Pith. sign in

REVIEW 4 major objections 6 minor 52 references

Observation of non-Hermitian topological disclination states and charge fractionalization

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper reports the first experimental observation of non-Hermitian topological disclination states and an associated fractional charge, produced in electric circuit lattices using only gain and loss.

desk verdict A genuine first experimental report of non-Hermitian disclination states with convincing spectra and localization data, but the fractional-charge headline is not verifiable until the authors supply the occupied-state rule and a well-defined biorthogonal charge. read the letter →

arxiv 2502.04922 v1 pith:B3GIAGD2 submitted 2025-02-07 cond-mat.mes-hall cond-mat.mtrl-sci

Ruifeng Li , Rimi Banerjee , Subhaskar Mandal , Da Li , Yang Long , Tianchi Ma , Jianwei Liu , Gui-Geng Liu
show 3 more authors
Yidong Chong Baile Zhang Er-Ping Li
This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords non-Hermitiantopologicalphasesdisclinationstateschargefractionalizationelectriccircuitlatticesgainandlossbi-orthogonaleigenvectorsbulk-defectcorrespondence
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 claims the first experimental observation of non-Hermitian topological disclination states, together with the fractional charge they trap. The experiments use electric circuit lattices in which the only non-Hermitian ingredient is a pattern of gain and loss on lattice sites. In a C5-symmetric lattice with a disclination at the core, the topological phase shows five localized midgap modes and a measured disclination charge of about 1/2 modulo 1, while a trivial phase shows neither. The result matters because it extends the bulk-defect correspondence into non-Hermitian systems and indicates that gain and loss alone can engineer localized defect modes and fractional charge in two dimensions.

What carries the argument

The central object is the non-Hermitian circuit Laplacian J evaluated at the LC resonance frequency, which maps the circuit equations to the tight-binding Hamiltonian with imaginary on-site masses ±iγ. Its complex eigenadmittance spectrum provides the quantity that calculation and experiment compare, and its bi-orthogonal right and left eigenvectors enter the charge formula that assigns a fractional charge to each bulk unit cell around the disclination core; the gain and loss themselves are produced by negative-impedance converters and ordinary resistors.

What would settle it

Compute the disclination charge from the measured circuit Laplacian using right eigenvectors only, omitting the bi-orthogonal product in the paper's Eq. (3); if the mod-1 charge moves away from approximately 1/2, the reported fractional value is a convention of bi-orthogonal calculus rather than a property of the lattice.

Watch

Extended reading notes

Core claim

In a circuit realization of a non-Hermitian tight-binding model with on-site gain and loss of magnitude γ relative to hopping t, the authors observe five midgap disclination states in a C5-symmetric lattice: one singlet and two doublets, all localized at the disclination core. From the measured circuit Laplacian, they compute the disclination charge of bulk unit cells near the core using a bi-orthogonal eigenvector sum over occupied states, obtaining a total charge of 0.57 in calculation and 0.47 in experiment, consistent with the predicted 1/2 modulo 1. In a comparison lattice with a different gain-loss pattern that is topologically trivial, the spectrum shows a pure bandgap and the same charge calculation gives 0.11 and 0.10. The authors also visualize the localized disclination mode by monochromatic field excitation and report degenerate zero-energy disclination states, without fractional charge, in a C4-symmetric non-Hermitian lattice.

Load-bearing premise

The 1/2 fractional charge is only meaningful if there is a single pre-agreed rule for which of the measured circuit modes count as occupied; that rule is deferred to a supplementary note that the preprint does not include.

Editorial extensions

If this is right

  • Gain and loss alone can induce topological disclination modes in a two-dimensional lattice, without magnetic fields or engineered hopping phases.
  • The measured charge near 1/2 mod 1 in the topological phase, versus 0 mod 1 in the trivial phase, extends the fractional-charge bulk-defect correspondence to non-Hermitian circuits.
  • The disclination mode remains observable as a localized voltage profile under monochromatic excitation, and its resonance frequency shifts with the gain-loss parameter γ, indicating tunability.
  • The C4-symmetric lattice hosts degenerate zero-energy disclination states without fractional charge, establishing a distinct class of non-Hermitian defect states.
  • Because the circuits can be driven into a nonlinear regime with gain saturation, the same platform could develop into active topological devices such as defect lasers.

Reading between the lines

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

  • An implication left implicit is that the validity of the 1/2 mod 1 charge depends on the filling rule for occupied states being fixed before inspecting the measured spectrum; re-deriving the charge with a stated rule would turn the two numbers into a quantitative test.
  • A testable extension is to compute the same charge using only right eigenvectors or only left eigenvectors; agreement would show the fractional value is independent of the bi-orthogonal convention, while disagreement would reveal the degree to which the result is a choice of inner product.
  • Varying the gain-loss parameter γ across an exceptional point could show whether the disclination charge jumps when the bulk gap closes, which would directly tie the fractional charge to non-Hermitian band topology rather than to the specific lattice geometry.
  • The observation of localised disclination modes under monochromatic excitation suggests a route to a disclination-based topological laser, a direction the authors mention but do not demonstrate.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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 implementation of non-Hermitian electric-circuit lattices with C5 and C4 symmetry, in which on-site gain and loss are claimed to produce topological disclination states without any Hermitian topological structure. The central experimental evidence consists of complex admittance spectra showing five mid-gap disclination modes in a C5 topological configuration versus a pure gap in a trivial control, direct voltage-profile visualization of the localized modes, and a fractional disclination charge computed from biorthogonal eigenvectors, with reported total values of 0.57 (calculation) and 0.47 (experiment) for the topological phase and about 0.1 for the trivial phase. The paper also reports degenerate zero-energy disclination states in a C4-symmetric configuration. The mode spectra and localization data are presented in detail, but the fractional-charge claim depends on a filling rule and a definition of the biorthogonal charge that are not fully specified in the submitted text and that are partly deferred to supplementary notes not included in the preprint.

Significance. If the charge-fractionalization measurement is correct, this would be the first experimental observation of non-Hermitian disclination states induced solely by gain and loss, and it would extend the topological bulk-defect correspondence to non-Hermitian systems, with potential implications for active topological photonic devices. The manuscript's strengths are the clean topological/trivial control experiment, the good agreement between calculation and experiment for the complex spectra, the direct visualization of the disclination mode profiles, and the inclusion of a second C4-symmetric geometry. The paper also benefits from a concrete circuit platform with explicit component values. However, the headline fractional-charge result is not independently assessable from the manuscript as written: the occupied-state prescription is deferred to an absent supplementary note, Eq. (3) does not specify how the biorthogonal product is made real before taking the mod-1 operation, and the reported 0.57/0.47 values carry no uncertainty. Because the tested theoretical prediction (Ref.

major comments (4)
  1. [§Results, Eq. (3); main text p. 5] The set of occupied states used in Eq. (3) is not specified in the main text; the reader is referred to Supplementary Note 2, which is not included in the arXiv preprint. For a non-Hermitian circuit Laplacian with a complex spectrum, ordering by Re(j), by Im(j), or by a point-gap projection can yield different occupied sets and therefore different values of Q_u. The authors should state the filling rule explicitly in the main text or in an included supplement, and should report Q_u for alternative reasonable fillings to demonstrate that the 1/2 mod 1 result is not an artifact of a post hoc choice.
  2. [§Results, Eq. (3)] Equation (3) multiplies the right and left biorthogonal eigenvectors as V^R V^L with no complex conjugation, absolute value, or real-part instruction. Because the circuit Laplacian is complex-symmetric rather than Hermitian, these products are generically complex, and 'mod 1' of the unit-cell sum is not defined. The authors must specify whether Q_u is Re Σ V^R V^L, |Σ V^R V^L|, Σ |V^R V^L|, or another convention, and must justify that convention against the theoretical prediction in Ref. 40.
  3. [§Results, p. 5] The text states that the trapped disclination charge in each bulk unit cell clusters around 1/2 mod 1 and then reports 'total disclination charges of 0.57 and 0.47 for calculation and experiment', without defining how the total is aggregated over unit cells. If several unit cells each carry a charge near 1/2 mod 1, the meaning of a single total is ambiguous. The authors should define the aggregation region, report the per-cell values and their deviations from 1/2, and provide an uncertainty estimate that propagates from the measured admittance matrices to Q_u.
  4. [Methods and Code availability] No raw admittance matrices or eigenstates are deposited, and no data availability statement is provided. Since the fractional charge is computed numerically from the measured circuit Laplacian, readers cannot independently verify the 0.47 and 0.57 values or check that the chosen filling rule is robust. The measured J(ω0) matrices used in Eq. (3) should be made publicly available together with the analysis scripts.
minor comments (6)
  1. [References] References 20 and 41 are the same paper (Deng et al., Phys. Rev. Lett. 128, 174301 (2022)) and should be consolidated.
  2. [§Results, Eq. (2)] The 'appendant term' in Eq. (2) that is said to vanish at the resonance condition is not written out explicitly; the derivation should be shown in the main text or in Supplementary Note 1 rather than asserted.
  3. [Methods] The impedance transformation Z = Z₀(I + S)(I - S)⁻¹ is stated without specifying the port-normalization convention; the sign convention depends on the VNA's definition of S, so this should be clarified.
  4. [Fig. 3 caption] The caption describes the experimental data as a 'green dashed line', while the text refers to 'green dots'; please reconcile the description and add error bars if uncertainty information is available.
  5. [General notation] The term 'charge' is used for a spectral quantity derived from circuit eigenvectors; the authors should clarify how this relates to the physical charge on the circuit nodes (capacitors), since readers may otherwise expect a direct charge measurement.
  6. [§Results, p. 4] The phrase 'To obtain the less lossy spectra, making the admittance easier to measure over the noise' should be rephrased for clarity; presumably the gain compensates losses so that the relevant admittance features are not buried in noise.

Circularity Check

0 steps flagged · score 2.0 of 10

No by-construction circularity: the fractional charge is a measured eigenvector observable, not a fitted parameter; the same-team theory (ref. 40) and the omitted filling rule create verification gaps, not circular steps.

full rationale

Walked the claimed derivation chain: Eq. (1) defines the tight-binding model, Eq. (2) maps the circuit Laplacian to that model at the resonance frequency, and the spectra in Fig. 2 come from numerical diagonalization of J(omega0) and from independent VNA admittance measurements. The fractional charge in Eq. (3) is evaluated from measured or calculated biorthogonal eigenvectors and is not adjusted to 1/2: the reported totals are 0.57 (calculation) and 0.47 (experiment), so there is no fitted-input-called-prediction pattern. The gain/loss ratio gamma/t=1.3 is a preset component choice, not a parameter fit to the target charge. The only same-team element is ref. 40, a prior PRL by overlapping authors that predicts the effect and motivates the chosen nontrivial/trivial gain-loss patterns; that is a same-team theory-experiment comparison, not an equivalence of output to input by construction. Two verifiability issues are flagged and located but are not circularity: (i) the occupied-state rule for Eq. (3) is deferred to the absent Supplementary Note 2 ('The methods for identifying both the bulk gap ... and the occupied states are described in Supplementary Note 2', Results, p. 4), so the 0.47 value cannot be independently recomputed from the preprint; (ii) the biorthogonal product in Eq. (3) lacks explicit conjugation/real-part conventions, making 'mod 1' ambiguous for a complex-spectrum Laplacian. These are validation gaps, not reductions, and justify a modest score rather than a circularity finding.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central demonstration rests on the circuit-to-Hamiltonian mapping, the non-Hermitian bulk-defect correspondence, finite-size faithfulness, and linear-regime INIC operation. The only numerical input tuned for the topological phase is gamma/t=1.3; the core-site capacitance is an ad hoc compensation. No new entities are introduced.

free parameters (2)
  • gain/loss amplitude ratio gamma/t = 1.3
    Circuit resistors R0 and Ra are chosen so the effective non-Hermiticity is gamma/t=1.3. The topological disclination modes exist only in a range of this parameter (Fig. 3a scans gamma/t=0.5 to 2.5), so it is a hand-set input rather than a derived value.
  • core-site capacitance C0 = 4.4 nF
    The ten disclination core sites use doubled capacitance 'to maintain the Laplacian form.' This is an ad hoc compensation for the reduced connectivity at the core and affects the on-site energy at the defect.
assumptions (4)
  • domain assumption The circuit Laplacian J(omega_0) is proportional to the tight-binding Hamiltonian H with gain and loss, with the frequency-dependent appended term vanishing at the resonance frequency.
    Invoked in Eq. (2) and the following paragraph; assumes identical LC resonators, ideal INIC negative resistances, and negligible parasitic effects on a 280-site PCB.
  • domain assumption The non-Hermitian bulk-defect correspondence and the biorthogonal charge formula in Eq. (3) are valid for this open, gain/loss lattice.
    The charge calculation follows the authors' earlier PRL (ref. 40) and refs. 51-52; the main text does not derive the formula or define the occupied-state set.
  • domain assumption The finite open-boundary circuit lattice of 280 sites reproduces the infinite-lattice topological phase without significant finite-size mixing.
    Used throughout when comparing measured spectra and mode profiles to tight-binding calculations on the finite lattice.
  • domain assumption The INICs operate in the linear regime so that gain sites behave as fixed negative resistors.
    The Methods state that resistor values Ra and R0 are calibrated to keep the LM6171 op-amps in their linear gain regime; if saturation or nonlinearity occurs, the measured Laplacian does not correspond to the model Hamiltonian.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Observation of non-Hermitian topological disclination states and charge fractionalization." pith.science (2026). https://pith.science/paper/B3GIAGD2

@misc{pith2026250204922,
  author       = {Pith},
  title        = {Pith review of: Observation of non-Hermitian topological disclination states and charge fractionalization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B3GIAGD2}},
  note         = {Machine review of arXiv:2502.04922}
}
read the original abstract

There has been significant interest in exploring topological disclination states, which effectively probe the band topology of the host material beyond the conventional bulk-edge correspondence. While most studies in this area have primarily focused on Hermitian systems, recent theoretical work predicts that non-Hermiticity can drive topological phase transitions and host topological disclination states associated with fractional charge. However, no experimental observations have been reported to date. Here, we report the first experimental observation of topological disclination states in electric circuits, induced solely by gain and loss. Through admittance matrix measurements and eigenstate analysis, we confirm their emergence and compute the corresponding fractional charge. Moreover, the disclination mode profile and localization effect can be directly visualized via monochromatic field excitation. Additionally, we demonstrate the emergence of degenerate zero-energy topological disclination states, devoid of fractional charge, in distinct non-Hermitian geometries. Our findings open the possibility of non-Hermiticity-induced fractional charges in two-dimensional non-Hermitian lattices, which may pave the way for advancements in active topological photonic devices.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

52 extracted references · 47 canonical work pages

  1. [1]

    Zhu, S. et al. Controlling water waves with artificial structures. Nat. Rev. Phys. 6, 231–245 (2024)

    work page 2024

  2. [2]

    Lin, Z.-K. et al. Topological phenomena at defects in acoustic, photonic and solid-state lattices. Nat. Rev. Phys. 5, 483–495 (2023)

    work page 2023

  3. [3]

    S., Neupert, T., Andrei Bernevig, B

    Schindler, F., Tsirkin, S. S., Neupert, T., Andrei Bernevig, B. & Wieder, B. J. Topological zero -dimensional defect and flux states in three-dimensional insulators. Nat. Commun. 13, 5791 (2022)

    work page 2022

  4. [4]

    Hasan, M. Z. & Kane, C. L. Colloquium : Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010)

    2010

  5. [5]

    Kosterlitz, J. M. Nobel Lecture: Topological defects and phase transitions. Rev. Mod. Phys. 89, 040501 (2017)

    work page 2017

  6. [6]

    Wei, Y . et al. The nature of strength enhancement and weakening by pentagon –heptagon defects in graphene. Nat. Mater. 11, 759–763 (2012)

    work page 2012

  7. [7]

    Xie, B. et al. Bulk-local-density-of-state correspondence in topological insulators. Nat. Commun. 14, 7347 (2023)

    work page 2023

  8. [8]

    Ren, B. et al. Observation of nonlinear disclination states. Light Sci. Appl. 12, 194 (2023)

    work page 2023

Show all 52 references
  1. [9]

    Ye, L. et al. Topological dislocation modes in three-dimensional acoustic topological insulators. Nat. Commun. 13, 508 (2022)

    2022

  2. [10]

    Teo, J. C. Y . & Hughes, T. L. Existence of Majorana- Fermion Bound States on Disclinations and the Classification of Topological Crystalline Superconductors in Two Dimensions. Phys. Rev. Lett. 111, 047006 (2013)

    2013

  3. [11]

    & Vishwanath, A

    Ran, Y ., Zhang, Y . & Vishwanath, A. One-dimensional topologically protected modes in topological insulators with lattice dislocations. Nat. Phys. 5, 298–303 (2009)

    2009

  4. [12]

    Li, F.-F. et al. Topological light-trapping on a dislocation. Nat. Commun. 9, 2462 (2018)

    2018

  5. [13]

    Liu, Y . et al. Bulk–disclination correspondence in topological crystalline insulators. Nature 589, 381–385 (2021)

    2021

  6. [14]

    W., Li, T., Jiang, W., Hughes, T

    Peterson, C. W., Li, T., Jiang, W., Hughes, T. L. & Bahl, G. Trapped fractional charges at bulk defects in topological insulators. Nature 589, 376–380 (2021)

    2021

  7. [15]

    -S., Kim, H

    Hwang, M. -S., Kim, H. -R. & Park, H. -G. Topological manipulation for advancing nanophotonics. Npj Nanophotonics 1, 32 (2024)

    2024

  8. [16]

    Li, T., Zhu, P., Benalcazar, W. A. & Hughes, T. L. Fractional disclination charge in two -dimensional C n - symmetric topological crystalline insulators. Phys. Rev. B 101, 115115 (2020)

    2020

  9. [17]

    W., Li, T., Benalcazar, W

    Peterson, C. W., Li, T., Benalcazar, W. A., Hughes, T. L. & Bahl, G. A fractional corner anomaly reveals higher- order topology. Science 368, 1114–1118 (2020)

    2020

  10. [18]

    A., Li, T

    Benalcazar, W. A., Li, T. & Hughes, T. L. Quantization of fractional corner charge in C n - symmetric higher- order topological crystalline insulators. Phys. Rev. B 99, 245151 (2019)

    2019

  11. [19]

    Liu, M. -Y. et al. Measurement of fractional charge in elastic plates with disclinations. Phys. Rev. Appl. 22, 014025 (2024)

    2024

  12. [21]

    & Chong, Y

    Wang, Q. & Chong, Y . D. Non-Hermitian photonic lattices: tutorial. J. Opt. Soc. Am. B 40, 1443 (2023)

    2023

  13. [22]

    J., Budich, J

    Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021)

    2021

  14. [23]

    Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics based on parity–time symmetry. Nat. Photonics 11, 752–762 (2017)

    2017

  15. [24]

    Shen, H., Zhen, B. & Fu, L. Topological Band Theory for Non- Hermitian Hamiltonians. Phys. Rev. Lett. 120, 146402 (2018)

    2018

  16. [25]

    Gong, Z. et al. Topological Phases of Non-Hermitian Systems. Phys. Rev. X 8, 031079 (2018). 11

    2018

  17. [26]

    & Sato, M

    Kawabata, K., Shiozaki, K., Ueda, M. & Sato, M. Symmetry and Topology in Non -Hermitian Physics. Phys. Rev. X 9, 041015 (2019)

    2019

  18. [27]

    St-Jean, P. et al. Lasing in topological edge states of a one- dimensional lattice. Nat. Photonics 11, 651–656 (2017)

    2017

  19. [28]

    Bandres, M. A. et al. Topological insulator laser: Experiments. Science 359, eaar4005 (2018)

    2018

  20. [29]

    Parto, M. et al. Edge-Mode Lasing in 1D Topological Active Arrays. Phys. Rev. Lett. 120, 113901 (2018)

    2018

  21. [30]

    Lee, T. E. Anomalous Edge State in a Non-Hermitian Lattice. Phys. Rev. Lett. 116, 133903 (2016)

    2016

  22. [31]

    & Ueda, M

    Kawabata, K., Shiozaki, K. & Ueda, M. Anomalous helical edge states in a non-Hermitian Chern insulator. Phys. Rev. B 98, 165148 (2018)

    2018

  23. [32]

