Photonic chiral bulk transports manipulated by boundary freedom in three-dimensional meta-crystals

Biao Yang; Hanyu Wang; Qinghua Guo; Yingxin Qi; Zhihong Zhu

REVIEW 3 major objections 4 minor 7 references

Photonic chiral bulk transports manipulated by boundary freedom in three-dimensional meta-crystals

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Boundary conditions alone can decide which chiral bulk state a photonic meta-crystal carries.

desk verdict A credible, well-scoped demonstration that PEC and PMC boundaries select opposite chiral bulk states in a 3D photonic nodal-line meta-crystal, with the main caveat being the uncharacterized resonant AMC boundary in the experiment. read the letter →

arxiv 2506.10861 v1 pith:IIKSYY5O submitted 2025-06-12 cond-mat.mes-hall physics.optics

Yingxin Qi , Hanyu Wang , Qinghua Guo , Zhihong Zhu , Biao Yang This is my paper · ORCID

classification cond-mat.mes-hallphysics.optics

keywords boundary-bulkcorrespondencechiralbulkstateszerothmodesnodallinemeta-crystalsphotonictopologicalPEC/PMCboundariesartificialmagneticconductorfinite-thicknesswaveguide

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a reversal of the usual topological logic: instead of the bulk dictating which boundary states appear, the boundary condition itself can decide which bulk mode carries chiral transport. In a three-dimensional photonic meta-crystal whose bulk hosts a mirror-protected nodal ring, the authors show analytically, numerically, and experimentally that capping the slab with perfect electric conductor (PEC) boundaries selects one nodal-ring mode, while perfect magnetic conductor (PMC) boundaries select the other. The two selected states are chiral zeroth modes with opposite dispersion—positive under PEC, negative under PMC—and they persist at any slab thickness. A PEC-PMC combination instead breaks the mirror symmetry and opens a complete gap. If the claim is right, boundaries become an independent, reconfigurable degree of freedom for topological transport, promising compact waveguides and transferable designs in acoustics, elasticity, and electronics.

What carries the argument

The carrying object is the boundary-selected zeroth mode of a finite-thickness nodal-line waveguide. The two nodal-ring modes have opposite mirror eigenvalues: TM (mirror-odd, only $E_z$) and LM (mirror-even, only tangential fields). PEC boundaries permit only $E_z$ and forbid the LM; PMC boundaries permit only tangential fields and forbid the TM; so each boundary condition pins the waveguide to one branch of the nodal ring. In the effective-medium equations, the symmetric PEC/PMC cases impose round-trip phases $2n\pi$; the $n=0$ solutions $\epsilon=0$ and $\omega=\pm k_y$ are independent of thickness $d$ and are the chiral bulk states, while $n\neq 0$ solutions are gapped ordinary modes. The PEC-PMC case imposes $(2n+1)\pi$, eliminating a chiral zeroth order and opening a complete gap.

What would settle it

Measure the AMC and AEC reflection phase across 4.6–5.0 GHz and scan the chiral band for slabs of 3, 5, and 8 stacked unit cells under identical boundaries; the boundary-selection claim predicts that the chiral zeroth mode's dispersion is unchanged with thickness and matched by ideal-PMC/PEC simulations, so a thickness-dependent shift or a match only with non-ideal reflection phases would falsify it.

Watch

Extended reading notes

Core claim

The paper asserts that in a finite-thickness photonic meta-crystal whose bulk hosts a mirror-protected nodal ring, the boundary condition itself selects which of the two degenerate nodal-ring modes survives as a chiral bulk state. With perfect electric conductor (PEC) boundaries on both top and bottom surfaces, only the mirror-odd transverse mode (normal electric field $E_z$) survives, and it forms a chiral bulk state with positive dispersion; with perfect magnetic conductor (PMC) boundaries, only the mirror-even longitudinal mode (tangential field) survives, forming a chiral bulk state with negative dispersion. Both states are the $n=0$ solutions of the slab's round-trip phase condition, so their dispersion contains no slab-thickness $d$ and they persist for arbitrarily thick slabs, unlike the $d$-dependent higher-order modes. When one surface is PEC and the other PMC, the round-trip phase changes from $2n\pi$ to $(2n+1)\pi$, the mirror symmetry of the nodal ring is broken, and the chiral states are replaced by a complete gap. The paper reports microwave measurements using artificial PMC/PEC plates that reproduce the opposite chiral bulk bands and the boundary-induced gap.

Load-bearing premise

The argument assumes the fabricated AMC/AEC plates reflect microwaves with phases close to ideal PMC ($\pi$) and PEC ($0$) across the measured band; if their reflection phase drifts, the measured chiral bands could be ordinary waveguide modes rather than boundary-selected topological states.

Editorial extensions

If this is right

Under PEC or PMC boundaries, a thin slab of a nodal-line meta-crystal can support a single chiral bulk mode across the pseudo-gap, so topological transport no longer requires half-infinite samples or thick slabs.
Switching boundary conditions between PEC-PEC and PMC-PMC should reverse the sign of the chiral bulk dispersion—positive to negative—without altering the crystal or applying a magnetic field.
Mixing PEC and PMC on opposite surfaces opens a complete photonic gap, giving a boundary-controlled way to switch from chiral transport to a gap.
Because the mechanism rests on boundaries selecting nodal-ring modes, the same recipe should work in acoustic, elastic, and electronic systems whose bulk hosts a Dirac or nodal-line degeneracy.
The measured AMC/AEC plates show that practical, non-ideal boundaries are sufficient to observe the effect in the microwave range, suggesting fabrication-tolerant devices.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: if the zeroth modes truly do not depend on thickness, the infinite-thickness limit would still carry boundary-controlled chiral transport, so the 'boundary-bulk' effect would survive where ordinary surface states have decayed away—an unusual thermodynamic limit worth probing directly.
Beyond the paper: a tunable metasurface whose reflection phase can be swept between $\pi$ and $0$ would let one flip the chiral transport direction in real time, converting this discovery into a reconfigurable topological switch.
Beyond the paper: the PEC/PMC selection looks like a polarization filter on the nodal ring; measuring the circular-polarization content of the transmitted field in the two configurations would quantify the claimed opposite chiral transport more directly than band-structure maps alone.
Beyond the paper: the AEC/AMC approximation restricts the effect to a finite band; extending the measurement to frequencies where the AMC reflection phase drifts would map the robustness boundary and could reveal how much phase error the zeroth-mode selection tolerates.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The core claim is that PEC and PMC boundaries select opposite chiral bulk transports in a finite-thickness 3D photonic nodal-line meta-crystal, with positive and negative dispersion respectively, and that this is independent of slab thickness. The concept is not new — boundary-induced chiral bulk states were shown in 2D Dirac systems and Weyl metamaterials — but the application to a 3D photonic nodal-line system, with the PEC/PMC selection of opposite chiralities, is a genuine and useful step. The paper backs the claim with analytic zeroth-mode solutions, full-wave simulations, and microwave near-field measurements of bands and equi-frequency surfaces. The measured bands in Fig. 5c,d align with simulations, the AEC-AMC case shows the expected gap, and the mirror-symmetry-preserving feature is clearly stated. I found no internal contradiction that would kill the central idea.

The soft spots are real but not fatal. The analytic derivation of Eqs. (3)-(5) is deferred to the SI, and the effective-medium parameters in Eq. (2) are chosen by hand. That makes the analytic 'prediction' partly circular: the model is built to reproduce the nodal ring, so the chiral zeroth modes are somewhat baked in. The boundary-selection effect, however, stands independently on the full-wave simulations and experimental data, so this is a presentation issue more than a validity issue.

The more serious experimental concern, which the stress-test note raises, is that the fabricated AMC is a resonant structure. Its reflection phase is near PMC only at one design frequency, and it varies steeply away from that. The AEC, by contrast, is a broadband PEC. This asymmetry means the measured negative-dispersion branch could, in principle, be a boundary-induced waveguide mode rather than the boundary-selected chiral zeroth mode of the nodal-line bulk. The paper defers AMC details to Supporting Notes 4 and 5 and gives no error bars or raw data. That said, the measured bands do match the ideal-boundary simulations across the displayed range, which reduces the worry but does not remove it. A referee should ask for the frequency-dependent reflection phase of the AMC and for a comparison of measured versus simulated field profiles.

This paper deserves a serious referee. It is a competent experimental and numerical study with a clear, testable central claim and honest acknowledgment of prior work. I would send it to peer review, with the explicit request that the SI derivation and AMC characterization be moved into the main text or at least made fully available. It will be of interest to the topological photonics and metamaterials community, and the boundary-control idea is worth citing. My verdict is conditional: the qualitative result is likely correct, but the experimental boundary implementation needs one more round of verification.

Referee Report

3 major / 4 minor

Summary. The paper proposes that the boundary conditions on a finite-thickness photonic nodal-line meta-crystal can select opposite chiral bulk 'zeroth' modes: PEC boundaries select a positive-dispersion TM-like chiral bulk state, PMC boundaries select a negative-dispersion LM-like chiral bulk state, and a mixed PEC-PMC configuration opens a complete gap. The authors support this with an effective-medium analytical model (Eqs. 1-5), full-wave supercell simulations, and microwave near-field measurements on a fabricated sample whose boundaries are implemented with artificial magnetic and electric conductors (AMC/AEC).

Significance. If the central claim holds, the paper establishes boundary conditions as an independent degree of freedom for controlling bulk chiral transport in three-dimensional photonic systems, which would be a useful conceptual addition to topological photonics and could inform compact device designs. The work has concrete strengths: full-wave simulations reproduce the predicted opposite dispersions, the near-field measurements in Figs. 5 and 6 show matching bands and equi-frequency surfaces, and the thickness scaling is checked in simulations (Fig. 3; SI Note 1). The main weaknesses are that the analytical derivation is not self-contained or independently validated, and the experimental realization of the PMC boundary is not characterized in the main text; both are load-bearing for the paper's strongest claims but appear fixable with additional data and analysis.

major comments (3)

[Analytical solutions, Eqs. (2)-(5)] The central analytical claim is not independently checkable from the main text. Equation (2) is introduced as an effective-medium model with the derivation deferred to Supporting Information Note 2, and the parameters a=1, b=10, c=1, L=1, omega0=2 are said to be 'set' rather than fitted. Because the model is constructed so that epsilon=0 and omega=pm k_y produce the nodal ring, the n=0 solutions in Eqs. (3b)/(4b) partly restate the input dispersion. I ask the authors to derive Eq. (2) from the I-resonator unit cell in Fig. 2a, fit the parameters to the full-wave bulk band structure of Fig. 2b, and show that the sign of the dispersion and the boundary-selection rules follow from the PEC/PMC conditions rather than from the chosen parameter values. Without this, the analytical 'prediction' is not an independent confirmation of the mechanism.
[Experimental observation of chiral bulk transports, Figs. 4 and 5] The experimental distinction between PEC and PMC boundary selection rests on the assumption that the fabricated AMC behaves as a near-ideal PMC across the measured frequency range, but the main text does not verify this. Figure 4 only states that the AMC has 'phase behavior similar to that of the PMC'; the AMC details are deferred to Supporting Notes 4 and 5. Since an AMC is a resonant patch-ground-via structure whose reflection phase crosses the ideal PMC value at one design frequency and varies steeply away from it, while the AEC is a broadband near-PEC, the comparison is asymmetric. Without a measured or simulated reflection-phase curve for the AMC over 4.6-4.9 GHz and a field profile showing that the observed branch extends through the bulk rather than localizing at the boundary, the negative-dispersion branch in Fig. 5c could be an AMC surface mode or an impedance-controlled waveguide mode. Please add the AMC reflection phase, a comparison with an ideal PMC, and the measured/simulated field profile of the chiral bulk state in the middle of the slab; provide the analogous characterization for the AEC.
[Analytical solutions, Eqs. (3)-(5)] Equations (3)-(5) mix dispersion relations, boundary-selection conditions, and transverse-resonance quantization in a way that is difficult to follow. The symbols d, ky, and epsilon are not defined in relation to the finite slab (is d the full thickness or half-thickness?), and the condition '2d sqrt(epsilon) sqrt(omega^2 - ky^2) = 2n pi' appears with different allowed sets of n in successive equations. The statement that the (2n+1)pi condition 'has no unique order such as the chiral zeroth order' also needs a derivation. A single derivation starting from Maxwell's equations with PEC/PMC boundary conditions and leading to Eqs. (3)-(5) would make the analytical claims checkable and would clarify which modes are bulk-extended and which are boundary-localized.

minor comments (4)

[Construction of boundary-induced chiral bulk states] The phrase 'on-local effect' in the paragraph describing the negative dispersion of LM appears to be a typo for 'nonlocal effect'; please correct it.
[Analytical solutions, Eq. (2)] The parameters a, b, c, L, and omega0 in Eq. (2) are given without units or dimension conventions; if this is a dimensionless effective model, state that explicitly.
[Figures 5e-h] The measured equi-frequency surfaces lack colorbars or intensity normalization information; please specify how the field maps were normalized so the suppression of one mode is quantitatively interpretable.
[References] Reference 44 is an arXiv preprint; if a peer-reviewed version is now available, it would be preferable to cite that version instead.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor analytic tautology in the effective-medium treatment; the central boundary-selection claim is independently validated.

fitted input called prediction [Analytical solutions, Eqs. (1)-(4) and text after Eq. (4); Figures 3a-f]
"The effective media of nodal ring can be accurately described by the following constitutive matrices... 𝜖 = 1 + 𝑙2/𝐿(𝜔02−𝜔2), 𝑙 = 1 − 𝑎(𝑘𝑥2+𝑘𝑦2)/𝑏+𝑐(𝑘𝑥2+𝑘𝑦2) (2)... [F]or the equation 2𝑑√𝜖√𝜔2 − 𝑘𝑦2 = 2𝑛𝜋 (𝑛 ∈ ℤ), when 𝑛 = 0, there are two independent solutions corresponding to the chiral zeroth modes, i.e. 𝜖 = 0 and 𝜔 = ±𝑘𝑦, which cross to form the nodal ring (or Dirac point on the 𝑘𝑥 = 0 plane)."

The analytic model in Eq. (2) is an effective-medium fit with free parameters a, b, c, L, and ω0, constructed to place a nodal ring in the dispersion. The n=0 solutions of the waveguide equation are precisely the two conditions ε=0 and ω=±ky whose crossing defines that same nodal ring. Calling these solutions a 'prediction' therefore restates the input dispersion. The boundary-selection content — PEC admits one solution and PMC the other — is not circular and is separately established by supercell simulation and by measurement of the fabricated meta-crystal (Figs. 2, 5, 6), so the circularity is local to the analytic validation, not to the central claim.

full rationale

The paper's central claim is that PEC/PEC versus PMC/PMC boundaries select opposite chiral bulk modes in a finite-thickness nodal-line meta-crystal. That claim is supported by full-wave supercell simulations and by microwave experiments with artificial boundaries, neither of which relies on the fitted effective medium of Eq. (2); hence it is not circular. The only partially circular element is the analytical section: Eq. (2) is parameterized to reproduce the nodal ring, and the n=0 'chiral zeroth modes' are the same ε=0 and ω=±ky conditions that define that fitted ring. This analytic result is a self-consistent model rather than an independent prediction, but it is not load-bearing for the main boundary-selection conclusion. Self-citations (e.g. refs 33, 34, 39, 48) are background, and the previously reported meta-crystal platform is independently re-simulated here; no uniqueness argument is imported from the authors' prior work. Experimental concerns about AMC phase dispersion are validity/correctness issues, not circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central analytical claim rests on an effective-medium model whose parameters a, b, c, L, and omega0 are chosen by hand, and on the equivalence of the fabricated AMC/AEC surfaces to ideal PMC/PEC boundaries. The model is used to produce the projected bands and to identify the two zeroth-order solutions, while the experimental interpretation depends on the boundary equivalence. No new physical entities are introduced. The supporting derivations and boundary-characterization data are deferred to the SI, which was not part of the provided text.

free parameters (5)

a (effective length parameter in Eq. 2) = 1 (chosen for analytical plots in Fig. 3)
Controls k-dependence of effective length; value chosen by hand in the main text and not fitted to full-wave data.
b (denominator parameter in Eq. 2) = 10
Denominator parameter chosen by hand for the analytical projected bands in Fig. 3.
c (denominator parameter in Eq. 2) = 1
Denominator parameter chosen by hand for the analytical projected bands in Fig. 3.
L (effective inductance in Eq. 2) = 1
Effective inductance chosen by hand for the analytical projected bands in Fig. 3.
omega0 (resonance frequency in Eq. 2) = 2
Resonance frequency chosen by hand for the analytical projected bands in Fig. 3.

assumptions (4)

domain assumption The nodal ring is protected by mirror symmetry M_z and a winding number w=±1.
Used to argue that the ring and its zeroth modes are topologically stable; introduced in Results around Fig. 1a.
domain assumption The effective-medium constitutive model in Eqs. (1)-(2) accurately describes the meta-crystal's low-energy band structure and nodal ring.
The analytic derivations and projected bands in Fig. 3 rest on this model; derivation is deferred to SI Note 2.
standard math Parallel-plate waveguide quantization conditions (round-trip phase 2nπ or (2n+1)π) apply to the nodal-line modes with PEC/PMC boundaries.
Used to obtain eigenmode dispersions in Eqs. (3)-(5).
domain assumption The fabricated AMC and AEC plates approximate ideal PMC and PEC boundaries across the measured band.
The experimental identification of chiral bulk states relies on this equivalence; details are in SI Notes 4-5.

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Cite this review

Pith. "Pith review of Photonic chiral bulk transports manipulated by boundary freedom in three-dimensional meta-crystals." pith.science (2026). https://pith.science/paper/IIKSYY5O

@misc{pith2026250610861,
  author       = {Pith},
  title        = {Pith review of: Photonic chiral bulk transports manipulated by boundary freedom in three-dimensional meta-crystals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IIKSYY5O}},
  note         = {Machine review of arXiv:2506.10861}
}

read the original abstract

In topological physics, one of the most intriguing phenomena is the presence of topological boundary states, accurately predicted by the well-established bulk-edge correspondence. For example, in three-dimensional Weyl semimetals, Fermi arcs emerge to connect projected Weyl points on the surface due to inheriting the bulk-edge correspondence from the integer quantum Hall effect. However, limited attention has been paid to exploring the reverse mechanism in topological crystals. In this study, we propose that boundaries can serve as an alternative degree of freedom to manipulate topological bulk transports. We analytically and experimentally validate our concept using a finite-thickness photonic meta-crystal that supports bulk nodal lines, with its zeroth modes exhibiting opposite chiral bulk transports under different boundary conditions. Notably, the mirror symmetry remains preserved across both configurations. These findings are applicable to other topological systems, providing new insights into systems with varied boundary conditions and offering the potential for the design of more compact and spatially efficient topological photonic devices.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

7 extracted references · 6 canonical work pages

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M.; Kane, C

(1) Young, S. M.; Kane, C. L. Dirac Semimetals in Two Dimensions. Phys. Rev. Lett. 2015, 115 (12), 126803. https://doi.org/10.1103/PhysRevLett.115.126803. 18 (2) Weng, H.; Dai, X.; Fang, Z. Topological Semimetals Predicted from First -Principles Calculations. J. Phys.: Condens. Matter 2016, 28 (30), 303001. https://doi.org/10.1088/0953 - 8984/28/30/303001...

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work page doi:10.3390/nano14070620 2024
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(49) Kim, S

https://doi.org/10.1038/s41467-018-03407-5. (49) Kim, S. -H.; Kee, C. -S. Discovery of Electromagnetic Surface Waves at the Interface between Perfect Electric Conductor and Perfect Magnetic Conductor Parallel -Plate Waveguides. Phys. Rev. Lett. 2024, 133 (18), 186901. https://doi.org/10.1103/PhysRevLett.133.186901

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https://doi.org/10.1038/s41467-023-37710-7. 21 (23) Ma, S.; Bi, Y.; Guo, Q.; Yang, B.; You, O.; Feng, J.; Sun, H. -B.; Zhang, S. Linked Weyl Surfaces and Weyl Arcs in Photonic Metamaterials. Science 2021, 373 (6554), 572 –576. https://doi.org/10.1126/science.abi7803. (24) Chen, W.-J.; Xiao, M.; Chan, C. T. Photonic Crystals Possessing Multiple Weyl Points...

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Boundary-induced topological chiral extended states in Weyl metamaterial waveguides

https://doi.org/10.48550/arXiv.2401.11780. (45) Zhang, X.; Zangeneh-Nejad, F.; Chen, Z.-G.; Lu, M.-H.; Christensen, J. A Second Wave of Topological Phenomena in Photonics and Acoustics. Nature 2023, 618 (7966), 687 –697. https://doi.org/10.1038/s41586-023-06163-9. (46) Ozawa, T.; Price, H. M.; Amo, A.; Goldman, N.; Hafezi, M.; Lu, L.; Rechtsman, M. C.; Sc...

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https://doi.org/10.1038/s41467-024-46759-x. (35) Dwivedi, V. Fermi Arc Reconstruction at Junctions between Weyl Semimetals. Phys. Rev. B 2018, 97 (6), 064201. https://doi.org/10.1103/PhysRevB.97.064201. (36) Yao, W.; Yang, S. A.; Niu, Q. Edge States in Graphene: From Gapped Flat -Band to Gapless Chiral Modes. Phys. Rev. Lett. 2009, 102 (9), 096801. https:...

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https://doi.org/10.1038/s41467-022-33447-x. (42) Xia, H. -R.; Xiao, M. Reversal of the Chiral Anomaly Bulk States with Periodically Staggered Potential. Phys. Rev. B 2023, 107 (3), 035144. https://doi.org/10.1103/PhysRevB.107.035144. (43) Zhang, Z. -D.; Lu, M. -H.; Chen, Y. -F. Observation of Free -Boundary-Induced Chiral Anomaly Bulk States in Elastic Tw...

