Graphene: Topological Properties, Chiral Symmetry and Their Manipulation

Abstract

AbstractThis chapter looks at graphene from the viewpoint of underlying chiral symmetry and topological properties. This reveals why a seemingly simple honeycomb lattice can harbour such a rich physics, which includes doubled Dirac cones at K and K′ points in the Brillouin zone, anomalously sharp Landau level and quantum Hall effect at the Dirac point in magnetic fields even with ripples, and a host of other peculiar features of graphene. After giving a self-contained description of these notions, we then describe how topological and chiral properties also dictate that there is a close link between bulk and edge states. We also emphasise that the notion of chiral and topological properties are so universal (and robust) that we can also examine various extensions to electron-hole asymmetric cones, tilted cones, cone + flat-band system, bilayer graphene, and many-body graphene. As a novel way of manipulating the system, we also describe a Floquet topological state for graphene in nonequilibrium.KeywordsChiral SymmetryLandau LevelEdge StateDirac FermionDirac PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.