Chiral condensate with topological degeneracy in graphene and its manifestation in edge states

Abstract

Role of chiral symmetry in many-body states of graphene in strong magnetic fields is theoretically studied with the honeycomb lattice model. For a spin-split Landau level where the leading electron-electron interaction is the nearest-neighbor repulsion, a chiral condensate is shown to be, within the subspace of n = 0 Landau level, an exact many-body ground state with a finite gap, for which calculation of Chern numbers reveals that the ground state is a Hall insulator with a topological degeneracy of two. The topological nature of the ground state is shown to manifest itself as a Kekuléan bond order along armchair edges, while the pattern melts in the bulk due to quantum fluctuations. The whole story can be regarded as a realization of the bulk-edge correspondence peculiar to the chiral symmetry.

5 pages, 4 figures, submitted to PRB

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Cited by in corpus (9)

• Many-body Chern number without integration
• Chiral symmetry and its manifestation in optical responses in graphene: interaction and multi-layers
• Zero modes of the generalized fermion-vortex system in magnetic field
• Many-Body Chern Numbers of $\nu =1/3$ and $1/2$ States on Various Lattices
• Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement
• Fractional Quantum Hall Effect in n=0 Landau Band of Graphene with Chern Number Matrix
• Spin-resoloved chiral condensate as a spin-unpolarized ν=0 quantum Hall state in graphene
• Adiabatic Continuity of the Spinful Quantum Hall States
• Chiral Symmetry and Many-Body Effect in Multilayer Graphene