Edge and surface states in the quantum Hall effect in graphene

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 nonuniversal tunneling exponent, and the Hall conductivity is not perfectly quantized in units of e²∕h. We argue that the magnetotransport properties of graphene depend strongly on the strength of electron-electron interactions, the amount of disorder, and the details of the edges.