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There are two types of edge states in graphene with/without magnetic field.One is a quantum Hall edge state, which is topologically protected againstsmall perturbation. The other is a chiral zero mode that is localized near theboundary with/without magnetic field. The latter is also topological but isguaranteed to be zero energy by the chiral symmetry, which is also responsiblefor massless Dirac like dispersion. Conceptual roles of the edge states arestressed and reviewed from a view point of the bulk-edge correspondence and thetopological order.

Bulk-edge correspondence in graphene with/without magnetic field: Chiral symmetry, Dirac fermions and Edge states