The DOI matches its Crossref record; 29 of the 30 references it cites were found in a registry or an index.
Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials
Abstract
A zero-refractive-index metamaterial is one in which waves do not experience any spatial phase change, and such a peculiar material has many interesting wave-manipulating properties. These materials can in principle be realized using man-made composites comprising metallic resonators or chiral inclusions, but metallic components have losses that compromise functionality at high frequencies. It would be highly desirable if we could achieve a zero refractive index using dielectrics alone. Here, we show that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency. In addition to many interesting properties intrinsic to a Dirac cone dispersion, we can use effective medium theory to relate the photonic crystal to a material with effectively zero permittivity and permeability. We then numerically and experimentally demonstrate in the microwave regime that such dielectric photonic crystals with reasonable dielectric constants manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Both the focusing effect through a concave lens and the waveguiding and cloaking effect through a waveguide filled with ε eff = μ eff = 0 photonic crystal were demonstrated.”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
In the citing paper
“In order to demonstrate that the photonic crystal with a band dispersion shown in Figure 1 does have ε eff (ω D ) = μ eff (ω D ) = 0 at the Dirac frequency, numerical simulations, and microwave experiments were carried out [66].”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
In the citing paper
“If this triply degenerate state is formed by monopole and dipole excitations, the system can be mapped to an effective medium with permittivity and permeability equal to zero simultaneously”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
In the citing paper
“We note that the emergence of linear bands as a consequence of accidental degeneracy at k = 0 can also be obtained using multiple scattering theory [66] or k • p perturbation [76,77].”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
In the citing paper
“Dirac cones can also be used to tailor the dispersion of photonic structures”
From Topological photonics (2019) · cites this paper as Huang et al., 2011
Citations
Cites
The electronic properties of graphene
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S., & Geim, A. K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.109 · Cited by 24,803
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
Experimental observation of the quantum Hall effect and Berry's phase in graphene
Zhang, Y., Tan, Y.-W., Stormer, H. L., & Kim, P. (2005) · Nature · doi:10.1038/nature04235 · Cited by 13,435
High-impedance electromagnetic surfaces with a forbidden frequency band
Sievenpiper, D. F., Zhang, L., Broas, R. F. J., Alexopolous, N. G., & Yablonovitch, E. (1999) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/22.798001 · Cited by 4,263
Haldane, F. D. M., & Raghu, S. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.013904 · Cited by 2,787
A Chiral Route to Negative Refraction
Pendry, J. B. (2004) · Science · doi:10.1126/science.1104467 · Cited by 1,495
Silveirinha, M. G., & Engheta, N. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.157403 · Cited by 1,356
