Theory of the quantum Hall effect in graphene

TL;DR

This paper presents a novel theoretical approach to the quantum Hall effect in graphene, emphasizing boundary conditions and contact effects over traditional edge-state and disorder models.

Contribution

It introduces a current injection model that explains the quantum Hall effect in graphene without relying on disorder or edge states.

Findings

Boundary conditions determine current-voltage characteristics.

Disorder and edge states are not essential in this model.

Provides a new perspective on quantum Hall effect mechanisms.

Abstract

We study the quantum Hall effect (QHE) in graphene based on the current injection model. In our model, the presence of disorder, the edge-state picture, extended states and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics.