Low Temperature Physics: 34, 778 (2008); https://doi.org/10.1063/1.2981387 (12 pages)
Физика Низких Температур: Том 34, Выпуск 10 (Октябрь 2008), c. 993-1006    ( к оглавлению , назад )

Edge states in quantum Hall effect in graphene
(Review Article)

V.P. Gusynin1, V.A. Miransky2,*, S.G. Sharapov3, and I.A. Shovkovy3,*

1 Bogolyubov Institute for Theoretical Physics, 03680, Kiev, Ukraine
E-mail: vgusynin@bitp.kiev.ua

2 Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada

3 Department of Physics, Western Illinois University, Macomb, IL 61455, USA

Received February 15, 2008


We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. In particular, a special attention is payed to the derivation of the conditions under which gapless edge states exist in the spectrum of graphene with zigzag and armchair edges.We find that in the case of a half-plane or a ribbon with a zigzag edges, there are gapless edge states only when a spin gap dominates over a Dirac mass gap. In the case of a half-plane with an armchair edge, the existence of the gapless edge states depends on the specific type of Dirac mass gaps. The implications of these results for the dynamics in the quantum Hall effect in graphene are discussed.

PACS: 73.43.Cd Theory and modeling;
PACS: 71.70.Di Landau levels;
PACS: 81.05.Uw Carbon, diamond, graphite.

Key words: graphene, quantum Hall effect, Dirac mass gap.