{"id":"e55f9bab-71ae-4e49-af5c-89738f4a3bae","arxiv_id":"1908.02759","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A reciprocal non-Hermitian 2D lattice shows skin-mode localization on opposite edges for opposite momenta, demonstrated experimentally in a passive RLC circuit.","lead":"This paper introduces a reciprocal skin effect: in a non-Hermitian but reciprocal two-dimensional system, modes with opposite momentum localize on opposite edges. The authors demonstrate it in a passive RLC circuit, expanding skin effects to platforms without non-reciprocal active elements.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The experimental demonstration rests on LTSPICE calibration of the resonance frequency and parasitics; independent component verification is missing, so the observed eigenmode localization may not be the reciprocal skin effect of Eq. (2).","rationale":"The reader's weakest assumption identifies the same load-bearing point: the experiment is only as good as the unvalidated mapping from the physical circuit to the tight-binding model H. I agree because the theoretical part of the paper is self-contained and the reciprocal skin effect follows from standard non-Bloch arguments, so the central scientific novelty is not in doubt from the theory alone. What would falsify the empirical claim is a demonstration that the observed eigenmode localization is an artifact of calibration, component tolerances, or off-resonance effects. The paper gives substantial supporting evidence that the circuit behaves as intended: the Hermitian pi-flux bands show Dirac cones, the non-Hermitian version shows branch cuts and exceptional points with the expected half-integer phase winding, and the measured spectra are consistent with LTSPICE simulations. These are real successes and should be credited. However, the specific claim that all eigenstates near ky = pi/2 are right-localized and near ky = 3pi/2 are left-localized depends on the eigenvector data extracted from the measured Green's function. That data is compared to a simulation whose parasitic model is calibrated rather than independently verified. A concrete test using measured component values would settle the concern. I also note the internal sign inconsistency between the main text and Appendix C about which ky sector localizes on which edge; while it does not affect the opposite-edge conclusion, it adds modest uncertainty to the experimental right/left assignment and should be clarified. Overall, the reader's CONDITIONAL verdict is appropriate, and no verdict change is needed from this stress-test pass.","tokens_in":14780,"tokens_out":11487,"duration_ms":144025,"concrete_test":"Reconstruct the full real-space Laplacian from independently measured component values, including the actual capacitances, resistances, inductor DC resistances and parasitics on the board, without any LTSPICE fitting, and recompute the eigenvector IPRs at ky = π/2 and 3π/2 in the 10x20 strip. If this parameter-free model does not reproduce both the right/left localization assignment and the fraction of IPR-identified localized states shown in Fig. 2(d), the experimental realization of Eq. (2) is not established. A minimal additional check is to remeasure at the nominal 1/sqrt(LC) frequency and at f0 ± 1 kHz to test whether the localization pattern is stable, as Eq. (C8) predicts for a broad ky range.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The theoretical construction (Eq. (2), Appendix C) is internally consistent, and the reciprocal skin effect follows from the non-Bloch analysis leading to Eq. (C8). The load-bearing step is the experimental mapping from the measured passive RLC network to that Hamiltonian. In Appendix C, the intended identification H = [J(ω0) - ir1]/(iω0C) requires that at the drive frequency the diagonal terms from Lg cancel the sublattice asymmetry (Eq. C3), and that the resistor term is exactly the off-diagonal -ir e^{±iky} term (Eqs. C4 and C6). In Appendix D, the resonance frequency f0 = 87.25 kHz is identified by matching features of frequency sweeps to an LTSPICE simulation that includes parasitic resistances, rather than by independent measurement of all components; capacitors and resistors (1% tolerance) are not characterized, and only inductors are pre-characterized. If the LTSPICE parasitic model or the assumed Lg value is inaccurate, the effective Hamiltonian realized at 87.25 kHz contains unknown diagonal (σz) and hopping renormalizations. The observed IPR coloring could then reflect disorder or an unintended off-resonance Hamiltonian rather than the reciprocal skin effect of Eq. (2). Since no raw data or code are provided and the eigenvector data are shown only as colored points, this calibration dependence is the least secured link in the central experimental claim. The internal sign inconsistency between the main text (right localization for ky in (0,π)) and Appendix C (left localization) is a separate convention issue and does not change the opposite-edge conclusion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a 'reciprocal skin effect' in non-Hermitian but reciprocal two-dimensional systems. Starting from the π-flux tight-binding model on a square lattice, the authors add a complex diagonal hopping term that breaks Hermiticity while preserving reciprocity, and show that for open boundary conditions along x, each fixed transverse