Three-dimensional photonic Dirac points stabilized by point group symmetry
Open accessAbstract
We discover a pair of stable three-dimensional (3D) Dirac points, a 3D photonic analog of graphene, in all-dielectric photonic crystals using structures commensurate with nanofabrication for visible-frequency photonic applications. The Dirac points carry nontrivial ${Z}_{2}$ topology and emerge for a large range of material parameters in hollow cylinder hexagonal photonic crystals. From Kramers theorem and group theory, we find that only the ${C}_{6}$ symmetry leads to point group symmetry stabilized Dirac points in 3D all-dielectric photonic crystals. The Dirac points are characterized using $\stackrel{P\vec}{k}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{P}$ theory for photonic bands in combination with symmetry analysis. Breaking inversion symmetry splits the Dirac points into Weyl points. The physical properties and experimental consequences of Dirac points are also studied. The Dirac points are found to be robust against parameter tuning and weak disorders.
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Weak disorders that preserve the crystalline symmetry on average should preserve the Dirac points and their topological surface states.
“Weak disorders that preserve the crystalline symmetry on average should preserve the DPs and their topological surface states.29,47”
From Type-II Dirac photons (2017) · cites this paper as [29]
Appendix H (p. 10) says that weak fabrication errors can preserve the Dirac points. Appendix E (pp. 8–10) describes topological boundary states in an inversion-symmetry-broken structure, but does not establish that weak disorder preserves those states. The paper also does not address the claim's specific condition that crystalline symmetry be preserved on average. (LLM, conf=0.88)
Experimental — accuracy not yet measuredWhen space symmetry is reduced, Weyl points can emerge from Dirac points.
“Thus when the space symmetry is reduced WPs can emerge from DPs. 29”
From Type-II Dirac photons (2017) · cites this paper as [29]
A Dirac point can be regarded as composed of a pair of Weyl points of opposite Chern numbers.
“A DP can be regarded as composed of a pair of WPs of opposite Chern numbers.”
From Type-II Dirac photons (2017) · cites this paper as [29]
The dispersion of the type-II Dirac point in the kx-ky plane is distinctive from existing type-I Dirac points.
“The dispersion of the type-II DP in the k x -k y plane is distinctive from the existing type-I DPs 29,31,32 (see Fig. 5d).”
From Type-II Dirac photons (2017) · cites this paper as [29]
Such Dirac points are monopoles of the SU(2) Berry-phase gauge fields.
“In fact, such DPs are monopoles of the SU(2) Berryphase gauge fields.29”
From Type-II Dirac photons (2017) · cites this paper as [29]
A Dirac point with synthetic Kramers double degeneracy and parity-inversion has nontrivial topological properties.
“It has been shown in ref. 29 that a DP with synthetic Kramers double degeneracy and parity-inversion has nontrivial topological properties.”
From Type-II Dirac photons (2017) · cites this paper as [29]
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Self-citationThree-dimensional Dirac semimetal metamaterial enabled by negative couplings
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Analogies for Dirac fermions physics in graphene
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Topological properties of artificial bandgap materials
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Photonic topological phases in Tellegen metamaterials
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Self-citationQi, Z., Hu, G., Song, X., Sun, H., Zhu, W., Sun, Y., Chen, S., Li, Y., Liu, S., Liu, B., et al. (2024) · Optics & Laser Technology · doi:10.1016/j.optlastec.2024.111667 · Cited by 3 · see citing works
Three-Dimensional Topological Valley Photonics
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Self-citationObservation of Gapless Spectral Flows in Elastic Metamaterials with Synthetic Dimension
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Self-citationManipulation of Photonic Topological Edge and Corner States via Trivial Claddings
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Weyl and Dirac Semimetals in Three Dimensional Solids
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“Recently, Chang et al., 2016e; Wang et al., 2016h proposed candidates for magnetic Weyl semimetals based on the Co-based magnetic Heusler compounds XCo2Z (X=V,Zr,Ti,Nb,Hf, Z=Si,Ge,Sn), VCo2Al and VCo2Ga.”
BackgroundInfluential
- Authors
- Wang, H., Xu, L., Chen, H., & Jiang, J.-H.
- Affiliations
- Soochow University (CN)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2016-06-27
- Volume
- 93
- Issue
- 23
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2236660155
- Cited by
- 75
- References
- 44
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 3 · 2023: 6 · 2022: 12 · 2021: 6 · 2020: 8 · 2019: 8 · 2018: 11 · 2017: 8 · 2016: 4
- FWCI
- 4.89
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Funders
- National Natural Science Foundation of China (61322504)
- 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 › Photonic Crystals and Applications
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- all-dielectric photonic crystals, point group symmetry, C6 symmetry, Weyl points, inversion symmetry breaking, photonic band structure, disorder robustness, nanofabrication
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