Topological aspect of graphene physics

TL;DR

This paper reviews the topological properties of graphene, emphasizing massless Dirac fermions, topological protection, and quantum Hall effects, highlighting the role of Berry connection and bulk-edge correspondence in its boundary phenomena.

Contribution

It provides a comprehensive review of the topological aspects of graphene, including protection of Dirac cones and the application of bulk-edge correspondence principles.

Findings

Dirac cones are topologically protected by chiral symmetry.

Quantum Hall effect involves non-Abelian gauge structures.

Bulk-edge correspondence explains boundary phenomena in graphene.

Abstract

Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is described by the Berry connection of a manybody state by the filled Landau levels which naturally possesses non-Abelian gauge structures. A generic principle of the topologically non trivial states as the bulk-edge correspondence is applied for graphene with/without magnetic field and explain some of the characteristic boundary phenomena of graphene.