momentum ky behaves as an effectively non-reciprocal one-dimensional model exhibiting skin localization. The localization length is derived analytically in Eq. (C8), and opposite ky values localize to opposite edges, with ky=0,π delocalized. The paper reports an experimental realization in a passive RLC circuit, using Green's-function reconstruction to extract the circuit Laplacian spectrum and eigenstates, and claims observation of exceptional points and of the reciprocal skin effect through inverse participation ratio (IPR) coloring of eigenstates. The authors also present a non-unitary transformation to an SSH-type model and propose a polarization-detection application. The theoretical derivation is coherent, while the experimental demonstration and the stated direction of localization contain issues that need to be resolved.","tokens_in":15087,"tokens_out":7752,"duration_ms":83522,"significance":"If the experimental mapping is sound, this is a conceptually important advance: it shows that extensive skin localization does not require non-reciprocal couplings, but can arise in reciprocal systems through momentum-resolved effective non-reciprocity in two dimensions. The analytic localization length in Eq. (C8) is a clean, checkable prediction, and the passive-circuit platform is a practical and accessible implementation. The measured IPR-based observation of opposite localization at opposite ky is suggestive and, if reproduced with error bars and independent component calibration, would be a valuable demonstration. The paper also provides a useful derivation of the circuit-Laplacian-to-Hamiltonian mapping and an SSH-type interpretation of the non-Hermitian model.","major_comments":[{"comment":"The direction of the predicted skin localization is stated inconsistently. Section II says 'For ky∈(0,π), all OBC bulk modes localize at the right edge, while the localization switches to the left edge for ky∈(π,2π)', and Fig. 2d colors states near ky=π/2 as right-localized and near ky=3π/2 as left-localized. However, the caption of Fig. 1c assigns ky=π/2 to the left and ky=3π/2 to the right, and Appendix C, in the text following Eq. (C8), concludes 'This leads to left edge localized modes, if ky∈(0,π) and to right edge localization, if ky∈(π,2π)'. With ψx∼e^{-x/ξ}, a positive ξ (ky∈(0,π)) corresponds to decay toward larger x and hence left-edge localization, so the Appendix C convention is the one consistent with the derivation. The authors must fix a single sign convention and state explicitly how the colors in Fig. 2d are assigned; this is load-bearing for the experimental claim and for the directional-detector application in Fig. 1c and Appendix F.","section":"II (Theory), Fig. 1c, Fig. 2d, and Appendix C 3"},{"comment":"The experimental identification of the realized Hamiltonian is under-determined. Appendix D states that the resonance frequency f0=87.25 kHz was found by matching features of a frequency sweep to an LTSPICE simulation that includes parasitic resistances, and that 'capacitors and resistors ... were therefore not characterized', with only inductors pre-characterized. The mapping H=[J(ω0)-ir1]/(iω0C) requires the diagonal terms to cancel at f0 (Eq. C3) and the resistor term to realize exactly the -ir e^{±iky} off-diagonal contribution (Eqs. C4 and C6). Any error in the parasitic model or in component values introduces unknown diagonal (σz) and hopping renormalizations. Because no error bars, raw Green's-function data, or independent component measurements are presented, it is not possible to verify that the measured eigenstates at 87.25 kHz are eigenstates of Eq. (2) rather than of a nearby off-resonance Hamiltonian. This is the least secured link of the central experimental claim.","section":"Appendix D and Fig. 2d"},{"comment":"The quantitative prediction of the reciprocal skin effect, the localization length ξ(ky) in Eq. (C8), is not compared with the experimental eigenstates. Fig. 2d reports only a binary coloring based on IPR; no spatial profiles, fitted localization lengths, or comparison to the theoretical ξ(ky) curve are shown. Since the paper emphasizes 'exponentially localized with localization length ξ', a profile fit or at least a scatter of IPR versus the predicted ξ would substantiate the claim and would help discriminate the skin effect from generic edge weighting or disorder. The IPR threshold used for the color assignment is also not defined. This comparison should be added, or the experimental claim should be softened to a qualitative statement.","section":"Eq. (C8), Fig. 2d"}],"minor_comments":[{"comment":"In §III, 'contstraints' should be 'constraints' in the phrase 'local connectivity contstraints'.","section":"III"},{"comment":"In Appendix D, 'LCR Brige' should be 'LCR Bridge'.","section":"Appendix D"},{"comment":"The sentence 'We observe, for PBC, a clear from slices at constant ky with a single circle and two circles' is missing a word; it should read 'a clear change from slices' or similar.","section":"Appendix E"},{"comment":"The precise definition of the IPR used and the threshold separating red and blue points in Fig. 2d are not given; please specify them.","section":"Fig. 2d"},{"comment":"The manuscript does not state whether raw measurement data and the LTSPICE netlist will be made available; a data availability statement would improve reproducibility.","section":"Appendix D"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the concept is timely. The main risk is the reliance on LTSPICE calibration for the central experimental claim and the unresolved left/right sign inconsistency. I would be willing to accept a revision that fixes the sign convention, adds quantitative localization data with error bars or raw data, and provides independent verification of at least a subset of components. The heavy self-citation of prior topolectrical-circuit work is not, by itself, disqualifying."