Topological aspect of graphene physics

Details Topological aspect of graphene physics Topological aspect of graphene physics

2010-08-27

arxiv.org/abs/1008.4653v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 8 figures. Proceedings for HMF-19

Scientific paper

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.

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