    Y ., Huang, C., Chong, Y

    Leykam, D., Bliokh, K. Y ., Huang, C., Chong, Y . D. & Nori, F. Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems. Phys. Rev. Lett. 118, 040401 (2017)

    2017

  24. [33]

    Weimann, S. et al. Topologically protected bound states in photonic parity–time-symmetric crystals. Nat. Mater. 16, 433–438 (2017)

    2017

  25. [34]

    & Szameit, A

    Ornigotti, M. & Szameit, A. Quasi $ \mathcal{P}\mathcal{T}$-symmetry in passive photonic lattices. J. Opt. 16, 065501 (2014)

    2014

  26. [35]

    & Notomi, M

    Takata, K. & Notomi, M. Photonic Topological Insulating Phase Induced Solely by Gain and Loss. Phys. Rev. Lett. 121, 213902 (2018)

    2018

  27. [36]

    Gao, H. et al. Observation of topological edge states induced solely by non -Hermiticity in an acoustic crystal. Phys. Rev. B 101, 180303 (2020)

    2020

  28. [37]

    Liu, S. et al. Gain- and Loss-Induced Topological Insulating Phase in a Non-Hermitian Electrical Circuit. Phys. Rev. Appl. 13, 014047 (2020)

    2020

  29. [38]

    & Zhang, C

    Luo, X.-W. & Zhang, C. Higher-Order Topological Corner States Induced by Gain and Loss. Phys. Rev. Lett. 123, 073601 (2019)

    2019

  30. [39]

    Gao, H. et al. Non-Hermitian route to higher -order topology in an acoustic crystal. Nat. Commun. 12, 1888 (2021)

    2021

  31. [40]

    Banerjee, R. et al. Topological Disclination States and Charge Fractionalization in a Non -Hermitian Lattice. Phys. Rev. Lett. 133, 233804 (2024)

    2024

  32. [41]

    Deng, Y . et al. Observation of Degenerate Zero-Energy Topological States at Disclinations in an Acoustic Lattice. Phys. Rev. Lett. 128, 174301 (2022)

    2022

  33. [42]

    Jin, F., Mandal, S., Wang, X., Zhang, B. & Su, R. Perovskite topological exciton-polariton disclination laser at room temperature

  34. [43]

    Zhang, W. et al. Experimental Observation of Higher-Order Topological Anderson Insulators. Phys. Rev. Lett. 126, 146802 (2021)

    2021

  35. [44]

    Helbig, T. et al. Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits. Nat. Phys. 16, 747–750 (2020)

    2020

  36. [45]

    & Franz, M

    Zhang, X.-X. & Franz, M. Non-Hermitian Exceptional Landau Quantization in Electric Circuits. Phys. Rev. Lett. 124, 046401 (2020)

    2020

  37. [46]

    Liu, S. et al. Non-Hermitian Skin Effect in a Non -Hermitian Electrical Circuit. Research 2021, 2021/5608038 (2021)

    2021

  38. [47]

    Zhang, X. et al. Observation of continuum Landau modes in non-Hermitian electric circuits. Nat. Commun. 15, 1798 (2024)

    2024

  39. [48]

    Zou, D. et al. Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits. Nat. Commun. 12, 7201 (2021)

    2021

  40. [49]

    Lee, C. H. et al. Topolectrical Circuits. Commun. Phys. 1, 39 (2018)

    2018

  41. [50]

    Stegmaier, A. et al. Topological Defect Engineering and P T Symmetry in Non -Hermitian Electrical Circuits. 12 Phys. Rev. Lett. 126, 215302 (2021)

    2021

  42. [51]

    Wu, D. et al. Effective impurity behavior emergent from non-Hermitian proximity effect. Commun. Phys. 6, 160 (2023)

    2023

  43. [52]

    Non -Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization

    Ezawa, M. Non -Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization. Phys. Rev. B 99, 201411 (2019)

    2019

  44. [53]

    H., Greiter, M

    Hofmann, T., Helbig, T., Lee, C. H., Greiter, M. & Thomale, R. Chiral voltage propagation in a self -calibrated topolectrical Chern circuit. Phys. Rev. Lett. 122, 247702 (2019). 13 Figures Fig. 1 | The photograph shows the fabricated samples and corresponding NH lat tices. a I...

    2019

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.