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe one thing you should know: this paper's central theoretical idea—a reciprocal 2D non-Hermitian model whose momentum slices carry opposite skin modes—is new and the derivation is sound. The passive RLC circuit realization is a nice step beyond active non-reciprocal setups. But the experimental evidence is not as secure as the theory: the circuit-to-model mapping depends on a resonance frequency calibrated against LTSPICE, not on independent component measurement, and no raw data or error bars are given.\n\nWhat is genuinely new: prior reciprocal 1D skin effects required extra symmetries (mirror, PT). Here the effect comes purely from dimensional enhancement—each ky slice of a reciprocal model breaks reciprocity locally, so all modes at a given ky pile on one edge, while reciprocity pairs ky with -ky to the opposite edge. The localization length formula (C8) is clean and the PBC/OBC spectral comparison is compelling. The measured IPR coloring in Fig. 2d does show opposite localization around ky=π/2 and 3π/2 as predicted. The exceptional-point phase winding is a nice extra confirmation.\n\nSoft spots, in order. (1) The experiment's load-bearing step is the identification of the operating frequency f0 = 87.25 kHz, found by matching frequency sweeps to LTSPICE simulations with parasitic resistances. Capacitors and resistors are not characterized (1% tolerance); only inductors are. If the parasitic model or assumed Lg values are off, the effective Hamiltonian at that frequency contains unknown diagonal and hopping renormalizations, and the observed localization could be an artifact of an off-resonance Hamiltonian or disorder. This is not fatal—the theory is solid and the qualitative agreement is good—but the experimental demonstration is not fully closed. (2) No raw data, no error bars on spectra or IPR. That is a reproducibility issue. (3) Minor sign inconsistency: the main text says ky in (0,π) right-localized; Appendix C says left-localized. Does not change the opposite-edge conclusion but should be fixed. (4) The direction/polarization detector application is only simulated; fine as speculation, but label it as such.\n\nThe self-citation pattern is heavy but understandable given that the circuit platform and skin-effect framework come from the same groups; not a fatal flaw.\n\nVerdict: this deserves a serious referee. The theoretical result is worth publishing even if the experiment is treated as a proof-of-principle. I'd bring it to a reading group and would cite the theoretical construction. Recommend major revision: add error bars and raw data, clarify the calibration, fix the sign convention, soften the application claim.","headline":"A genuinely new reciprocal 2D skin effect with a solid theoretical core, but the circuit experiment is only as good as the LTSPICE calibration and needs more transparency.","tokens_in":15681,"tokens_out":3219,"would_cite":true,"duration_ms":31355,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A reciprocal, non-Hermitian two-dimensional lattice can push eigenmodes of opposite momenta to opposite edges, and a passive resistor–inductor–capacitor circuit realizes it.","keywords":["reciprocal skin effect","non-Hermitian topology","skin effect","topolectrical circuits","exceptional points","pi-flux model","bulk-boundary correspondence","passive RLC circuit"],"falsifier":"Drive the circuit from two bulk sites with a $+\\pi/2$ phase difference and separately with a $-\\pi/2$ phase difference, following the protocol of Appendix F: if the $+\\pi/2$ drive does not build up a voltage concentrated at the right edge and the $-\\pi/2$ drive at the left edge, the reciprocal skin effect is not present in the realized circuit. A second check is to sweep the drive frequency away from the calibrated value and confirm that the localization direction and edge accumulation follow the sign of $\\sin(k_y)$ rather than reflecting a parasitic resonance.","tokens_in":14604,"feed_emoji":"⚡","tokens_out":11227,"duration_ms":109959,"temperature":0.7,"pith_summary":"The paper introduces and experimentally demonstrates the reciprocal skin effect: in a non-Hermitian but reciprocal two-dimensional system, eigenmodes with opposite momentum along the boundary become exponentially localized on opposite transverse edges. A system is non-Hermitian when it exchanges energy with its environment, and reciprocal when it responds the same way upon interchange of input and response; earlier skin effects were thought to require non-reciprocity, typically implemented by direction-dependent hoppings or active amplifiers. The paper shows that a reciprocal lattice with a lossy, complex-valued coupling can instead be sliced by momentum, so that each fixed-momentum slice behaves like a non-reciprocal one-dimensional chain, with opposite momenta pushed to opposite edges. The