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
Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern
Alù, A., Silveirinha, M. G., Salandrino, A., & Engheta, N. (2007) · Physical Review B · doi:10.1103/physrevb.75.155410 · Cited by 1,066
Edwards, B. E., Alù, A., Young, M. E., Silveirinha, M. G., & Engheta, N. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.033903 · Cited by 764
Flagged first, then by citations
1 of the 30 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Items 901–990 of 990
Moradi, S., & Jahangiri, F. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.11993
Pursuing complex optical energy through Exceptional Points of Degeneracy (EPDs)Preprint
Moradi, S. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.00283
Design and Simulation of Nano-Optical Beam Generators Based on Zero-Index Materials
Eriş, Ö., Abanuzoglu, T., & Ergül, Ö. (2019) · International Electromagnetic Compatibility Conference (EMC Turkiye) · doi:10.1109/emcturkiye45372.2019.8976011
Precise Distance Measurement via Single-beam Interferometry of Photonic Crystal
Qiao, P., & Dong, G. (2019) · Photonics & Electromagnetics Research Symposium - Fall (PIERS-Fall) · doi:10.1109/piers-fall48861.2019.9021758
Dong, G., Qiao, P., & Zheng, S. (2019) · Photonics & Electromagnetics Research Symposium - Fall (PIERS-Fall) · doi:10.1109/piers-fall48861.2019.9021754
Terahertz bound states in the continuum
Han, S. H. (2020) · doi:10.32657/10356/137303
Evolution of accidental degenerate Dirac point in 2D photonic crystals
Guo, Y.-H., Zhao, L.-M., & Zhou, Y.-S. (2020) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/130/44002
Electromagnetic Metasurface Fabricated by Printed Electronics and Its Applications
Gao, J. (2020) · Scholarship@Western (Western University)
Low-loss Zero-Index Metamaterials with Bound State in the Continuum
Tang, H., DeVault, C., Camayd-Muftoz, P., Jia, D., Liu, Y., Du, F., Mello, O., Li, Y., & Mazur, E. (2020) · Conference on Lasers and Electro-Optics · doi:10.1364/cleo_qels.2020.fm1b.8
Universal method to describe multiple localized modes in photonic crystal heterojunction
Chen, S., Zhao, L., Zhou, Y.-S., & Wei, G.-M. (2021) · Modern Physics Letters B · doi:10.1142/s0217984921503656
Solution box: SOLBOX-20: Electromagnetic interactions with near-zero-index triangular prisms
Ergül, Ö., & Eriş, Ö. (2020) · URSI Radio Science Bulletin · doi:10.23919/ursirsb.2020.9523812
Yu, H., Zhang, Q., & Gu, M. (2021) · Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) · doi:10.1109/cleo/europe-eqec52157.2021.9542030
ENZ-metamaterial–induced perfect transparency for the highly directive plano-concave lens
Jia, Y., Yang, R., & Weng, Z. B. (2021) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/ac3189
Peripherally-Excited Antenna Arrays: A Practical Realization
Dorrah, A. H., & Eleftheriades, G. V. (2021) · International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) · doi:10.1109/metamaterials52332.2021.9577195
Dirac Points and Topological Modes in Photonic Nanostructures
Deng, H., & Ye, F. (2021) · Metamaterials science and technology · doi:10.1007/978-981-13-0261-9_42-1
Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry
Louvet, T., Delplace, P., Goerbig, M. O., & Carpentier, D. (2023) · SciPost Physics · doi:10.21468/scipostphys.15.4.129
Nesting and Degeneracy of Mie Resonances of Dielectric Cavities embedded in Zero-Index Materials
