Spectrum of edge states in the $\nu=0$ quantum Hall phases in graphene

TL;DR

This paper analyzes edge states in the $ u=0$ quantum Hall phase in graphene, deriving analytical wave functions and dispersion relations for various symmetry-breaking phases, and examining the impact of next-nearest neighbor hopping.

Contribution

It provides analytical expressions for edge state wave functions and dispersion relations across different phases and boundary types in graphene's quantum Hall regime, including the effects of next-nearest neighbor hopping.

Findings

Gapless edge states depend on phase and boundary type.

Next-nearest neighbor hopping significantly influences edge spectra.

Criteria for gapless edge states are established for each phase.

Abstract

Edge excitations of the $\nu=0$ quantum Hall state in monolayer graphene are studied within the mean-field theory with different symmetry-breaking terms. The analytical expressions for the continuum (Dirac) model wave functions are obtained for the charge density wave, Kekul\'e distortion, ferromagnetic, and (canted) antiferromagnetic phases. The dispersion equations for each phase and boundary type (zigzag and armchair) are derived, numerically solved, and compared to the results of the corresponding effective tight-binding model. The effect of the next-to-nearest neighbor hopping parameter on the edge state spectrum is studied and revealed to be essential. The criteria for the existence of gapless edge states are established for each phase and edge type.