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

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