Topological low-energy modes in N=0 Landau levels of graphene: a possibility of a quantum-liquid ground state

TL;DR

This paper explores how electron interactions in graphene's Landau levels can lead to a Kekule bond order, resulting in topological in-gap states and suggesting a potential quantum-liquid ground state.

Contribution

It introduces a novel mechanism for splitting zero-energy Landau levels in graphene via Kekule bond ordering, highlighting topological in-gap states and the possibility of a quantum-liquid ground state.

Findings

Kekule pattern induces level splitting in graphene's Landau levels.

Topological in-gap states are localized along domain boundaries.

A quantum-liquid ground state in graphene under magnetic fields is proposed.

Abstract

We point out that the zero-energy Landau level of Dirac fermions in graphene can be, in the presence of a repulsive electron-electron interaction, split into two (levels) associated with a "bond ordering" formation having a "Kekule pattern", which respects the chiral symmetry. Since the Kekule pattern has a three-fold degeneracy, domain structures are implied, for which we show that in-gap states localized along the domain boundaries exist as topological states. Based on this a possibility of a quantum-liquid ground state of graphene in magnetic fields is discussed.