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Edge and Surface States in the Quantum Hall Effect in Graphene

A. H. Castro Neto·F. Guinea·N. M. R. Peres
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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.

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A. H. Castro Neto, F. Guinea, N. M. R. Peres. 2006-05-15. Edge and Surface States in the Quantum Hall Effect in Graphene. https://doi.org/10.1103/physrevb.73.205408

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