Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states
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This paper investigates the topological phase transition in honeycomb lattice photonic crystals with and without time-reversal and space-inversion symmetries through extensive analysis on bulk and edge states. In the system with both the symmetries, there appear multiple Dirac cones in the photonic band structure, and the mass gaps are controllable via symmetry breaking. The zigzag and armchair edges of the photonic crystals can support novel edge states that reflect the symmetries of the photonic crystals. The dispersion relation and the field configuration of the edge states are analyzed in detail in comparison to electronic edge states. Leakage of the edge states to free space, which is inherent in photonic systems, is fully taken into account in the analysis. A topological relation between bulk and edge states, which has been discussed in the context of electronic quantum Hall effect, is also examined in the photonic system with leaky edge states.
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Photonic graphene, a honeycomb array of evanescently coupled waveguides, is a useful tool for investigating graphene physics in various optical settings.
“In particular, photonic graphene (a honeycomb array of evanescently coupled waveguides 14 ) has proven to be a useful tool for investigating graphene physics in various optical settings [15][16][17][18][19][20][21][22][23] .”
From Unveiling pseudospin and angular momentum in photonic graphene (2015) · cites this paper as [16]
A special case of the Dirac-Kronig-Penney model is V0 = π/2; the resulting superstructure FBG comprises a periodic sequence of π phase slips, which has been proposed and demonstrated to realize slowing down of optical pulses.
“A special case of the Dirac Kronig Penney model corresponds to case V 0 = π/ 2. In this case, the resulting superstucture FBG comprises a periodic sequence of π phase slips, which has been proposed and demonstrated to realize slowing down of optical pulses [83].”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [83]
The Introduction (p. 1) and Summary (p. 8) describe a two-dimensional honeycomb photonic crystal and its edge states. Searches for the Dirac–Kronig–Penney model, V0 = π/2, fiber Bragg gratings, π phase slips, and optical-pulse slowing found no passage addressing the attributed claim. (LLM, conf=0.76)
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Cites
Geim, A. K., & Novoselov, K. S. (2007) · Nature Materials · doi:10.1038/nmat1849 · Cited by 39,979 · see citing works
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
Electrodynamics of Continuous Media
LANDAU, L. D., LIFSHITZ, E. M., & King, A. L. (1961) · American Journal of Physics · doi:10.1119/1.1937882 · Cited by 11,365 · see citing works
Quantum Spin Hall Effect in Graphene
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.226801 · Cited by 8,197 · see citing works
Haldane, F. D. M. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2015 · Cited by 6,301 · see citing works
Edge state in graphene ribbons: Nanometer size effect and edge shape dependence
Nakada, K., Fujita, M., Dresselhaus, G. F., & Dresselhaus, M. S. (1996) · Physical review. B, Condensed matter · doi:10.1103/physrevb.54.17954 · Cited by 4,327 · see citing works
Peculiar Localized State at Zigzag Graphite Edge
Fujita, M., Wakabayashi, K., Nakada, K., & Kusakabe, K. (1996) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.65.1920 · Cited by 2,800 · see citing works
Haldane, F. D. M., & Raghu, S. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.013904 · Cited by 2,787 · see citing works
Halperin, B. I. (1982) · Physical Review B · doi:10.1103/physrevb.25.2185 · Cited by 2,547 · see citing works
The Electrodynamics of Continuous Media
Römer, H. (2004) · doi:10.1002/3527604294.ch2 · Cited by 2,393 · see citing works
Condensed-Matter Simulation of a Three-Dimensional Anomaly
Semenoff, G. W. (1984) · Physical Review Letters · doi:10.1103/physrevlett.53.2449 · Cited by 1,832 · see citing works
Low-energy electron diffraction
Mitchell, K. A. R. (1973) · Contemporary Physics · doi:10.1080/00107517308210753 · Cited by 1,519 · see citing works
Chern number and edge states in the integer quantum Hall effect
Hatsugai, Y. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.3697 · Cited by 1,499 · see citing works
Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
Wang, Z., Chong, Y. D., Joannopoulos, J. D., & Soljačić, M. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.013905 · Cited by 1,444 · see citing works
Analogs of quantum-Hall-effect edge states in photonic crystals
Raghu, S., & Haldane, F. D. M. (2008) · Physical Review A · doi:10.1103/physreva.78.033834 · Cited by 1,290 · see citing works
Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac
Klein, O. (1929) · Zeitschrift f�r Physik · doi:10.1007/bf01339716 · Cited by 1,080 · see citing works
Low-Energy Electron Diffraction
Pendry, J. B. (1990) · Springer eBooks · doi:10.1007/978-1-4684-8777-0_7 · Cited by 1,026 · see citing works
Homotopy and Quantization in Condensed Matter Physics
Avron, J. E., Seiler, R., & Simon, B. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.51 · Cited by 600 · see citing works
Yu, Z., Veronis, G., Wang, Z., & Fan, S. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.023902 · Cited by 469 · see citing works
