Edge structure of graphene monolayers in the {\nu} = 0 quantum Hall state

TL;DR

This paper investigates how the edges of monolayer graphene influence its quantum Hall states at neutrality, revealing smooth connections between bulk phases and edge states, with implications for electronic excitations and phase transitions.

Contribution

It introduces a Hartree-Fock approach with space-dependent ordering to model edge effects in graphene's quantum Hall states, connecting bulk phases to edge phenomena.

Findings

All bulk phases connect smoothly to Kekule9 edges.

Single-particle excitations vary with spatial order parameters.

Metal-insulator transition depends on Zeeman energy, not just bulk order.

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$\'e$ distortion are smoothly connected to a Kekul$\'e$-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.