Topological aspect of graphene physics

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.

12 pages, 8 figures. Proceedings for HMF-19

References in corpus (7)

• Unconventional Integer Quantum Hall effect in graphene
• Gauge field induced by ripples in graphene
• Four-dimensional graphene and chiral fermions
• Quantum Hall plateau transition in graphene with spatially correlated random hopping
• Symmetry protected Z2-quantization and quaternionic Berry connection with Kramers degeneracy
• Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields
• Edge states in graphene in magnetic fields -- a speciality of the edge mode embedded in the n=0 Landau band

Cited by in corpus (17)

• Electronic and optical properties of strained graphene and other strained 2D materials: a review
• The Rare Two-Dimensional Materials with Dirac Cones
• Nonlinear quantum optical properties of graphene: the role of chirality and symmetry
• Antichiral states in twisted graphene multilayers
• Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice
• Landau Levels in Uniaxially Strained Graphene: A Geometrical Approach
• SU(3) Dirac electrons in the 1/5-depleted square-lattice Hubbard model at 1/4 filling
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
• Bulk-edge correspondence with generalized chiral symmetry
• Topologically protected Landau levels in bilayer graphene in finite electric fields
• Dirac fermions in graphene and analogues: magnetic field and topological properties
• Pseudo chiral anomaly in zigzag graphene ribbons
• Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions
• Fermi point in graphene as a monopole in momentum space
• Green functions in graphene monolayer with Coulomb interactions taken into account
• On topological aspects of 2D graphene like materials
• Chiral Symmetry and Many-Body Effect in Multilayer Graphene