A study of the magnetotransport properties of the graphene (II. Fractional Quantum Hall Effect)

TL;DR

This paper explores the fractional quantum Hall effect in graphene by adapting a model originally developed for 2D electron systems, emphasizing symmetry breaking in the Hamiltonian under magnetic fields and impurity effects.

Contribution

It introduces a novel approach to explaining fractional quantum Hall states in graphene based on symmetry breaking of the Hamiltonian, extending previous models to this material.

Findings

Predicts odd fractional states p/3 in graphene

Explains the formation of quantum Hall plateaux in graphene

Shows the evolution of Hamiltonian symmetry with magnetic field strength

Abstract

We present an approach to the fractional quantum Hall effect observed in grapheme (GFQHE), basing us on the model developed previously for the fractional quantum Hall effect in a two-dimensional electron system embedded in a quantum well (FQHE) [Hidalgo, 2013(*)]. The main idea in the view proposed f0r the FQHE is the breaking of the symmetry of the Hamiltonian of every electron in a two-dimensional electron gas (2DEG) under the application of a magnetic field and in the presence of an electrostatic potential due to the ionized impurities. As the magnetic field increases the effect of that electrostatic potential evolves; changing in turn the spatial symmetry of the Hamiltonian: from continuous to discrete one. The model provides the odd fractional states, and corresponding plateaux, p/3, p being any integer, observed in graphene.