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

• Published in: Физика низких температур
• Date: 2008
• Main Authors: Gusynin, V.P., Miransky, V.A., Sharapov, S.G., Shovkovy, I.A.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2008
• Subjects: Graphene and graphite multilayers
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/117555
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Edge states in quantum Hall effect in graphene
 (Review Article) / V.P. Gusynin, V.A. Miransky, S.G. Sharapov, I.A. Shovkovy // Физика низких температур. — 2008. — Т. 34, № 10. — С. 993-1006. — Бібліогр.: 52 назв. — англ.

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.