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

TL;DR

This paper reviews the bulk-edge correspondence in graphene, focusing on topologically protected edge states, including quantum Hall states and chiral zero modes, highlighting their relation to chiral symmetry and Dirac fermions.

Contribution

It provides a comprehensive review of edge states in graphene with and without magnetic fields, emphasizing the role of chiral symmetry and topological order.

Findings

Quantum Hall edge states are topologically protected.

Chiral zero modes are guaranteed by chiral symmetry.

Edge states are linked to bulk topological properties.

Abstract

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.