Zero modes and edge states of the honeycomb lattice
Open accessAbstract
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 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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The input waveguide resides on the armchair edge of the honeycomb lattice, which has no localized states associated with it.
“Importantly, this input waveguide resides on the armchair edge of the honeycomb lattice, which has no localized states associated with it 31 .”
From Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures (2013) · cites this paper as [31]
The strain introduces edge states that are normally associated with the zig-zag and bearded edges at β/c0=0.
“Furthermore, the strain introduces edge states that are normally associated with the zig-zag and bearded edges 31 at .”
From Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures (2013) · cites this paper as [31]
The strained armchair edge does have edge states associated with it, all lying at propagation constant β/c0=0, like the zig-zag and bearded edge states.
“As was mentioned previously, the strained armchair edge does have edge states associated with it, all lying at propagation constant 31 , like the zig-zag and bearded edge states.”
From Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures (2013) · cites this paper as [31]
Cites
Two-dimensional gas of massless Dirac fermions in graphene
Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Katsnelson, M. I., Grigorieva, I. V., Dubonos, S. V., & Firsov, A. A. (2005) · Nature · doi:10.1038/nature04233 · Cited by 21,611 · see citing works
Electronic properties of disordered two-dimensional carbon
Peres, N. M. R., Guinea, F., & Castro Neto, A. H. (2006) · Physical Review B · doi:10.1103/physrevb.73.125411 · Cited by 1,445 · see citing works
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Photonic Floquet topological insulators
Rechtsman, M. C., Zeuner, J. M., Plotnik, Y., Lumer, Y., Podolsky, D., Dreisow, F., Nolte, S., Segev, M., & Szameit, A. (2013) · Nature · doi:10.1038/nature12066 · Cited by 3,332 · see citing works
Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures
Rechtsman, M. C., Zeuner, J. M., Tünnermann, A., Nolte, S., Segev, M., & Szameit, A. (2013) · Nature Photonics · doi:10.1038/nphoton.2012.302 · Cited by 453 · see citing works
Observation of unconventional edge states in ‘photonic graphene’
Plotnik, Y., Rechtsman, M. C., Song, D., Heinrich, M., Zeuner, J. M., Nolte, S., Lumer, Y., Malkova, N., Xu, J., Szameit, A., et al. (2014) · Nature Materials · doi:10.1038/nmat3783 · Cited by 389 · see citing works
Topological Creation and Destruction of Edge States in Photonic Graphene
Rechtsman, M. C., Plotnik, Y., Zeuner, J. M., Song, D., Chen, Z., Szameit, A., & Segev, M. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.103901 · Cited by 302 · see citing works
Observing movement of Dirac cones from single-photon dynamics
Lu, Y.-H., Wang, Y., Chang, Y.-J., Li, Z.-M., Cui, W.-H., Gao, J., Zhou, W.-H., Zheng, H., & Jin, X.-M. (2021) · Physical Review B · doi:10.1103/physrevb.103.064304 · Cited by 7 · see citing works
“Applying the ‘tightbinding approximation’ to the ‘photonic graphene’ [28], the Hamiltonian can be described by”
BackgroundDirac Dynamics in Waveguide Arrays: From Zitterbewegung to Photonic Topological Insulators
Dreisow, F., Rechtsman, M. C., Zeuner, J. M., Plotnik, Y., Keil, R., Nolte, S., Segev, M., & Szameit, A. (2017) · Quantum Science and Technology · doi:10.1007/978-3-319-52025-4_8 · Cited by 4 · see citing works
- Authors
- Kohmoto, M., & Hasegawa, Y.
- Affiliations
- The Institute for Solid State Physics, The University of Tokyo (JP)
- University of Hyogo (JP)
- ORCID
- Hasegawa, Yasumasa
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2007-11-02
- Volume
- 76
- Issue
- 20
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1987705333
- Cited by
- 130
- References
- 2
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 15 · 2023: 8 · 2022: 4 · 2021: 6 · 2020: 5 · 2019: 6 · 2018: 9 · 2017: 9 · 2016: 6 · 2015: 6 · 2014: 7 · 2013: 8 · 2012: 3
- FWCI
- 3.47
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Surface and Thin Film Phenomena
- Keywords
- honeycomb lattice, edge states, zero modes, tight-binding model, zigzag edge, armchair edge, cylinder geometry, anisotropic systems, localized states, extended states, graphene
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