Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 680

The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.

Weyl points and line nodes in gyroid photonic crystals

Open access
Lu, Ling, Fu, Liang, Joannopoulos, John D., Soljačić, Marin·2013·Nature Photonics
DOI 10.1038/nphoton.2013.42
Open this paper in CoChat — free account

Abstract

Weyl points and line nodes are three-dimensional linear point and line degeneracies between two bands. In contrast to two-dimensional Dirac points, which are their lower-dimensional analogues, Weyl points are stable in momentum space, and the associated surface states are predicted to be topologically non-trivial. However, Weyl points are yet to be discovered in nature. Here, we report photonic crystals based on double-gyroid structures, exhibiting frequency-isolated Weyl points with complete phase diagrams by breaking the parity and time-reversal symmetries. Gapless surface dispersions associated with non-zero Chern numbers are demonstrated. Line nodes are also found in similar geometries, the associated surface states forming flat dispersion bands. Our results are based on realistic ab initio calculations with true predictive power and should be readily realizable experimentally from microwave to optical frequencies. Materials exhibiting three-dimensional (3D) linear dispersion relations between frequency and wavevector are expected to display a wide range of interesting phenomena. 3D linear point degeneracies between two bands (“Weyl points”) have yet to be observed. Based on analytical and numerical analysis, researchers predict Weyl point formation in 3D photonic crystals.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1038/nphoton.2013.42

