Edge structure of graphene monolayers in the ν = 0 quantum Hall state

Abstract

Monolayer graphene at neutrality in the quantum Hall regime has many competing ground states with various types of ordering. The outcome of this competition is modified by the presence of the sample boundaries. In this paper we use a Hartree-Fock treatment of the electronic correlations allowing for space-dependent ordering. The edge influence is modeled by a simple perturbative effective magnetic field in valley space. We find that all phases found in the bulk of the sample, ferromagnetic, canted antiferromagnetic, charge-density wave and Kekul$\acute{e}$ distortion are smoothly connected to a Kekul$\acute{e}$-distorted edge. The single-particle excitations are computed taking into account the spatial variation of the order parameters. An eventual metal-insulator transition as a function of the Zeeman energy is not simply related to the type of bulk order.

18 pages, 11 figures, corresponds to published version

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• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Phase diagram of a graphene bilayer in the zero-energy Landau level
• Symmetry characterization of the collective modes of the phase diagram of the $\nu =0$ quantum Hall state in graphene: Mean-field and spontaneously broken symmetries
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• SU(4) Symmetry Breaking and Induced Superconductivity in Graphene Quantum Hall Edges
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• Quantum Monte Carlo at the Graphene Quantum Hall Edge
• Landau Level Phases in Bilayer Graphene under Pressure at Charge Neutrality
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
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