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

M.; Kane, C

(1) Young, S. M.; Kane, C. L. Dirac Semimetals in Two Dimensions. Phys. Rev. Lett. 2015, 115 (12), 126803. https://doi.org/10.1103/PhysRevLett.115.126803. 18 (2) Weng, H.; Dai, X.; Fang, Z. Topological Semimetals Predicted from First -Principles Calculations. J. Phys.: Condens. Matter 2016, 28 (30), 303001. https://doi.org/10.1088/0953 - 8984/28/30/303001...

doi:10.1103/physrevlett.115.126803 2015

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(34) Wang, H.; Xu, W.; Wei, Z.; Wang, Y.; Wang, Z.; Cheng, X.; Guo, Q.; Shi, J.; Zhu, Z.; Yang, B

https://doi.org/10.3390/nano14070620. (34) Wang, H.; Xu, W.; Wei, Z.; Wang, Y.; Wang, Z.; Cheng, X.; Guo, Q.; Shi, J.; Zhu, Z.; Yang, B. Twisted Photonic Weyl Meta-Crystals and Aperiodic Fermi Arc Scattering. Nat Commun 2024, 15 (1),

work page doi:10.3390/nano14070620 2024

[3] [950]

(49) Kim, S

https://doi.org/10.1038/s41467-018-03407-5. (49) Kim, S. -H.; Kee, C. -S. Discovery of Electromagnetic Surface Waves at the Interface between Perfect Electric Conductor and Perfect Magnetic Conductor Parallel -Plate Waveguides. Phys. Rev. Lett. 2024, 133 (18), 186901. https://doi.org/10.1103/PhysRevLett.133.186901

work page doi:10.1038/s41467-018-03407-5

[4] [1991]

21 (23) Ma, S.; Bi, Y.; Guo, Q.; Yang, B.; You, O.; Feng, J.; Sun, H

https://doi.org/10.1038/s41467-023-37710-7. 21 (23) Ma, S.; Bi, Y.; Guo, Q.; Yang, B.; You, O.; Feng, J.; Sun, H. -B.; Zhang, S. Linked Weyl Surfaces and Weyl Arcs in Photonic Metamaterials. Science 2021, 373 (6554), 572 –576. https://doi.org/10.1126/science.abi7803. (24) Chen, W.-J.; Xiao, M.; Chan, C. T. Photonic Crystals Possessing Multiple Weyl Points...

work page doi:10.1038/s41467-023-37710-7 2021

[5] [2024]

Boundary-induced topological chiral extended states in Weyl metamaterial waveguides

https://doi.org/10.48550/arXiv.2401.11780. (45) Zhang, X.; Zangeneh-Nejad, F.; Chen, Z.-G.; Lu, M.-H.; Christensen, J. A Second Wave of Topological Phenomena in Photonics and Acoustics. Nature 2023, 618 (7966), 687 –697. https://doi.org/10.1038/s41586-023-06163-9. (46) Ozawa, T.; Price, H. M.; Amo, A.; Goldman, N.; Hafezi, M.; Lu, L.; Rechtsman, M. C.; Sc...

work page Pith review arXiv doi:10.48550/arxiv.2401.11780 2023

[6] [2440]

(35) Dwivedi, V

https://doi.org/10.1038/s41467-024-46759-x. (35) Dwivedi, V. Fermi Arc Reconstruction at Junctions between Weyl Semimetals. Phys. Rev. B 2018, 97 (6), 064201. https://doi.org/10.1103/PhysRevB.97.064201. (36) Yao, W.; Yang, S. A.; Niu, Q. Edge States in Graphene: From Gapped Flat -Band to Gapless Chiral Modes. Phys. Rev. Lett. 2009, 102 (9), 096801. https:...

work page doi:10.1038/s41467-024-46759-x 2018

[7] [5916]

(42) Xia, H

https://doi.org/10.1038/s41467-022-33447-x. (42) Xia, H. -R.; Xiao, M. Reversal of the Chiral Anomaly Bulk States with Periodically Staggered Potential. Phys. Rev. B 2023, 107 (3), 035144. https://doi.org/10.1103/PhysRevB.107.035144. (43) Zhang, Z. -D.; Lu, M. -H.; Chen, Y. -F. Observation of Free -Boundary-Induced Chiral Anomaly Bulk States in Elastic Tw...

work page doi:10.1038/s41467-022-33447-x 2023