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REVIEW 4 major objections 6 minor 58 references

Observation of non-Hermitian boundary induced hybrid skin-topological effect excited by synthetic complex frequencies

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Boundary-only loss creates skin-topological corner states in a transmission-line network.

desk verdict Direct imaging of a complex-frequency corner state via synthetic excitation is a real step, but the snapshot evidence is thin and the asymmetric-transmission claim needs to be reconciled with reciprocity. read the letter →

arxiv 2411.13221 v1 pith:33E2VPWG submitted 2024-11-20 physics.optics cond-mat.mtrl-sci

Tianshu Jiang , Chenyu Zhang , Ruo-Yang Zhang , Yingjuan Yu , Zhenfu Guan , Zeyong Wei , Zhanshan Wang , Xinbin Cheng
show 1 more author
C. T. Chan
This is my paper · ORCID
classification physics.opticscond-mat.mtrl-sci
keywords hybridskin-topologicaleffectnon-HermitianskincomplexfrequencyexcitationtransmissionlinenetworkHaldanemodelcornerstatesphotonicsasymmetric
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 tries to establish that the hybrid skin-topological effect (HSTE) — the collapse of chiral topological edge states into a corner under the non-Hermitian skin effect — can be observed in a passive transmission-line network, and that its occurrence is controlled solely by the loss distribution on the boundaries, not by whether the bulk is lossy. To see the corner states, whose eigenfrequencies are complex, the authors synthesize complex-frequency excitations by Fourier-transforming an array of real-frequency response measurements, a method that recovers the eigenstate field patterns that ordinary real-frequency driving cannot excite. They demonstrate the HSTE corner state at a lower-left corner, observe asymmetric transmission through the topological band gap, and identify a second family of corner states arising from non-chiral boundary modes. If the claim stands, non-Hermitian topological devices such as topological lasers can be designed with Hermitian bulk, and the corner-state position can be relocated by changing only the boundary terminations.

What carries the argument

The load-bearing object is the transmission-line network obeying Eq. (4), whose node voltages map onto a tight-binding model with three stacked honeycomb layers and cyclic interlayer couplings, so that the $m=1$ sector is an effective Haldane model with a topological band gap near 31–36.3 MHz. Non-Hermiticity enters as on-site loss $-i\gamma$ on B sublattices, implemented by terminators; because only certain boundary meta-atoms are terminated, the point-gap winding number $\nu$ (Eq. 6) becomes nonzero without altering the bulk. To observe the complex-frequency eigenstates, the experiment measures responses $A(\omega_j)$ at many real frequencies and reconstructs the complex-frequency response via $\psi(\omega_0,t)\approx \sum_j [i A(\omega_j)/(\omega_j-\omega_0)] e^{-i\omega_j t}\Delta\omega/2\pi$, a discrete Fourier synthesis whose time windows isolate the target eigenstate. The combination of a nontrivial point gap in both x- and y-strip geometries causes the chiral edge states to collapse to a single corner, the HSTE corner state.

What would settle it

Reverse the loss asymmetry by terminating the upper-left corner rather than the lower-left corner; the boundary-control claim predicts the HSTE corner state should move to the new lossy corner. If the corner remains pinned at the lower-left, the claim fails. Alternatively, if the same localized lower-left pattern appears under real-frequency excitation at 33.49 MHz alone, then the complex-frequency synthesis is not necessary for observing the state.

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Extended reading notes

Core claim

The central claim is that a finite two-dimensional transmission-line network, in the angular-momentum sector $m=1$ of an effective Haldane model, develops hybrid skin-topological corner states when on-site loss is applied asymmetrically to the boundary meta-atoms, and that these states can be directly imaged using synthetic complex-frequency excitation. The authors verify this in a $4\times5$ network with terminators on B sublattices: the complex eigenfrequency spectrum shows a point gap with winding number $\nu_x=\nu_y=1$, and the field pattern at $f=(33.49-1.19i)$ MHz is concentrated at the lower-left corner, matching simulation. They also show that removing loss from the bulk does not destroy the effect, while rebalancing the boundary loss removes it, so the boundary non-Hermiticity, not the bulk, is the controlling ingredient. In the real-frequency domain, the same corner state yields asymmetric transmission $|S_{21}|>|S_{12}|$ along the anti-diagonal inside the topological band gap.

Load-bearing premise

The identification of the measured lower-left-localized field as an HSTE corner state assumes that the small $4\times5$ transmission-line network is faithfully described by the effective $m=1$ Haldane tight-binding model with cyclic three-layer couplings and boundary on-site loss, including negligible hybridization between the angular-momentum sectors and between opposite boundaries; the authors themselves note a noticeable upper-left intensity because of the small sample size.

Editorial extensions

If this is right

  • Topological lasers could be built with Hermitian bulk and loss engineered only at the boundaries, simplifying fabrication.
  • The corner-state position can be relocated by changing which boundary meta-atoms carry loss, enabling tunable non-Hermitian devices.
  • Synthetic complex-frequency excitation provides a general route to observe eigenstates with complex eigenfrequencies in passive systems.
  • Asymmetric transmission in the topological band gap can be used as a real-frequency signature of HSTE.

Reading between the lines

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

  • Because the paper shows the bulk can be Hermitian, a natural extension is to design topological lasers with gain only at chosen edges; the same Fourier-synthesis technique should allow direct imaging of the lasing mode's complex eigenfrequency.
  • The discrete Fourier synthesis has a temporal periodicity $T=2\pi/\Delta\omega$; in other platforms with faster dynamics, the method's resolution will be limited by the need to keep $T$ larger than the transient response time, a design constraint worth testing.
  • The boundary-loss control suggests that HSTE corner-state positions could be reprogrammed electronically in circuit or transmission-line networks by toggling terminators, enabling reconfigurable non-Hermitian routing.
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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

4 major / 6 minor

Summary. The manuscript reports an experimental transmission-line realization of the hybrid skin-topological effect (HSTE), in which topological chiral edge states are argued to collapse into a corner state due to boundary-induced non-Hermitian point gaps. The authors formulate an effective Haldane model in an angular-momentum sector, compute supercell spectra showing that loss distributions breaking the spectral symmetry f(k)=f(-k) produce winding-number-one point gaps, and observe in a 4x5 network a lower-left-localized field pattern under synthesized complex-frequency excitation at f=(33.49-1.19i) MHz. They also present transmission spectra claimed to show asymmetric propagation in the topological band gap and argue that only boundary loss, not bulk loss, is needed for HSTE.

Significance. If all claims hold, the paper would be a useful contribution: it would provide a direct procedure for accessing complex-frequency eigenstates in non-Hermitian topological systems and evidence that boundary-only loss engineering is sufficient for HSTE. The synthesis formalism (Eqs. 7-14) is clearly derived, the periodicity of the synthesized pulse is demonstrated experimentally (T=20 us, Fig. 5), and the supplementary material appears to address robustness, sample shapes, and winding-number variations. However, the central experimental evidence is currently qualitative: single hand-picked snapshots, no quantitative mode-overlap metrics, a small network with acknowledged finite-size hybridization, and fitted attenuation parameters. The strength of the conclusions is therefore not yet commensurate with the claims.

major comments (4)
  1. [Experimental demonstration; Fig. 4d; Methods Eqs. (12)-(19), Fig. 7b] The identification of the lower-left-localized pattern in Fig. 4d as an HSTE corner eigenstate is supported by a single snapshot at t=0.57 us chosen from the synthesized transient (Fig. 6a) and by a mode-coefficient analysis (Fig. 7b) performed with the ideal tight-binding model (t1=-1, t2=-2, gamma=1), not with the physical network equation containing the frequency-dependent coth/sinh couplings and cable attenuation (Eqs. 4-5). Because the 4x5 network has dense eigenfrequencies that are not independently verified, and because the authors acknowledge noticeable upper-left intensity from finite-size coupling (Supplementary Note 4), the dominance window 4<t<10 in Fig. 7b has no demonstrated counterpart at the experimental time. The authors should quantify the overlap between the measured field and the full-network eigenmode, test the stability of the pattern across the predicted time window, and exclude the possibility that the snapshot is a traveling wavefront launched from the lower-right source.
  2. [Experimental demonstration; Fig. 4g] For a passive linear network composed of reciprocal coaxial cables and resistive terminators, the two-port scattering matrix must be symmetric, implying |S21|=|S12| for the same two ports. The clear asymmetry in Fig. 4g therefore contradicts reciprocity unless the network contains unmentioned nonreciprocal or active elements, the measurement is not a standard two-port S-parameter measurement, or the ports are not equivalent. Since this asymmetric transmission is presented as a real-frequency manifestation of HSTE, the authors need to specify the exact measured quantity, port definitions, and normalization, and ideally perform a port-swap check. As written, this claim is not supported.
  3. [HSTE in the transmission line network; Fig. 3a vs Fig. 4b] The experimental network is only 4x5 cells, far smaller than the 9x9 model of Fig. 3a used to establish the HSTE corner-state concept. The authors report noticeable intensity at the upper-left corner due to interactions between opposite boundaries (Supplementary Note 4). With such a small sample, the field pattern may be dominated by finite-size hybridization or by boundary-wave propagation rather than by exponential corner localization of an HSTE mode. A finite-size scaling analysis (e.g., localization length extracted from 6x6, 9x9, and larger networks) or a quantitative comparison of the experimental field with the full-network eigenstate is needed to show that the observed localization is a true HSTE eigenstate.
  4. [Methods; Fig. 7b; Figs. 4d-f] The time window of the mode-dominance calculation is presented in dimensionless tight-binding units ('about 4 < t < 10'), while the experimental snapshot is taken at t=0.57 us. No mapping between the dimensionless time and the physical network time is provided, so the claim that t=0.57 us lies in the dominance window is unsubstantiated. Moreover, the complex excitation frequencies (e.g., f=(33.49-1.19i) MHz) are taken from the model spectrum but are never verified against the realized 4x5 network; the authors should show that these frequencies correspond to actual poles of the measured response, for example by fitting the complex Lorentzian line shape of A(omega) or by measuring the temporal decay rate.
minor comments (6)
  1. [Global] There are typos: 'conner' should be 'corner' in the sentence describing Fig. 4f, and 'exitation' should be 'excitation' in the Methods section.
  2. [Introduction] In the sentence 'Experimental observations of HSTE have been reported in circuit systems 40, photonic crystals41,42, photonic crystals43 and active matter systems 44', the phrase 'photonic crystals' is duplicated; the citation list should be cleaned.
  3. [Fig. 7b] Please specify the units of time and energy in the tight-binding calculation and state how the dimensionless parameters t1=-1, t2=-2, gamma=1 are related to the physical network parameters (cable lengths, permittivity, attenuation).
  4. [Fig. 4g] Report measurement repetitions and error bars for the transmission spectra; the current single spectra do not allow the reader to judge whether the asymmetry exceeds experimental uncertainty.
  5. [Abstract and Introduction] The text calls the technique 'synthetic complex frequency excitations'; to avoid confusion, clarify earlier that the network is driven at multiple real frequencies and the complex-frequency response is synthesized in post-processing.
  6. [Data availability] The statement 'available from the corresponding authors on request' is weaker than current community norms; consider depositing the raw transmission data and simulation scripts in a public repository.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the HSTE corner-state observation is an experimental test of a computed eigenmode, not a fit renamed as a prediction.

full rationale

The paper's central chain is: build a transmission-line network modeled by the network equation (Eqs. 4-5); solve the effective Haldane model for eigenfrequencies and eigenstates; compute point-gap winding numbers; predict corner states; then measure fields using synthesized complex-frequency excitation. The complex-frequency synthesis derivation (Eqs. 7-19) is self-contained, and the observation time is selected from an independent mode-coefficient calculation (Fig. 7b), not fitted to the measured field pattern. The measured patterns (Fig. 4d-f) are compared with simulations and are not used to adjust the model parameters. The cable attenuation law is an empirical input, but it is not the source of the predicted HSTE and does not define the corner-state pattern. Ref. 51, while author-overlapping, provides a prior published angular-momentum Haldane mapping and is externally established; it is used as a model input rather than as an appeal to a uniqueness theorem. The acknowledged finite-size hybridization (Supplementary Note 4) weakens the cleanliness of the observation but does not make the claim definitionally equivalent to its inputs. Therefore no step reduces by construction to a fitted parameter or a self-citation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the tight-binding mapping, sector decoupling, the Fourier synthesis mathematics, and two fitted attenuation coefficients. No new physical entities are introduced.

free parameters (3)
  • Cable attenuation coefficients alpha and beta = alpha = 338 m MHz^beta, beta = 0.6123
    Fitted to coaxial cable loss measurements (Supplementary Note 1, Supplementary Fig. 2) and used in the simulations that are compared with the experiment.
  • Display time windows for complex-frequency synthesis = t = 0.57, 0.24, 0.39 microseconds
    Hand-selected observation times at which the target eigenstate is claimed to dominate the synthesized response; the displayed field pattern is sensitive to this choice.
  • Excitation complex frequencies = (33.49 - 1.19i) MHz, (27.34 - 1.78i) MHz, (27.72 - 0.94i) MHz
    Chosen to match computed eigenfrequencies of the model; these are predictions from the simulation rather than post-hoc fits, but they are still hand-selected operating points.
assumptions (4)
  • domain assumption Eqs. (4)-(5) map the transmission line network to a tight-binding model with frequency-dependent hoppings and on-site loss.
    Invoked in the 'Transmission line network' section; if cable parasitics or non-nearest couplings are significant, the simulated spectra and eigenstate identification break down.
  • domain assumption The three-layer cyclic model decouples into angular momentum sectors and the m=1 sector is an effective Haldane model.
    Taken from Ref. 51 and used throughout; sector decoupling is required for the Chern-number argument and for interpreting the measured field as a single-sector HSTE state.
  • standard math The complex-frequency response is obtained by the discrete Fourier synthesis of Eq. (13), and the residue expansion of Eqs. (15)-(19) gives a time window where the target eigenstate dominates.
    Used in the Methods section; the derivation is conventional Fourier analysis, but no formal proof is shipped.
  • standard math Adding a uniform imaginary shift to all eigenfrequencies does not change the eigenstates.
    Used in the gain argument in the Results section to connect the gain-assisted picture to the lossy sample.

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Cite this review

Pith. "Pith review of Observation of non-Hermitian boundary induced hybrid skin-topological effect excited by synthetic complex frequencies." pith.science (2026). https://pith.science/paper/33E2VPWG

@misc{pith2026241113221,
  author       = {Pith},
  title        = {Pith review of: Observation of non-Hermitian boundary induced hybrid skin-topological effect excited by synthetic complex frequencies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/33E2VPWG}},
  note         = {Machine review of arXiv:2411.13221}
}
read the original abstract

The hybrid skin-topological effect (HSTE) has recently been proposed as a mechanism where topological edge states collapse into corner states under the influence of the non-Hermitian skin effect (NHSE). However, directly observing this effect is challenging due to the complex frequencies of eigenmodes. In this study, we experimentally observe HSTE corner states using synthetic complex frequency excitations in a transmission line network. We demonstrate that HSTE induces asymmetric transmission along a specific direction within the topological band gap. Besides HSTE, we identify corner states originating from non-chiral edge states, which are caused by the unbalanced effective onsite energy shifts at the boundaries of the network. Furthermore, our results suggest that whether the bulk interior is Hermitian or non-Hermitian is not a key factor for HSTE. Instead, the HSTE states can be realized and relocated simply by adjusting the non-Hermitian distribution at the boundaries. Our research has deepened the understanding of a range of issues regarding HSTE, paving the way for advancements in the design of non-Hermitian topological devices.

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.