Toward theory of quantum Hall effect in graphene

TL;DR

This paper develops a theoretical framework for understanding the quantum Hall effect in graphene, showing that magnetic field-induced order parameters coexist and may influence edge state properties.

Contribution

It introduces a gap equation analysis revealing the coexistence of ferromagnetic and excitonic order parameters in graphene under magnetic fields, advancing the theoretical understanding of quantum Hall phenomena.

Findings

Coexistence of ferromagnetic and excitonic order parameters in graphene.

Description of solutions matching experimental quantum Hall plateaus.

Implications for the existence of gapless edge states.

Abstract

We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic catalysis dynamics necessarily coexist (the latter have the form of Dirac masses and correspond to excitonic condensates). This feature of graphene could lead to important consequences, in particular, for the existence of gapless edge states. Solutions of the gap equation corresponding to recently experimentally discovered novel plateaus in graphene in strong magnetic fields are described.