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Antichiral hinge states in a higher-order photonic nodal ring semimetal

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A pair of antichiral hinge states is observed in a 3D photonic nodal-ring semimetal, with both hinges carrying unidirectional modes in the same direction.

desk verdict A credible first observation of antichiral hinge states in a photonic crystal, though the hinge-selection rule would benefit from a direct open-boundary eigenmode calculation. read the letter →

arxiv 2607.25688 v1 pith:5676GVBV submitted 2026-07-28 physics.optics

Yuchen Peng , Deep Mondal , Yuting Yang , Wanting Wu , Bo Zhao , Shuaiyang Wei , Zhenzhi Liu , Wenrong Qi
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Xiaokang Dai Minqi Cheng Weili Li Xinyi Zhang Fei-Fei Li Rimi Banerjee Minggui Wei Jingyi Tian Peiheng Zhou Subhaskar Mandal Baile Zhang Gui-Geng Liu
This is my paper · ORCID
classification physics.optics
keywords antichiralhingestateshigher-ordertopologicalsemimetalnodalringgyromagneticphotoniccrystalsurfacepolarizationdrumheadphotonicsunidirectionaltransport
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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 reports the experimental observation of antichiral hinge states—one-dimensional boundary modes that propagate in the same direction on two parallel hinges even though the system is closed. Working with a three-dimensional gyromagnetic photonic crystal whose bulk is a nodal-ring semimetal, the authors show that two diagonal hinges each carry a unidirectional mode of the same chirality, with the expected counter-propagating channels replaced by gapless bulk modes. They also observe drumhead surface states and antichiral surface states in the same sample, forming a full hierarchy of first- and second-order topological boundary states. If correct, this is the first realization of antichiral transport in a higher-order topological semimetal, and it demonstrates a reconfigurable on-chip routing platform.

What carries the argument

The central object is the termination-dependent surface polarization $\nu_z^{\mathrm{surface}}(k_x)$, computed as the Berry phase of the isolated antichiral surface band along $k_z$. A value of $1/2$ in the momentum window $2/3 < k_x/(\pi/a) < 4/3$ predicts a hinge state wherever this polarization changes from $1/2$ to $0$ between two boundaries. The antichiral surface band itself provides the two-dimensional topological channel, so the one-dimensional hinge response is governed by the topology of that surface band, in analogy to an SSH chain of coupled surface layers.

What would settle it

Recompute the surface polarization of the antichiral surface band with the termination-defining unit cell shifted by one layer: the criterion then predicts the opposite diagonal hinge pair. Measuring which pair actually carries unidirectional modes in a sample with that termination would settle whether the hierarchy is determined by surface polarization.

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Extended reading notes

Core claim

In a designed 3D photonic crystal made of stacked gyromagnetic layers with alternating interlayer couplings, the bulk hosts two nodal rings at shifted frequencies plus vertical Dirac lines. Near-field microwave measurements show that two parallel diagonal hinges—and only those—carry co-propagating unidirectional modes in the 7.0–8.8 GHz window between the rings, with transmission contrast up to about 30 dB and no backscattering from metallic obstacles. The hinge positions are set by a surface polarization of 1/2 that lives on the antichiral surface band, and adding a single photonic layer moves the hinge from one diagonal pair to the other. The authors interpret the hinge states as the higher-order counterpart of previously observed antichiral edge and surface states.

Load-bearing premise

The argument's load-bearing premise is that a chosen convention for grouping layers into unit cells, anchored at the top versus bottom boundary, is not merely a bookkeeping choice but is physically forced; if that convention is arbitrary, the predicted diagonal hinge positions do not follow from the theory alone.

Editorial extensions

If this is right

  • Antichiral transport now extends into higher-order topology: the previously missing class of unidirectional boundary channels in three dimensions is filled, so gapless higher-order semimetals become a general setting for one-way hinge transport.
  • Hinge channels are reconfigurable by adding or removing a photonic layer, allowing on-demand selection of which edges route light without refabrication.
  • The observed robustness against metallic scatterers, with no obvious increase in reflected field intensity, supports the use of these channels as reconfigurable nonreciprocal waveguides.
  • The coexistence of drumhead surface states, antichiral surface states, and hinge states in one sample demonstrates that a single semimetal can host a complete hierarchy of topological boundary responses.

Reading between the lines

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

  • If the surface-polarization mechanism is robust, the same stacking principle could be translated to other wave domains where gyromagnetic response is unavailable, using time-reversal-breaking analogues in acoustics or mechanics.
  • The co-propagating hinge modes cannot close a loop on a rectangular block, but a triangular-prism geometry would allow such loops; one could test whether this enables a three-dimensional one-way circulator.
  • Dynamic control of the interlayer coupling, for instance by mechanically tuning layer spacing or using shutters at the coupling holes, might extend the demonstrated static reconfiguration into fast switching of hinge channels.
  • The surface-polarization criterion is valid only where the antichiral surface band is isolated from the bulk continuum; a testable extension is whether coupling the surface states into the bulk continuum softens or removes the protection over wider frequency bands.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper reports the theoretical proposal and experimental observation of antichiral hinge states in a three-dimensional gyromagnetic photonic crystal that realizes a higher-order nodal-ring semimetal. The authors design a periodic stack of modified Haldane layers with alternating interlayer couplings, producing bulk nodal rings and Dirac lines. Near-field scanning measurements reveal drumhead surface states, antichiral surface states with positive group velocity, and a pair of hinge states at two parallel hinges propagating unidirectionally in the same direction, with claimed robustness against metallic scatterers. Adding or removing a photonic layer is shown to reconfigure the spatial locations of the hinge states. The interpretation uses surface-polarization and termination-dependent unit-cell arguments to identify the observed diagonal hinge selection as a higher-order topological response.

Significance. If the central claim holds, this is the first experimental realization of antichiral hinge states in a higher-order topological semimetal, extending antichiral boundary transport beyond first-order systems and demonstrating a hierarchy of drumhead, antichiral surface, and hinge states in one platform. The evidence is multi-pronged: near-field field maps at multiple hinges, transmission spectra with up to about 30 dB forward/backward contrast, measured dispersions with positive group velocity, and a layer-addition reconfiguration experiment. The manuscript also explicitly states the validity regime of the surface-polarization criterion, which is a useful limitation. However, the load-bearing interpretive step—the selection of specific hinges—depends on a termination-dependent unit-cell convention that is introduced after the observation, and the robustness claim lacks quantitative backscattering data. These gaps are fixable and do not negate the experimental observation, but they must be addressed to make the higher-order hierarchy interpretation convincing.

major comments (3)
  1. [Experimental observation of antichiral hinge states, paragraph starting 'Notably, both diagonal hinges...' and…] The selection of hinges A and C is presented as a prediction of the surface-polarization criterion after those hinges were observed. The unit-cell convention for the odd-layer sample is introduced in this paragraph, and Eq. (2) is acknowledged to be valid only where the antichiral surface band is isolated from the projected bulk continuum. Because surface polarization is a bulk quantity that depends on the unit-cell choice, the physical termination must uniquely determine the convention used for the top and bottom boundaries. The manuscript does not show that the actual 11-layer copper-plate termination forces the 1/2-versus-0 assignment, nor does it report an open-boundary eigenmode calculation (with PEC boundaries along y and z, as described in Methods) that resolves the hinge positions to A and C from the real-space termination alone. Please provide this direct eigenmode calculation or a detailed termination-resolved surface-polarization derivation, and likewise for the 12-layer sample, so that the hinge selection is an independently derived consequence of the model rather than a post hoc assignment.
  2. [Experimental observation of antichiral hinge states, Fig. 3d–g] Robustness to metallic scatterers is asserted qualitatively from near-field maps showing no obvious increase in reflected-field intensity. The abstract claims 'robust transport against metallic scatterers', but no quantitative transmission measurements with and without obstacles are provided. Please report forward and backward transmission spectra (or S-parameters) for the pristine and obstructed hinges, including repeated measurements or uncertainty estimates, to substantiate the backscattering-immune behavior in the presence of defects.
  3. [Spatial reconfiguration of the antichiral hinge states, Fig. 4] The reconfiguration from hinges A/C to hinges A/B is explained by a change in surface polarization induced by the added Dirac semimetal layer, but no computed surface polarization for the 12-layer termination or an eigenmode calculation of the reconfigured hinge states is shown. This is the same termination-dependence issue as in the odd-layer case. The reader should be able to verify that the same criterion applied to the 12-layer sample yields hinges A and B; without that, the 'on-demand control' claim rests on a single experimental observation without independent theoretical support.
minor comments (4)
  1. [Abstract and Introduction] There are spacing/OCR artifacts in several early uses of key terms (e.g., 'a ntichiral hinge state s', 'high er-order', 'e dge states' in the first paragraph). These should be cleaned in the final typeset version.
  2. [Fig. 3b] The 'up to approximately 30 dB' forward/backward contrast is quoted without specifying the frequency range over which the contrast is large. Please state the frequency band where the contrast exceeds, say, 20 dB, and indicate whether the contrast degrades near the nodal-ring frequencies.
  3. [Experimental observation of antichiral hinge states, paragraph after Eq. (2)] The statement that Eq. (2) is valid only where the antichiral surface band is isolated from the projected bulk continuum should be reconciled with the measured hinge-state dispersion, which must be defined over an actual frequency band. Clarify how the hinge state is identified in the wavevector regions where the surface polarization is ill-defined.
  4. [Code availability] The codes are available only 'upon request'. For reproducibility, consider depositing the tight-binding model and the COMSOL simulation scripts in a permanent public repository.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: hinge-state positions are reproduced by direct open-boundary eigenmode calculations, and the termination-dependent surface-polarization argument rests on a fixed geometric fact rather than a fitted input.

full rationale

The paper's derivation chain is self-contained and not circular. The central hinge-state prediction is supported by a full open-boundary eigenmode calculation in the Methods: 'Antichiral hinge states: PBC were applied only along the propagation direction (x), while PEC boundaries were imposed along both transverse directions (y and z).' The calculated hinge dispersions shown as green lines in Fig. 3c therefore are not obtained by fitting to the observed hinge positions; they follow directly from the model Hamiltonian. The termination-dependent surface-polarization argument is also a derived geometric fact rather than an adjustable input: for an odd-layer stack, 'the two-layer unit cells defined from the top and bottom boundaries differ by one layer; therefore, the surface polarization for the same lateral surface has 1/2 at one z-termination but 0 at the other.' Shifting the unit-cell origin by one layer flips the quantized Wannier/surface polarization between 0 and 1/2, so the diagonal A-C selection follows from the odd-layer stacking parity plus the physical terminations, not from a parameter chosen to match the data. The stated limitation that Eq. (2) 'is valid only in the wavevector region where the antichiral surface band remains isolated from the projected bulk continuum' defines the applicable momentum window and does not make the prediction equivalent to the observation. The self-citations (refs [9], [13], [17]) provide design context and prior experimental platforms but are not the load-bearing justification for the antichiral hinge states; the load-bearing evidence is the measured unidirectional transport, dispersions, robustness against metallic obstacles, and the layer-count reconfiguration (A-C to A-B) that is independently confirmed by theoretical calculations. No step in the paper reduces, by construction or by self-citation, to its own inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim depends on the fidelity of the tight-binding model, the validity of the surface-polarization criterion in a restricted momentum window, and the physical correctness of the termination-dependent unit-cell assignment. The main free parameters are the model hoppings and the resulting nodal-ring frequency splitting. No new fundamental entities are introduced.

free parameters (2)
  • Tight-binding interlayer coupling strengths t_A(k_z), t_B(k_z) and in-plane Haldane parameters = Not given in main text; staggered weak/strong coupling chosen to match the observed band structure
    The Hamiltonian in Eqs. 3-4 defines the model that produces the shifted nodal rings and Dirac lines; the parameter values are not stated in the main text and are inferred to be selected to reproduce the measured frequencies around 7.0 and 8.8 GHz.
  • Nodal-ring frequency splitting = Approximately 7.0 GHz (K') and 8.8 GHz (K)
    The frequency window between the two nodal rings is the operating range for the hinge states; it is a designed outcome of the staggered coupling rather than an independent prediction from first principles.
assumptions (5)
  • domain assumption The photonic crystal is faithfully described by the four-band tight-binding Hamiltonian (Eq. 3) with nearest-layer staggered couplings and no significant higher-order hoppings.
    The entire topological classification and hinge-state prediction rest on this model; additional couplings, magnet inhomogeneity, and fabrication disorder are not treated in the main text.
  • domain assumption The antichiral surface band remains isolated from the projected bulk continuum over the wavevector window 2/3 < k_x/(pi/a) < 4/3 where the surface polarization is quantized.
    The paper explicitly states that the surface-polarization criterion is valid only where the surface band is isolated; outside this region the polarization is undefined, limiting the predictive range of the higher-order criterion.
  • ad hoc to paper The termination-dependent unit-cell convention is the correct way to define surface polarization for the finite odd-layer sample.
    The diagonal hinge positions (A and C) are explained by choosing unit cells from top and bottom that differ by one layer; this convention is not derived from an independent principle in the main text.
  • standard math Wilson-loop bulk polarization and surface polarization are valid topological invariants for this open-boundary system.
    Equations 1 and 2 rely on established Berry-phase and Wilson-loop formalism from Refs [19,33], which the paper cites.
  • domain assumption Microwave absorbers and copper cladding implement open and PEC boundary conditions that do not disturb the topological modes.
    The experimental boundary treatments approximate the idealized simulation boundaries; residual reflections or absorption are not quantified in the main text.

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Pith. "Pith review of Antichiral hinge states in a higher-order photonic nodal ring semimetal." pith.science (2026). https://pith.science/paper/5676GVBV

@misc{pith2026260725688,
  author       = {Pith},
  title        = {Pith review of: Antichiral hinge states in a higher-order photonic nodal ring semimetal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5676GVBV}},
  note         = {Machine review of arXiv:2607.25688}
}
read the original abstract

Antichiral states propagate in the same direction on opposite boundaries, defying the conventional constraint that boundary modes must cancel net chirality. Previously found antichiral states have been limited to first-order topological semimetals. However, antichiral hinge states, the antichiral counterpart of recently discovered higher-order chiral hinge states, remain elusive. Here, we report the observation of antichiral hinge states in a higher-order nodal-ring semimetal made of a three-dimensional gyromagnetic photonic crystal. Near-field scanning measurements reveal a pair of hinge states at two parallel one-dimensional boundaries propagating unidirectionally along the same direction, with robust transport against metallic scatterers. Their spatial positions can be reconfigured by adding or removing photonic layers. The additionally observed antichiral and drumhead surface states manifest a hierarchy of first- and second-order topological boundary states within a single photonic system. Our work extends antichiral states to higher-order topological semimetals and has potential applications in robust and reconfigurable photonic routing.

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