Half-integer contributions to the quantum Hall conductivity from single Dirac cones

Abstract

While the quantum Hall effect in graphene has been regarded as a realization of the anomaly associated with the massless Dirac particle carrying half the usual topological integer, this is hidden due to the doubling of the Dirac cones. In order to confirm the half-integer contribution from each Dirac cone, here we theoretically consider a lattice model in which the relative energy between the two Dirac points is systematically shifted. With an explicit calculation of the topological (Chern) number, we have demonstrated that each Dirac cone does indeed contribute to the Hall conductivity as the half odd integer series (... -3/2, -1/2, 1/2, 3/2, ...) when the Fermi energy traverses the (shifted sets of) Landau levels. The picture is also endorsed, via the bulk-edge correspondence, from the edge mode spectrum for the present model.

4 pages, 4 figures

References in corpus (4)

• The electronic properties of graphene
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields

Cited by in corpus (19)

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• Parity Anomaly in the non-linear response of Nodal-Line Semimetals
• Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model
• Edge modes and non local conductance in graphene superlattices
• The influence of anti-chiral edge states on Andreev reflection in graphene-superconductor junction
• Characterizing the weak topological properties: Berry phase point of view
• Different models of gravitating Dirac fermions in optical lattices
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
• Trigonal distortion of topologically confined channels in bilayer Graphene
• Probing Half-odd Topological Number with Cold Atoms in a Non-Abelian Optical Lattice
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene
• Elastic gauge fields and zero-field 3D quantum Hall effect in hyperhoneycomb lattices
• Chiral edge mode for single-cone Dirac fermions
• Bulk-Boundary Correspondence for Topological Insulators with Quantized Magneto-Electric Effect
• Out-of-plane spin polarization of edge currents in Chern insulator with Rashba spin-orbit interaction
• Distribution of Chern number by Landau level broadening in Hofstadter's butterfly
• Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice