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Cited by 314Topological Materials and PhenomenaQuantum Mechanics and Non-Hermitian PhysicsMetamaterials and Metasurfaces Applications

Experimental observation of optical Weyl points and Fermi arc-like surface states

Open access
Noh, Jiho, Huang, Sheng, Leykam, Daniel, Chong, Y. D., Chen, Kevin P., Rechtsman, Mikael C.·2017·Nature Physics
DOI 10.1038/nphys4072
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Abstract

Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called ‘Weyl points’, carry a topological charge and are therefore highly robust. There has been much excitement over recent observations of Weyl points in microwave photonic crystals and the semimetal TaAs. Here, we report on the experimental observation of ‘type-II’ Weyl points of light at optical frequencies, with the photons having a strictly positive group velocity along one spatial direction. We use a 3D structure consisting of laser-written waveguides, and show the presence of type-II Weyl points by observing conical diffraction along one axis when the frequency is tuned to the Weyl point; and observing the associated Fermi arc-like surface states. The realization of Weyl points at optical frequencies allows these novel electromagnetic modes to be further explored in the context of linear, nonlinear, and quantum optics. Three-dimensional laser-written waveguide arrays are used to demonstrate type-II Weyl points, along with Fermi arc-like surface states, for light at optical wavelengths.

Integrity signals

Registry

Crossref · 10.1038/nphys4072

Cites

60 of 60 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

5 of 13 cited sources checked · 1 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    In the paraxial limit, the envelope function of the linearly-polarized electric field obeys a (2+1)D Schrödinger wave equation with z as time and transverse dimensions as space.

    “In previous works, optical diffraction through such an array has been conceptualized in terms of a reduced-dimensionality system [25]: in the paraxial limit, the envelope function of the linearly-polarized electric field, ψ, is found to obey a (2+1)D Schrödinger wave equation”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [25] Szameit, A. & Nolte, S. Discrete optics in femtosecond-laser-written photonic structures. J. Phys. B 43, 163001 (2010). source
  • Findingown data

    The edge band structures show that states confined to opposite edges emerge after the topological transition at the Dirac point.

    “Clearly, the band structures show that states confined to opposite edges (marked in red and blue) emerge after the topological transition at the Dirac point.”
    Quote in the paperSubstantial claim
  • Findingown data

    The dispersion diagrams for the edge states are equifrequency contours of Fermi arc states occupying the surface of the 3D structure.

    “Indeed, the dispersion diagrams shown in Figs.4(m-o) for the edge states in the transverse (x, y)-plane are equifrequency contours of Fermi arc states occupying the surface of the 3D structure.”
    Quote in the paperSubstantial claim
  • Findingown data

    For a = 29 μm and λ = 1450 nm, the Floquet band structure has a topologically trivial band gap at quasienergy β = π/Z.

    “In Fig. 2(d), we see that for a = 29 µm and λ = 1450 nm, the Floquet band structure has a topologically trivial band gap at quasienergy β = π/Z.”
    Quote in the paperSubstantial claim
  • Findingnone given

    The helical waveguide modulation breaks inversion symmetry of the structure.

    “The helical waveguide modulation breaks the inversion symmetry of the structure-a necessary condition for the realization of Weyl points in time-reversalinvariant systems such as this one.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 3
  • May combine two claims. 20

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Weyl points take two distinct forms, type-I and type-II, which have point-like and conical Fermi surfaces respectively.

    “Weyl points take two distinct forms, type-I and type-II, which have point-like and conical Fermi surfaces respectively [12].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [12] Xu, Y., Zhang, F. & Zhang, C. Structured Weyl points in spin-orbit coupled fermionic superfluids. Phys. Rev. Lett. 115, 265304 (2015). source

      The toy-model discussion (p. 1) describes bands crossing only at a zero-energy point, and the discussion on p. 2 describes an infinite cone-shaped zero-energy surface before adding a cubic term. These passages support the point-like and conical distinction, but the paper does not label them type-I and type-II or state that Weyl points take only those two forms; it focuses on an additional structured form. (LLM, conf=0.83)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingcitation

    The Weyl point pair is separated in frequency, which is a generic property of type-II Weyl points but not realized in previous Weyl photonic crystal designs.

    “Our Weyl point pair is separated in frequency, which is a generic property of type-II Weyl points [12], but not realized in previous Weyl photonic crystal designs [13].”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [12] Xu, Y., Zhang, F. & Zhang, C. Structured Weyl points in spin-orbit coupled fermionic superfluids. Phys. Rev. Lett. 115, 265304 (2015). source

      The citation is attached to the claim that frequency separation is a generic property of type-II Weyl points, not to the separate claim about previous photonic-crystal designs. The toy-model discussion (pp. 1–2) describes changes in band energies and a zero-energy pair of gapless spheres, but does not say that a pair of type-II Weyl points is generically separated in frequency. Searches for type-II points and energy-separated pairs found no passage establishing that property. (LLM, conf=0.75)

      Experimental — accuracy not yet measured
    • cites [13] Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015). source

      The Figure 3 caption (Type II Weyl Semimetals, p. 3) places a pair of type-II Weyl points in WTe₂ at different energies, 0.052 and 0.058 eV. But Appendix A (p. 4) defines type-II points by their tilted dispersion and open Fermi surface, not by energy separation between paired points; the paper does not establish that separation as a generic property. The statement about earlier photonic-crystal designs is attached to a different citation [13]. (LLM, conf=0.86)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Interpretationcitation

    Since the system has time-reversal symmetry, reversing the propagation direction yields another Weyl point with opposite sign of k_z but identical charge and frequency.

    “Since our system has time-reversal symmetry, reversing the propagation direction yields another Weyl point, with the opposite sign of k z , but identical charge and frequency [1].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [1] Lu, L. et al. Experimental observation of Weyl points. Science 349, 622–624 (2015). source

      The main text (page unavailable) says the remaining Weyl points are at opposite momentum locations, are related by time-reversal symmetry, and have identical dispersions, supporting the opposite-momentum and same-frequency parts. It does not explicitly say that time-reversal-related points have identical topological charge or identify the reversed component specifically as k_z. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
    • Rests on an assumption: The system has time-reversal symmetry.

  • May combine two claims.

    Findingreasoning

    Increasing a shifts the crossing to longer wavelengths, but the transition necessarily occurs at a particular wavelength.

    “In particular, increasing a shifts the crossing to longer wavelengths-but the transition necessarily occurs at a particular wavelength, λ.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    For a = 29 μm and a = 25 μm, the Floquet band structure is in conventional insulator and topological insulator phases respectively, and filled-in disc-like diffraction patterns are observed.

    “For lattice constants a = 29 µm and a = 25 µm, for which the Floquet band structure is in a conventional insulator and topological insulator phase respectively, we observe a filled-in disc-like diffraction pattern, which is characteristic of band edge modes.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In the topological region (a = 26, 25 μm), most of the light stays confined to the edge and proceeds in a clockwise sense, indicating a chiral edge state.

    “However, in the topological region (a = 26, 25 µm, Fig. 4(d,e)), most of the light stays confined to the edge and proceeds in a clockwise sense, an indicator of the chiral edge state.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The monotonic behavior of C for a = 29 μm and 25 μm shows that the Weyl point does not occur within the wavelength range 1450-1650 nm, or is very near the boundary.

    “The monotonic behavior of Figs.3(g) and 3(i) show that for lattice constants a = 29µm, 25µm the Weyl point does not occur within the wavelength range of the tunable laser (1450-1650 nm), or is very near the boundary (i.e., the gap is small but does reach zero).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Decreasing a and/or increasing λ decreases the band gap and eventually closes it at Bloch wavevector q = Γ = (0,0).

    “As we decrease a and/or increase λ, the band gap decreases in size and eventually closes at Bloch wavevector q = Γ = (0, 0).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation

    The topological phase observed here is anomalous, with a chiral edge state but the single band in the 2D Floquet band structure has Chern number zero.

    “In fact, the topological phase observed here is anomalous [34][35][36][37], in the sense that despite the presence of a chiral edge state, the single band in the 2D Floquet band structure has Chern number zero.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [34][35][36][37]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Findingreasoning

    For still smaller a and larger λ, the bulk band gap reopens after a topological transition, and this gap is topological and associated with gapless chiral edge states along the lattice edge.

    “For still smaller a and larger λ, the bulk band gap reopens after having undergone a topological transition; this gap is topological, and thus associated with gapless chiral edge states along the lattice edge (Fig.2(f)).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Numerical simulations reveal that the partner Weyl points occur outside the range of the laser, but are accessible using shorter lattice periods.

    “Numerical simulations reveal that this occurs outside the range of our laser, but is accessible using shorter lattice periods.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    In a lattice of period a = 22 μm, the band gap closes and the edge modes terminate at λ = 1650 nm.

    “For example, in a lattice of period a = 22 µm the band gap closes and the edge modes terminate at λ = 1650 nm.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The Weyl points in the orthogonal polarization have identical charges but are split along the k_z axis due to structural birefringence of the waveguides.

    “Moreover, the Weyl points in the orthogonal polarization not only have identical charges, but they are also split along the k z axis as a result of the structural birefringence of the individual waveguides, which have elliptical cross-sections (see Fig. 2(b)).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    At a specific value of ω, the 3D band structure possesses a spectral degeneracy in the form of a Weyl point, and the (2+1)D system possesses a massless 2D Dirac equation.

    “At a specific value of ω, the 3D band structure possesses a spectral degeneracy in the form of a Weyl point; correspondingly, the (2+1)D system at that parametric choice of ω possesses a spectral degeneracy in the form of a massless 2D Dirac equation.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The refractive index difference δn is periodic in the z direction, as well as in x and y.

  • May combine two claims.

    Premisenone given

    Weyl points are protected because they carry a quantized topological charge; they can only be destroyed by annihilating with a Weyl point of opposite charge.

    “However, Weyl points are protected because they carry a quantized topological charge (chirality or Berry flux); they can only be destroyed by annihilating with a Weyl point of opposite charge.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Weyl points are protected by a quantized topological charge and can only be destroyed by annihilating with a Weyl point of opposite charge.

  • Classified as probably not a substantial claim.

    Premisenone given

    Type-II Weyl points are distinguished by strongly anisotropic dispersion with a conical isofrequency surface in a particular direction.

    “Type-II Weyl points are distinguished by the strongly anisotropic dispersion depicted schematically in Fig. 1, with a conical isofrequency surface in a particular direction.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The topological transition signifies that the Dirac mass changes sign by crossing zero; small perturbations cannot destroy the band crossing point, only shift it.

    “In terms of the 2D Dirac equation, it signifies that the Dirac mass m (gap size) changes sign by crossing zero; small perturbations cannot destroy the band crossing point, only shift it.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given

    The topologically trivial phase of the lattice (large a) should have no edge states, whereas the topologically nontrivial phase (small a) has chiral unidirectional edge states.

    “To study this, we use the fact that the topologically trivial phase of the lattice (large a) should have no edge states, whereas the topologically nontrivial phase (small a) has chiral unidirectional edge states.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The topologically trivial phase of the lattice has no edge states, whereas the topologically nontrivial phase has chiral unidirectional edge states.

  • May combine two claims.

    Premisenone given

    The waveguide array can be regarded as a 3D photonic crystal with a photonic band structure describing frequency as a function of Bloch wavevector.

    “But we can also regard the waveguide array as a 3D photonic crystal, with a photonic band structure that describes the frequency ω as a function of the Bloch wavevector (k x , k y , k z ).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In honeycomb photonic lattices, conical diffraction is observable over a continuous range of probe wavelengths.

    “In the latter class of systems, which include honeycomb photonic lattices [32], conical diffraction is observable over a continuous range of probe wavelengths.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [32] Peleg, O. et al. Conical diffraction and gap solitons in honeycomb photonic lattices. Phys. Rev. Lett. 98, 103901 (2007). source

  • May combine two claims.

    Premisecitation

    For type-II Weyl points, an encircling loop at a single frequency cannot avoid bulk states, so the procedure must be modified by dividing the loop into two segments within the bulk band gap at frequencies on either side of the Weyl point.

    “Because of the tilted dispersion at a type-II Weyl point, an encircling loop at a single frequency cannot avoid bulk states and this procedure has to be modified according to Ref. [51]: instead of a loop at a single frequency, one should instead divide the loop into two segments within the bulk band gap at frequencies on either side of the Weyl point, e.g. as in Figs.4(k,o) of the main text.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [51]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Premisecitation

    As long as no bulk states are encountered, contours corresponding to topologically trivial surface states must be closed, while Fermi arcs form open contours terminating at Weyl points of opposite chirality.

    “As long as no bulk states are encountered, contours corresponding to topologically trivial surface states must be closed, while Fermi arcs form open contours terminating at Weyl points of opposite chirality [49,50].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [49]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [50]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

22 of 22

  • The authors state this as an assumption.

    The refractive index difference δn is periodic in the z direction, as well as in x and y.

    “We take δn to be periodic in the z direction, as well as in x and y, so that Eq. ( 1) corresponds to a Floquet lattice (i.e., a periodically-driven crystal).”

  • The paper relies on this without support.

    The system has time-reversal symmetry.

    “Since our system has time-reversal symmetry, reversing the propagation direction yields another Weyl point, with the opposite sign of k z , but identical charge and frequency [1].”

  • The paper relies on this without support.

    The topologically trivial phase of the lattice has no edge states, whereas the topologically nontrivial phase has chiral unidirectional edge states.

    “To study this, we use the fact that the topologically trivial phase of the lattice (large a) should have no edge states, whereas the topologically nontrivial phase (small a) has chiral unidirectional edge states.”

  • The paper relies on this without support.

    Weyl points are protected by a quantized topological charge and can only be destroyed by annihilating with a Weyl point of opposite charge.

    “However, Weyl points are protected because they carry a quantized topological charge (chirality or Berry flux); they can only be destroyed by annihilating with a Weyl point of opposite charge.”
4 of 4

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?

  • A single Dirac cone has been demonstrated to exist in the quasienergy spectrum of Floquet systems simulated using 3D photonic structures of coupled waveguides.

    “Floquet systems have been experimentally simulated using 3D photonic structures of coupled waveguides33–36, and a single Dirac cone has been demonstrated to exist in the “quasienergy” spectrum (where on-axis momentum plays the role of energy)34.”

    From Observation of an unpaired photonic Dirac point (2020) · cites this paper as [34]

  • Noh et al., 2017 have observed photonic type-II Weyl points at optical frequencies, in a 3D photonic crystal structure consisting of evanescently-coupled waveguides.

    “Using a 3D structure consisting of laser-written waveguides, Noh et al. , 2017 have observed photonic type-II Weyl points at optical frequencies, in a 3D photonic crystal structure consisting of evanescently-coupled waveguides.”

    From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Noh et al., 2017

Self-check

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

Each contradiction between two passages listed here was confirmed by an independent check.

  • The Dirac-cone citation points to a gapped panel

    Minor

    The text identifies Fig. 2(d) as having a trivial band gap, then cites that same panel for the Dirac cone at the Weyl point. The figure caption assigns the transition to the middle panel instead.

  • Rescaling operator has the wrong sign for the stated eigenproblem

    Minor

    Equation (11) puts I + bσz on the right-hand side, whereas equation (12) defines the operator used to rescale that eigenproblem using I − bσz. For nonzero b, the stated rescaling does not convert equation (11) into equation (13).

  • Conical-diffraction minimum is assigned to the wrong figure

    Minor

    The wavelength-dependent C plots are identified as Fig. 3(g-i), making their middle plot Fig. 3(h). The subsequent reference to Fig. 2(h) conflicts with that location.

  • Edge-state simulations are assigned to two different figures

    Minor

    The main text locates the simulations corresponding to Fig. 4(a-e) in Fig. 3(f-j), while the figure description places those simulations in the second row, f-j, of Fig. 4.

4 of 4

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Related

Authors
Noh, J., Huang, S., Leykam, D., Chong, Y. D., Chen, K. P., & Rechtsman, M. C.
Affiliations
  • Pennsylvania State University (US)
  • University of Pittsburgh (US)
  • Nanyang Technological University (SG)
Corresponding author
Rechtsman, Mikael C.
ORCID
Venue
Nature Physics
Publisher
Springer Science and Business Media LLC
Published
2017-03-20
Volume
13
Issue
6
Pages
611-617
ISSN
  • 1745-2473 (ISSN-L)
  • 1745-2481
DOI
10.1038/nphys4072
OpenAlex
W2599966633
Semantic Scholar
51521d7bcaaf92e12bc266e14eb8eecd6a9e6c89
Cited by
314
References
41
Citations by year
2026: 18 · 2025: 18 · 2024: 30 · 2023: 29 · 2022: 29 · 2021: 42 · 2020: 46 · 2019: 43 · 2018: 41 · 2017: 17
FWCI
19.71
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Nature Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DR-NTU (Nanyang Technological University) (submittedVersion)
Funders
  • National Science Foundation (1509546, 1420620)
  • Alfred P. Sloan Foundation (FG‐2016‐6418)
  • University of Pennsylvania
  • Pennsylvania State University (DMR-1420620)
  • National Research Foundation
  • National Research Foundation Singapore (NRFF2012-02)
  • Ministry of Education, India
  • Materials Research Science and Engineering Center, Harvard University (DMR 1420620, 1420620)
  • Division of Materials Research (1420620, DMR‐1420620)
  • Division of Electrical, Communications and Cyber Systems
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 › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
Keywords
Weyl points, Weyl fermions, conical diffraction, topological charge, three-dimensional photonic structures

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