Edge States in Graphene: From Gapped Flat-Band to Gapless Chiral Modes
Yao, W., Yang, S. A., & Niu, Q. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.096801 · Cited by 406 · see citing works
Gapless boundary excitations in the quantum Hall states and in the chiral spin states
Wen, X.-G. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.43.11025 · Cited by 404 · see citing works
Observing<i>Zitterbewegung</i>for Photons near the Dirac Point of a Two-Dimensional Photonic Crystal
Zhang, X. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.113903 · Cited by 315 · see citing works
Extremal transmission at the Dirac point of a photonic band structure
Sepkhanov, R. A., Bazaliy, Y. B., & Beenakker, C. W. J. (2007) · Physical Review A · doi:10.1103/physreva.75.063813 · Cited by 250 · see citing works
Effective theory of quadratic degeneracies
Chong, Y. D., Wen, X.-G., & Soljačić, M. (2008) · Physical Review B · doi:10.1103/physrevb.77.235125 · Cited by 146 · see citing works
Compact optical one-way waveguide isolators for photonic-band-gap microchips
Takeda, H., & John, S. (2008) · Physical Review A · doi:10.1103/physreva.78.023804 · Cited by 117 · see citing works
Geometrical aspects in optical wave-packet dynamics
Onoda, M., Murakami, S., & Nagaosa, N. (2006) · Physical Review E · doi:10.1103/physreve.74.066610 · Cited by 95 · see citing works
Self-citationDirac Spectra and Edge States in Honeycomb Plasmonic Lattices
Han, D., Lai, Y., Zi, J., Zhang, Z.-Q., & Chan, C. T. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.123904 · Cited by 91 · see citing works
Photonic band gaps in a two-dimensional graphite structure
Cassagne, D., Jouanin, C., & Bertho, D. (1995) · Physical review. B, Condensed matter · doi:10.1103/physrevb.52.r2217 · Cited by 89 · see citing works
Ohtaka, K., Ueta, T., & Amemiya, K. (1998) · Physical review. B, Condensed matter · doi:10.1103/physrevb.57.2550 · Cited by 78 · see citing works
Ono, Y., Ohtsuki, T., & Krämer, B. (1989) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.58.1705 · Cited by 62 · see citing works
Designing Spinning Bloch States in 2D Photonic Crystals for Stirring Nanoparticles
Onoda, M., & Ochiai, T. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.033903 · Cited by 28 · see citing works
Self-citationExtinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum
Sepkhanov, R. A., Ossipov, A., & Beenakker, C. W. J. (2009) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/85/14005 · Cited by 27 · see citing works
Anomalous refractive properties of a two-dimensional photonic band-gap prism
Bravo‐Abad, J., Ochiai, T., & Sánchez‐Dehesa, J. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.67.115116 · Cited by 21 · see citing works
Self-citationDerivation of the density of states of leaky photonic bands
Ohtaka, K., Inoue, J., & Yamaguti, S. (2004) · Physical Review B · doi:10.1103/physrevb.70.035109 · Cited by 20 · see citing works
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Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655 · see citing works
Huang, X., Lai, Y., Hang, Z. H., Zheng, H., & Chan, C. T. (2011) · Nature Materials · doi:10.1038/nmat3030 · Cited by 993 · 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
Dirac cones in two-dimensional artificial crystals for classical waves
Lu, J., Qiu, C., Xu, S., Ye, Y., Ke, M., & Liu, Z. (2014) · Physical Review B · doi:10.1103/physrevb.89.134302 · Cited by 192 · see citing works
Unveiling pseudospin and angular momentum in photonic graphene
Song, D., Paltoglou, V., Liu, S., Zhu, Y., Gallardo, D., Tang, L., Xu, J., Ablowitz, M., Efremidis, N. K., & Chen, Z. (2015) · Nature Communications · doi:10.1038/ncomms7272 · Cited by 183 · see citing works
Dirac Dispersion in Two-Dimensional Photonic Crystals
Chan, C. T., Hang, Z. H., & Huang, X. (2012) · Advances in OptoElectronics · doi:10.1155/2012/313984 · Cited by 86 · see citing works
Classical simulation of relativistic quantum mechanics in periodic optical structures
Longhi, S. (2011) · Applied Physics B · doi:10.1007/s00340-011-4628-7 · Cited by 72 · see citing works
Chan, C.-T., Huang, X., Liu, F., & Hang, Z. H. (2012) · Progress In Electromagnetics Research B · doi:10.2528/pierb12082103 · Cited by 41 · see citing works
Nonlinear wave dynamics in honeycomb lattices
Bahat-Treidel, O., & Segev, M. (2011) · Physical Review A · doi:10.1103/physreva.84.021802 · Cited by 26 · see citing works
- Authors
- Ochiai, T., & Onoda, M.
- Affiliations
- National Institute for Materials Science (JP)
- Akita University (JP)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2009-10-02
- Volume
- 80
- Issue
- 15
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2077193646
- Cited by
- 243
- References
- 34
- Citations by year
- 2026: 5 · 2025: 10 · 2024: 17 · 2023: 13 · 2022: 16 · 2021: 12 · 2020: 13 · 2019: 11 · 2018: 14 · 2017: 20 · 2016: 22 · 2015: 14 · 2014: 14 · 2013: 21 · 2012: 19
- FWCI
- 7.61
- 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 Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photonic Crystals and Applications
- Keywords
- Dirac cones, topological phase transition, time-reversal symmetry, inversion symmetry, edge states, zigzag edge, armchair edge, mass gap, symmetry breaking, bulk-boundary correspondence, photonic band structure
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