Ma, Y., Duan, X., Chen, H., Qian, Z., Zhang, Q., Lai, Y., Peng, R., Gong, Q., & Gu, Y. (2021) · Frontiers in Optics · doi:10.1364/fio.2021.jw7a.44
Self-citationControl of LED radiation with functional dielectric metasurfaces
Khaidarov, E. (2020) · doi:10.32657/10356/137392
Lossless Zero-Index Guided Modes via Bound States in the Continuum
Minkov, M., Williamson, I. A. D., Xiao, M., & Fan, S. (2019) · Conference on Lasers and Electro-Optics · doi:10.1364/cleo_qels.2019.fm1b.2
Theory for Zero-Index Conductive Cloaks: Constant-Temperature Scheme
Xu, L., & Huang, J.-P. (2022) · Springer eBooks · doi:10.1007/978-981-19-5908-0_5
Size effect on light propagation modulation near band edges in one-dimensional periodic structures
Tang, Y., Wang, J., Zhao, X., Li, T., & Ши, Л. (2022) · Chinese Physics B · doi:10.1088/1674-1056/acac0d
Design Method for Broadband Invisible Cloaks by Using Straight and Meander Transmission-Lines
Nagayama, T. (2022) · IEEE International RF and Microwave Conference · doi:10.1109/rfm56185.2022.10065136
Novel topological phases in gyromagnetic photonic crystals
Liu, G.-G. (2023) · DR-NTU (Nanyang Technological University) · doi:10.32657/10356/165931
Integrated Photonics with Near-Zero Index Materials
Vertchenko, L., & Lavrinenko, A. V. (2023) · Springer eBooks · doi:10.1007/978-3-031-24617-3_13
Enhancing plane-wave emission with a combination device based on acoustic metamaterial
Yang, R., Zhang, X., & Wang, G. (2023) · Applied Physics Letters · doi:10.1063/5.0159459
Report on scipost_202303_00001v1
Louvet, T., Delplace, P., Goerbig, M. O., et al. (2023) · SciPost Physics · doi:10.21468/scipost.report.7011
Electromagnetic Beam Splitters Based on Near-Zero-Index Materials
Güneş, D., Eriş, Ö., & Ergül, Ö. (2023) · International Electromagnetic Compatibility Conference (EMC Turkiye) · doi:10.1109/emcturkiye59424.2023.10287489
Origin of the flat-envelope cavity mode of Berkeley surface-emitting lasers (BerkSELs)
Papapanos, C., Contractor, R., Noh, W., Redjem, W., Qarony, W., Martin, E., & Kanté, B. (2023) · Frontiers in Optics · doi:10.1364/ls.2023.lw6f.3
Cheng, S.-C., & Chen, T.-W. (2024) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/1361-6455/ad2184
Deciphering cavity modes in Berkeley surface-emitting lasers (BerkSELs)
Papapanos, C., Contractor, R., Noh, W., Redjem, W., Qarony, W., Martin, E., Seclì, M., & Kanté, B. (2024) · Photonic and Phononic Properties of Engineered Nanostructures · doi:10.1117/12.3001977
Wave Propagation and Field Manipulation in Non-Hermitian Metastructures
Moccia, M., Coppolaro, M., Savoia, S., Castaldi, G., & Galdi, V. (2023) · Springer eBooks · doi:10.1007/978-3-031-39824-7_7
Highly homogeneous zero-index metamaterials make devices more compact and perform better
Jiang, W. (2024) · Light Science & Applications · doi:10.1038/s41377-024-01458-6
Dual-band semi-Dirac cones in two-dimensional photonic crystal and zero-index material
Ji, Y., Zhang, M., & Li, Y. (2024) · Acta Physica Sinica · doi:10.7498/aps.73.20240800
Eremenko, Z. E., & Charnukha, A. (2024) · USNC-URSI Radio Science Meeting · doi:10.23919/inc-usnc-ursi61303.2024.10632307
Scaling of Single-Mode Surface-Emitting Lasers with a Perturbed Dirac-Cone
Wong, W. W., Haggrén, T., Neshev, D. N., Tan, H. H., Sukhorukov, A. A., Jagadish, C., & Song, Y. (2024) · IEEE International Semiconductor Laser Conference (ISLC) · doi:10.1109/islc57752.2024.10717355