Cites

17 of 17 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 17 references

Research works printed but not linked: 32

  1. Bonaccorso, F., Sun, Z., Hasan, T. & Ferrari, A. C. Graphene photonics and optoelectronics. Nature Photon. 4, 611–622 (2010). · DOI · Paper page
  2. Bravo-Abad, J., Joannopoulos, J. D. & Soljačić, M. Enabling single-mode behavior over large areas with photonic Dirac cones. Proc. Natl Acad. Sci. USA 109, 9761–9765 (2012). · DOI
  3. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010). · DOI · Paper page
  4. Khanikaev, A. B. et al. Photonic topological insulators. Nature Mater. 12, 233–239 (2013). · DOI · Paper page
  5. Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011). · DOI · Paper page
  6. Halász, G. B. & Balents, L. Time-reversal invariant realization of the Weyl semimetal phase. Phys. Rev. B 85, 035103 (2012). · DOI · Paper page
  7. Xu, G., Weng, H., Wang, Z., Dai, X. & Fang, Z. Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4 . Phys. Rev. Lett. 107, 186806 (2011). · DOI · Paper page
  8. Yang, K-Y., Lu, Y-M. & Ran, Y. Quantum Hall effects in a Weyl semimetal: possible application in pyrochlore iridates. Phys. Rev. B 84, 075129 (2011). · DOI · Paper page
  9. Aji, V. Adler–Bell–Jackiw anomaly in Weyl semimetals: application to pyrochlore iridates. Phys. Rev. B 85, 241101 (2012). · DOI · Paper page
  10. Schoen, A. Infinite Periodic Minimal Surfaces without Self-intersections, NASA Technical Note No. D-5541 (NASA, 1970).
  11. Wohlgemuth, M., Yufa, N., Hoffman, J. & Thomas, E. L. Triply periodic bicontinuous cubic microdomain morphologies by symmetries. Macromolecules 34, 6083–6089 (2001). · DOI · Paper page
  12. Hahn, T. International Tables for Crystallography (Volume A): Space-group Symmetry Part 7 (Kluwer Academic, 2002).
  13. Mañes, J. L. Existence of bulk chiral fermions and crystal symmetry. Phys. Rev. B 85, 155118 (2012). · DOI · Paper page
  14. Aroyo, M. I., Kirov, A., Capillas, C., Perez-Mato, J. M. & Wondratschek, H. Bilbao crystallographic server. II. Representations of crystallographic point groups and space groups. Acta Crystallogr. A 62, 115–128 (2006). · DOI · Paper page
  15. Maldovan, M., Urbas, A. M., Yufa, N., Carter, W. C. & Thomas, E. L. Photonic properties of bicontinuous cubic microphases. Phys. Rev. B 65, 165123 (2002). · DOI · Paper page
  16. Meade, R. D., Brommer, K. D., Rappe, A. M. & Joannopoulos, J. D. Electromagnetic Bloch waves at the surface of a photonic crystal. Phys. Rev. B 44, 10961–10964 (1991). · DOI · Paper page
  17. Bouchaud, J. P. & Zérah, P. G. Spontaneous resonances and universal behavior in ferrimagnets: effective-medium theory. Phys. Rev. Lett. 63, 1000–1003 (1989). · DOI
  18. Bernevig, B., Hughes, T., Raghu, S. & Arovas, D. Theory of the three-dimensional quantum Hall effect in graphite. Phys. Rev. Lett. 99, 146804 (2007). · DOI
  19. Raghu, S. & Haldane, F. D. M. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834 (2008). · DOI · Paper page
  20. Pouya, C. & Vukusic, P. Electromagnetic characterization of millimetre-scale replicas of the gyroid photonic crystal found in the butterfly parides sesostris. Interface Focus 2, 645–650 (2012). · DOI · Paper page
  21. Özbay, E. et al. Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods. Phys. Rev. B 50, 1945–1948 (1994). · DOI · Paper page
  22. Saba, M. et al. Circular dichroism in biological photonic crystals and cubic chiral nets. Phys. Rev. Lett. 106, 103902 (2011). · DOI · Paper page
  23. Hyde, S., Andersson, S., Ericsson, B. & Larsson, K. A cubic structure consisting of a lipid bilayer forming an infinite periodic minimum surface of the gyroid type in the glycerolmonooleat-water system. Z. Kristallogr. 168, 213–219 (1984). · DOI · Paper page
  24. Kresge, C., Leonowicz, M., Roth, W., Vartuli, J. & Beck, J. Ordered mesoporous molecular sieves synthesized by a liquid-crystal template mechanism. Nature 359, 710–712 (1992). · DOI · Paper page
  25. Saranathan, V. et al. Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales. Proc. Natl Acad. Sci. USA 107, 11676–11681 (2010). · DOI · Paper page
  26. Hur, K. et al. Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks. Angew. Chem. 123, 12191–12195 (2011). · doi:10.1002/ange.201104888
  27. Armatas, G. S. & Kanatzidis, M. G. Mesostructured germanium with cubic pore symmetry. Nature 441, 1122–1125 (2006). · DOI
  28. García-Santamara, F. et al. A germanium inverse woodpile structure with a large photonic band gap. Adv. Mater. 19, 1567–1570 (2007). · DOI
  29. Ullal, C. K. et al. Triply periodic bicontinuous structures through interference lithography: a level-set approach. J. Opt. Soc. Am. A 20, 948–954 (2003). · DOI
  30. Turner, M., Schröder-Turk, G. & Gu, M. Fabrication and characterization of three-dimensional biomimetic chiral composites. Opt. Express 19, 10001–10008 (2011). · DOI
  31. Yablonovitch, E., Gmitter, T. J. & Leung, K. M. Photonic band structure: the face-centered-cubic case employing nonspherical atoms. Phys. Rev. Lett. 67, 2295–2298 (1991). · DOI · Paper page
  32. Lu, L. et al. Three-dimensional photonic crystals by large-area membrane stacking. Opt. Lett. 37, 4726–4728 (2012). · DOI

Cited by

See all 680

Metadata

Authors
Lu, L., Fu, L., Joannopoulos, J. D., & Soljačić, M.
Venue
Nature Photonics
Publisher
Springer Science and Business Media LLC
Published
2013-03-17
Volume
7
Issue
4
Pages
294-299
ISSN
  • 1749-4885 (ISSN-L)
  • 1749-4893
DOI
10.1038/nphoton.2013.42
OpenAlex
W2001087841
Cited by
680
References
17
FWCI
24.50
Type
journal article
Language
en
Open access
green
Licence
www.springer.com/tdm (tdm)

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

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Weyl points and line nodes in gyroid photonic crystals. https://app.cochat.ai/papers/10.1038/nphoton.2013.42
The paper
Lu, L., Fu, L., Joannopoulos, J. D., & Soljačić, M. (2013). Weyl points and line nodes in gyroid photonic crystals. Nature Photonics. https://doi.org/10.1038/nphoton.2013.42

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.