Topological aspect of graphene physics

Understand

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.