Full polarization power combination based on a double-near-zero photonic crystal
Wang, M., Shi, Q., Li, L., & Zheng, N. (2024) · Journal of Nanophotonics · doi:10.1117/1.jnp.18.046008
Harnessing epsilon-near-zero materials for tunable accelerating beams in micro-cavities
Naserpour, M., & Zapata-Rodrı́guez, C. J. (2025) · Optics Communications · doi:10.1016/j.optcom.2024.131464
Zhao, L., Li, J., & Wu, H. (2025) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2025.116195
Dirac Points and Topological Modes in Photonic Nanostructures
Deng, H., & Ye, F. (2025) · Metamaterials science and technology · doi:10.1007/978-981-19-0716-6_42
Eldegail, M. H., Kong, L., Bai, Y., & Xu, C. (2025) · Journal of Applied Physics · doi:10.1063/5.0255320
Light reflects as a vortex off a metamaterial with unusual optical properties
Zhang, R.-Y., & Cui, X. (2025) · Nature · doi:10.1038/d41586-025-01624-9
Tunable unidirectional large-area surface magnetoplasmons in a stratified waveguide
Shen, Q., You, Y., Tang, Z., Gao, J., & Xu, J. (2025) · Optics Express · doi:10.1364/oe.563713
Wang, J.-B., Sun, X., He, C., & Chen, Y. (2025) · Physical review. B./Physical review. B · doi:10.1103/lqkm-44dr
Wang, Y., & Yuan, J. (2025) · Axioms · doi:10.3390/axioms14060445
Opto-band tuning in a liquid crystal elastomer phononic crystal plate
Liang, T., Liu, Y., & Gu, Q. (2025) · Wave Motion · doi:10.1016/j.wavemoti.2025.103599
Gyro route towards spatiotemporal vortex
Ma, G. (2025) · 中国科学通报：英文版 · doi:10.1016/j.scib.2025.08.016
Anwar, S. H., Ahmed, S., Aslam, F., Qurashi, Y., Asif, M., & Ouyang, Z. (2025) · Journal of Optics · doi:10.1088/2040-8986/ae0b8c
Xu, Z., Du, Z., Lin, J.-Z., Xiao, P., & Wang, Y. (2025) · Optics Letters · doi:10.1364/ol.575037
Temporal effective medium for programmable acoustic metamaterials with multiple resonances
Zhu, X., Wu, H., & Li, J. (2025) · npj Acoustics · doi:10.1038/s44384-025-00030-9
Asymptotic limit of a class of nonlinear Maxwell’s equations
Liu, T., & Yang, W. (2025) · Zeitschrift für angewandte Mathematik und Physik · doi:10.1007/s00033-025-02618-3
Controllable reconstruction of superhoneycomb plasma photonic crystals in air barrier discharges
Wang, J., Yuan, J., Yu, S., Li, X., Li, R., Liu, F., Wang, S., & Fan, W. (2025) · Physics of Plasmas · doi:10.1063/5.0289272
Acoustic Leaky-Wave Antenna Based on Phononic Crystals
Lyu, K., & Wu, Y. (2025) · Photonics & Electromagnetics Research Symposium - Spring (PIERS-Spring) · doi:10.1109/piers-spring66516.2025.11276471
Acoustic vortex tunneling through subwavelength channels with topological-pair metasurfaces
Wang, L., Hu, C., Li, X., Lu, Y., Shi, Y., Liu, Y., Ji, H., Xu, Y., & Fu, Y. (2025) · Physical Review Applied · doi:10.1103/q8qn-1mcq
Dispersion-engineered Floquet–Bloch phonon polaritons for extreme infrared beam control
Devarapu, G. C. R., & Foteinopoulou, S. (2026) · Photonics and Nanostructures - Fundamentals and Applications · doi:10.1016/j.photonics.2026.101521
Eremenko, Z. E., & Volovichev, I. N. (2026) · Physica Scripta · doi:10.1088/1402-4896/ae5031
Theories on classical electromagnetic metamaterials
Xu, B., & Zhong, R. (2026) · Frontiers in Physics · doi:10.3389/fphy.2026.1783199
Quantitative analysis of the photonic spin Hall effect in an epsilon-near-zero metamaterial
Badshah, F., Zhou, Y., Idrees, M., Li, H.-J., Boukhris, I., Al-Buriahi, M. S., Ziauddin, & Ban, X. (2026) · Chinese Journal of Physics · doi:10.1016/j.cjph.2026.03.036
