electron interactions both in the weak-coupling limit, where the electron-hole excitations are determined by collective modes, and in the strong-coupling regime of partially filled relativistic Landau levels. In the latter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states. Furthermore, we discuss briefly the electron-phonon coupling in a strong magnetic field. Although the present review has a dominating theoretical character, a close connection with available experimental observation is intended.