Zero modes and the edge states of the honeycomb lattice

Abstract

The honeycomb lattice in the cylinder geometry with zigzag edges, bearded edges, zigzag and bearded edges (zigzag-bearded), and armchair edges are studied. The tight-binding model with nearest-neighbor hoppings is used. Edge states are obtained analytically for these edges except the armchair edges. It is shown, however, that edge states for the armchair edges exist when the the system is anisotropic. These states have not been known previously. We also find strictly localized states, uniformly extended states and states with macroscopic degeneracy.

6 pages 8 figures

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• Half-Metallic Graphene Nanoribbons
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• Peculiar Width Dependence of the Electronic Property of Carbon Nanoribbons
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
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• Edge states of zigzag bilayer graphite nanoribbons
• Quantum Phase Transition in Hall Conductivity on an Anisotropic Kagome Lattice
• Edge states in the three-quarter filled system, $\alpha$-(BEDT-TTF)${}_2$I${}_3$