The Quantum Hall Effect in Graphene

TL;DR

This paper explores how the quantum Hall effect in graphene involves dynamical mass generation that breaks valley degeneracy at the n=0 Landau level, explaining new quantum Hall plateaus.

Contribution

It introduces a mechanism for dynamical mass generation in graphene under magnetic fields, explaining the emergence of the ν=±1 quantum Hall plateaus.

Findings

Dynamical mass generation occurs in graphene with magnetic fields.

Valley degeneracy is broken only at the n=0 Landau level.

The mechanism accounts for observed quantum Hall plateaus at ν=±1.

Abstract

We investigate the quantum Hall effect in graphene. We argue that in graphene in presence of an external magnetic field there is dynamical generation of mass by a rearrangement of the Dirac sea. We show that the mechanism breaks the lattice valley degeneracy only for the $n=0$ Landau levels and leads to the new observed $\nu = \pm 1$ quantum Hall plateaus. We suggest that our result can be tested by means of numerical simulations of planar Quantum Electro Dynamics with dynamical fermions in an external magnetic fields on the lattice.