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

Abstract

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.