Edge and Surface States in the Quantum Hall Effect in Graphene

TL;DR

This paper investigates how edge reconstruction in graphene's quantum Hall effect, influenced by interactions, disorder, and edge details, affects tunneling behavior and quantization of Hall conductivity.

Contribution

It reveals the interplay between edge states, disorder, and interactions causes non-universal tunneling exponents and deviations from perfect quantization in graphene.

Findings

Edge reconstruction occurs due to interactions and disorder.

Tunneling exponents become non-universal.

Hall conductivity deviates from perfect quantization.

Abstract

We study the integer and fractional quantum Hall effect on a honeycomb lattice at half-filling (graphene) in the presence of disorder and electron-electron interactions. We show that the interactions between the delocalized chiral edge states (generated by the magnetic field) and Anderson-localized surface states (created by the presence of zig-zag edges) lead to edge reconstruction. As a consequence, the point contact tunneling on a graphene edge has a non-universal tunneling exponent, and the Hall conductivity is not perfectly quantized in units of $e^2/h$. We argue that the magneto-transport properties of graphene depend strongly on the strength of electron-electron interactions, the amount of disorder, and the details of the edges.