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Observation of non-local impedance response in a passive electrical circuit
by Xiao Zhang, Boxue Zhang, Weihong Zhao, Ching Hua Lee
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Xiao Zhang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202305_00013v1 (pdf) |
| Date submitted: | May 10, 2023, 8:12 a.m. |
| Submitted by: | Xiao Zhang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Experimental, Computational |
Abstract
In media with only short-ranged couplings and interactions, it is natural to assume that physical responses must be local. Yet, we discover that this is not necessarily true, even in a system as commonplace as an electric circuit array. This work reports the experimental observation of non-local impedance response in a designed circuit network consisting exclusively of passive elements such as resistors, inductors and capacitors (RLC). Measurements reveal that the removal of boundary connections dramatically affects the two-point impedance between certain distant nodes, even in the absence of any amplification mechanism for the voltage signal. This non-local impedance response is distinct from the reciprocal non-Hermitian skin effect, affecting only selected pairs of nodes even as the circuit Laplacian exhibits universally broken spectral bulk-boundary correspondence. Surprisingly, not only are component parasitic resistances unable to erode the non-local response, but they in fact give rise to novel loss-induced topological modes at sufficiently large system sizes, constituting a new manifestation of the critical non-Hermitian skin effect. Our findings chart a new route towards attaining non-local responses in photonic or electrical metamaterials without involving non-linear, non-local, active or amplificative elements.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2023-8-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202305_00013v1, delivered 2023-08-04, doi: 10.21468/SciPost.Report.7606
Strengths
Weaknesses
Report
I understand that the authors have fabricated an $N=8$ device and performed complementary simulations for different, in particular larger values of $N$. However, it is not always clear from the text which results are experimental findings and which ones obtained by simulation. I believe that this point needs clarification.
On another note, the manuscript seems to have been prepared for a different target journal, and I think that it would be useful if the authors could reformat it according to the SciPost Physics guidelines, see https://scipost.org/SciPostPhys/authoring. In particular, the "Methods" sections should be either integrated into the main text (no length limitation) or moved to Appendices.
I have one question: the values $C=1\,{\rm nF}$, $L=1\,{\rm mH}$, $R=5\,{\rm k \Omega}$, $r=50\,{\rm k\Omega}$ are nominal values (?). Have the authors verified if their components agree with the specifications? In view of parasitic resistances on the order of 0.2 to 1.7%, one might imagine deviations from nominal values on the same order of magnitude.
Further more specific items are listed as "Requested changes".
Requested changes
1- State clearly which results are experimental ones and which one come from simulations. A comparison between the two may also be appropriate. 2- Reformat the manuscript according to SciPost Physics guidelines, https://scipost.org/SciPostPhys/authoring. 3- Clarify if the values for $C$, $L$, $R$, and $r$ are nominal ones, or if the components actually have these values. 4- First paragraph of the Introduction: The list of 33 references [6-38] is not very helpful to the reader. The authors should either break this down into smaller units with appropriate comments, or reduce the list to really relevant references. 5- At the bottom left of page 2, the authors say that the Laplacian $J$ relates ${\bf V}$ to ${\bf I}$, but then they write the opposite equation ${\bf I} = J{\bf V}$. As long as $J$ is invertible, the two are of course equivalent, but presentation should nevertheless be coherent. 6- Format Eq. (4) properly, i.e., it should start with a new paragraph, not in line with the text. 7- Some figures use fonts that are too small. This applies in particular to Figs. 2, 5, and 7, and their legends. 8- On page 4, there is a discussion of "parasitic" resistance, but this is not properly explained before page 6 (one point where the manuscript would benefit from restructuring). 9- Units are missing after the $10^6$ below Eq. (9) (${\rm Hz}$?). 10- Caption of Fig. 6: the definition of $t$ is hidden somewhere in the text. For clarity, I recommend to recall it here. 11- Update references, specifically: [29] Science Bulletin 67, 1865-1873 (2022) [30] Phys. Rev. B 106, 075158 (2022) [34] Phys. Rev. A 107, L010202 (2023) [35] Phys. Rev. B 107, L220301 (2023) [61] Phys. Rev. Research 5, L012041 (2023) [70] Nature Photonics, 120–125 (2023) ... and add DOIs.
Report #1 by Anonymous (Referee 1) on 2023-7-20 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202305_00013v1, delivered 2023-07-20, doi: 10.21468/SciPost.Report.7539
Strengths
- This research is on a topic which is very important and is being very actively studied in recent years.
- The theoretical predictions are corroborated by real experiments.
- This work is nicely put into the context of quite extensive literature and variety of results from different research groups.
Weaknesses
- I found that the interpretation of the main result, given in the subsection "Size-dependent topological phase crossover..." lacks physical clarity and rigor. The feature they found apparently is not a continuous /discontinuous transition, or disorder line. It is a finite-size effect, and I don't think that one can call it "a crossover".
Report
I have however one concern regarding the "topological phase crossover" (or "critical non-Hermitian skin effect"). The nature of this phenomenon needs to be clarified and explained in a self-contained form in the manuscript. As discussed in Ref. 55, it can be related to the behavior of energy zeros on the complex plane of wave numbers $z=e^{ik}$. Is it a disorder line of the first or second kind? (According to the definitions of Stephenson, PRB 1, 4405 (1970)). If it is a finite-size effect, where are the parametric boundaries for it to disappear and how it is related to the positions of zeros $z$ on the complex plane?
I think this issue needs to be addressed before the manuscript can be recommended for publication.
Requested changes
- Subsection "Size-dependent topological phase crossover..." needs to be revised as discussed above.
- Consequently, some related comments on the physical nature of the phenomenon in question would improve the Introduction and Conclusion.