Zero modes and the edge states of the honeycomb lattice

Details Zero modes and the edge states of the honeycomb lattice Zero modes and the edge states of the honeycomb lattice

2007-02-07

arxiv.org/abs/cond-mat/0702162v2

Phys. Rev. B 76, 205402 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages 8 figures

Scientific paper

10.1103/PhysRevB.76.205402

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.

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