Etude des propriétés spectro-spatiales des cristaux photoniques membranaires à symétrie brisée
Dubois, F. (2018) · theses.fr (ABES) · doi:10.70675/b0bab6b3zffa4z48fdz923dzff2ca3b7d0c5
Fluorescence Inhibition in the Vicinity of Spherical ENZ Nanoparticles
Atwi, H. (2022) · theses.fr (ABES) · doi:10.70675/6edc7ca7z3e8fz4509z9a6fz39a19e2b41f2
Ideal long-range quantum-resource generator in zero-index photonic crystal waveguide
Qin, Y., Wang, J., Zhu, Y., Li, M., Khakhomov, S. A., Wang, Y., & Hu, Z.-D. (2026) · Applied Physics Letters · doi:10.1063/5.0321451
Inverse Design of Photonic Crystal Lasers Through Automatic Differentiation Optimization
Crisan, M., & Arafin, S. (2026) · IEEE Journal of Selected Topics in Quantum Electronics · doi:10.1109/jstqe.2026.3687110
Loss Compensation and Coherent Virtual Absorption via Virtual Complex Frequency Wave Excitation
Zhang, X., & Hang, Z. H. (2026) · Nanophotonics · doi:10.1002/nap2.70125
Self-citationSymmetry-engineered band structure in two-dimensional multiferroic photonic crystals
Chen, J., Zhu, J., Su, X., Yuan, T., Li, F., Zhang, H., Chen, K., Sui, X., & Lu, J. (2026) · Journal of Applied Physics · doi:10.1063/5.0331950
Arbitrary Zero-Index Wave Transport Enabled by Reconfigurable Photonic Crystals
Yang, C., Li, J., Liu, J., Zeng, Y., Huang, C., Yuanhang, J., Zhang, Z., Yao, J., Zhou, Z., Song, Q., et al. (2026) · ACS Photonics · doi:10.1021/acsphotonics.6c00529
Yue, Z., Wang, S., Zhang, Z. D., Liao, D., Zhang, H., Cheng, Y., Liu, X., & Christensen, J. (2026) · National Science Review · doi:10.1093/nsr/nwag346
Li, Y., Fu, P., Zhou, Z., Zhang, Y., Yan, W., Hu, M., Wang, S., Li, P., Liu, X., Li, K., et al. (2026) · Optical Materials Express · doi:10.1364/ome.604768
Yichen, 曾. Z., Shouqi, 张. Z., & Yongquan, 曾. Z. (2026) · Laser & Optoelectronics Progress · doi:10.3788/lop252316
Latent-Geometry Correspondence: Unraveling Hidden Symmetry Groups with Graph Theory
Anonymous, Ye, R., Röntgen, M., Chen, M. L. N., Wei, S., Zhang, S., & Gao, W. (2026) · Physical Review Letters · doi:10.1103/hrdv-qcf6
From non-resonant to resonant meta-devices: imaging, color routing, displaying, and beyond
Liu, W., Liang, Y., Leng, B., Chen, S., Feng, P.-Y., & Tsai, D. P. (2026) · Opto-Electronic Science · doi:10.29026/oes.2026.260016 · Cited by 1
Multidimensional Radar Deception via Programmable Metasurfaces: Status and Prospects
Zhu, Y., Li, M., Gu, J., Ramaccia, D., Toscano, A., Bilotti, F., & Ding, D. (2026) · IEEE Journal of Selected Topics in Electromagnetics Antennas and Propagation · doi:10.1109/jsteap.2026.3707874
Kong, L., & Xu, C. (2026) · APS Open Science · doi:10.1103/hw5x-jg5w
General method of wavelength-tuning of Dirac-like cones in photonic crystals
Vallar, E., Madera, C. R., Santagiustina, M., Semenova, E. S., Huck, A., & Lavrinenko, A. V. (2026) · Optical Materials Express · doi:10.1364/ome.605588
Zhao, Y., Yan, J.-Y., Yang, Z., Xie, N., & Yang, Y. (2026) · Physical Review A · doi:10.1103/v57h-vwyw
Fang, A., & Liu, S. (2026) · Optics Express · doi:10.1364/oe.603224
Chiral Lasing via Broken Parity-Time Symmetry in Bound-State-in-the-Continuum Metasurfaces
Parry, M., Smirnova, D. A., Sukhorukov, A. A., & Neshev, D. N. (2026) · ACS Photonics · doi:10.1021/acsphotonics.6c00719
General Double-Zero-Index Photonic Crystals
