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

TL;DR

This paper theoretically investigates the role of chiral symmetry in the many-body states of graphene under strong magnetic fields, revealing a topologically degenerate Hall insulator with edge Kekulé bond order.

Contribution

It demonstrates that the chiral condensate in graphene's n=0 Landau level is an exact ground state with topological degeneracy and edge manifestations, highlighting a unique bulk-edge correspondence.

Findings

Ground state is a Hall insulator with topological degeneracy of two.

Edge states exhibit Kekulé bond order pattern.

Bulk pattern melts due to quantum fluctuations.

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 Kekul\'ean 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.