Integer Quantum Hall Effect in Graphene

TL;DR

This paper investigates the quantum Hall effect in monolayer graphene using thermodynamical methods, considering Dirac particles in electromagnetic fields and edge effects, to derive Hall conductivity from thermodynamic properties.

Contribution

It introduces a thermodynamical approach to analyze the quantum Hall effect in graphene, explicitly incorporating edge effects and Dirac particle behavior.

Findings

Derived thermodynamical potential at low temperature and weak electric field

Established quantized Hall conductivity from thermodynamic quantities

Linked particle numbers to magnetic flux for conductivity calculation

Abstract

We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges effect as a pseudo-potential varying continuously along the $x$ direction. At low temperature and in the weak electric field limit, we explicitly determine the thermodynamical potential. With this, we derive the particle numbers in terms of the quantized flux and therefore the Hall conductivity immediately follows.