Anonymous, Zhao, D., Wang, Z., Yang, X., Jiang, L., & Gao, Z. L. (2026) · Physical Review Letters · doi:10.1103/xb4y-tl1w
Anisotropic metamaterials analogue to non-asymptotically flat spacetime geometries
Sánchez, M. A. G., López-Picón, J. L., & Mena-Barboza, E. A. (2026) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2026.117705
Progress in Dirac-cone-based double-zero-index materials
Wu, Z., Gao, Z., Chen, X.-D., & Dong, J. (2026) · Chinese Science Bulletin (Chinese Version) · doi:10.1360/csb-2026-0597
Graphene-tuned near-zero index waveguides [Invited]
Jafargholi, A., Fleury, R., & Ahadi, M. (2026) · Optical Materials Express · doi:10.1364/ome.592233
Spin-1 Weyl Points in Isotropic Chiral Metamaterials
Ozaktas, E. G., & Fan, S. (2026) · Physical Review Letters · doi:10.1103/7ty7-d15f
Chiral Quasi‐BICs Stemming From a Γ‐point Degeneracy
Zhang, B., Yang, D., Wu, Y., Zheng, M., Zhu, W. M., Kang, L., Du, K., Werner, D. H., & Wang, S. (2026) · Laser & Photonics Review · doi:10.1002/lpor.71850
Feng, Z., Guo, W., Mu, Y., Yuan, L., Chen, Z., Li, S., Liu, F., Sun, Y., Zeng, Y., Chen, H., et al. (2026) · Applied Physics Reviews · doi:10.1063/5.0342780
Awan, Z. A., Zeb, S., Rahim, S., & Hussain, A. (2026) · International Journal of Microwave and Wireless Technologies · doi:10.1017/s175907872610381x
Spatially extended chiral states in T -broken zero-index heterostructures
Yang, C., Li, J., Liu, J., Yuanhang, J., Yao, J., Zhou, Z., & Yuan, C. (2026) · Physical Review A · doi:10.1103/lt1q-dfll
Kozlov, A. G., Meng, F., Feng, Y., Li, W., Zhang, T., Namsaraev, Z. Z., Mariya, K., Prikhodchenko, A. V., Bazrov, M. A., Letushev, M., et al. (2026) · Advanced Quantum Technologies · doi:10.1002/qute.70529
Topological modes for light propagation inside a 2D photonic square lattice crystal with p4 symmetry
Tun-Carrillo, M. A., Medina-Vázquez, J. A., Mora-Ramos, M. E., Gómez-Urrea, H. A., & Quintana, I. (2026) · Revista Mexicana de Física · doi:10.31349/revmexfis.72.061302
Breaking through the robustness-transparency tradeoff in polymer composites by fractal interfaces
Huang, W., Wu, X., Xie, Y., Meng, X., & Qiu, D. (2026) · Composites Part B Engineering · doi:10.1016/j.compositesb.2026.114376
Metadata
- Authors
- Huang, X., Lai, Y., Hang, Z. H., Zheng, H., & Chan, C. T.
- Affiliations
- Hong Kong University of Science and Technology (HK)
- Corresponding author
- Chan, C. T.
- Venue
- Nature Materials
- Published
- 2011-05-29
- Volume
- 10
- Issue
- 8
- Pages
- 582-586
- ISSN
- 1476-1122 (ISSN-L)
- 1476-4660
- OpenAlex
- W1964548562
- Cited by
- 993
- References
- 30
- Citations by year
- 2026: 41 · 2025: 63 · 2024: 48 · 2023: 72 · 2022: 62 · 2021: 74 · 2020: 81 · 2019: 89 · 2018: 79 · 2017: 94 · 2016: 89 · 2015: 62 · 2014: 54 · 2013: 38 · 2012: 41
- FWCI
- 17.62
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Nature Materials (publishedVersion)
- PubMed (publishedVersion)
- Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
- Topics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photonic Crystals and Applications
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Acoustic Wave Phenomena Research
- Keywords
- Dirac cones, Dirac point, photonic crystals, zero refractive index, zero-index metamaterials, accidental degeneracy, dielectric photonic crystals, effective medium theory, wave manipulation, Brillouin zone
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