authors build a passive circuit of capacitors, inductors, and resistors whose circuit Laplacian reproduces the model, and measure eigenstates that localize right at $k_y\\approx\\pi/2$ and left at $k_y\\approx 3\\pi/2$. If correct, the finding widens the platforms for skin-mode localization and points toward passive directional and polarization detectors for electromagnetic waves.","feed_headline":"Opposite momenta land on opposite edges in a passive circuit","feed_subtitle":"A lossy but reciprocal lattice splits modes by momentum, sending each to a different edge—no amplifiers needed.","key_machinery":"The carrying object is the momentum-dependent non-Hermitian coupling term $-ir\\begin{pmatrix}0&e^{ik_y}\\\\e^{-ik_y}&0\\end{pmatrix}$, a reciprocal off-diagonal hopping in which the forward and reverse amplitudes are equal rather than conjugate. Fixing $k_y$ as a parameter converts the two-dimensional model into an effectively one-dimensional chain with an induced non-reciprocal hopping proportional to $r\\sin(k_y)$; because $\\sin(k_y)$ is odd, opposite momenta see opposite effective non-reciprocity and therefore accumulate on opposite edges, while the translational symmetry of the full two-dimensional system prevents the reciprocal partners from hybridizing. In the circuit, the same term is produced by a resistor across the diagonal of each plaquette, whose admittance contribution enters the circuit Laplacian as the same matrix; the circuit Laplacian $J(\\omega_0)$ is the measured object whose eigenvalues and eigenstates represent the model Hamiltonian.","core_discovery":"The central claim is that non-Hermiticity alone, without non-reciprocity, can produce extensive skin-mode localization in two dimensions. Starting from the Hermitian $\\pi$-flux model on a square lattice, the paper adds a single reciprocal, non-Hermitian diagonal hopping term, giving $H(k_x,k_y) = H_\\pi(k_x,k_y) - i r\\begin{pmatrix}0&e^{ik_y}\\\\e^{-ik_y}&0\\end{pmatrix}$. The same complex amplitude $ir$ multiplies a hop and its reverse, so the model satisfies $H(k_x,k_y)^T = H(-k_x,-k_y)$, yet the eigenvalues become complex and each Dirac point splits into a pair of exceptional points, degeneracies where two eigenstates coalesce. With open boundaries in $x$ and periodic boundaries in $y$, treating $k_y$ as a parameter turns the model into an effective one-dimensional non-reciprocal chain: for $k_y\\in(0,\\pi)$ all bulk modes localize on the right edge, for $k_y\\in(\\pi,2\\pi)$ they localize on the left edge, and at $k_y=0,\\pi$ they are delocalized; the localization is strongest near the former Dirac points at $k_y=\\pi/2$ and $3\\pi/2$, and the localization length vanishes at $r=1$. The experiment realizes this in a $10\\times20$ unit-cell circuit: a resistor connecting sublattice nodes supplies the lossy reciprocal coupling, and measured Green's functions give eigenstates whose inverse participation ratio, a measure of localization, shows the predicted momentum-dependent edge accumulation.","pith_inferences":["The momentum-slice picture suggests a three-dimensional extension: with open boundaries in two directions, different patches of the surface Brillouin zone should localize modes on different edges or hinges, forming higher-dimensional reciprocal skin accumulations that the paper does not explicitly formulate.","The Appendix F response calculation implies a concrete device test: a two-port input with a $\\pm\\pi/2$ phase difference should act as a passive switch that routes a signal to one edge or the other; measuring output impedance versus input phase would quantify bandwidth and efficiency.","Because only reciprocal loss is required, a photonic lattice with absorption or an acoustic lattice with damping should reproduce the effect as long as the internal degrees of freedom carry the complex phase, making the phenomenon platform-independent."],"forward_implications":["The reciprocal skin effect should appear in any non-Hermitian reciprocal two-dimensional lattice whose couplings connect different internal degrees of freedom, because the momentum-slice argument depends only on the sign of $\\sin(k_y)$, not on the electrical implementation.","The breakdown of bulk-boundary correspondence is now observable without active or non-reciprocal elements: a passive RLC network suffices, so the effect transfers to optical, acoustic, and mechanical metamaterials built from lossy reciprocal components.","Because localization direction is fixed by the sign of $\\sin(k_y)$, an incident wave with a definite propagation direction and polarization drives a voltage buildup at a selectable edge, making the same circuit a passive direction or polarization detector for electromagnetic waves.","Tuning the resistance so that $r=1$ makes the localization length vanish at $k_y=\\pi/2$ and $3\\pi/2$, giving infinitely localized skin modes there while Su-Schrieffer-Heeger-type one-dimensional edge modes coexist in the gapped bulk spectrum."],"supporting_citations":[{"why":"Defines the non-Hermitian skin effect and the non-Bloch band theory that the momentum-slice analysis relies on.","marker":"[16]"},{"why":"Documents the failure of bulk-boundary correspondence in non-Hermitian models, the phenomenon the reciprocal skin effect instantiates.","marker":"[17]"},{"why":"Supplies the biorthogonal bulk-boundary correspondence used to interpret open-boundary spectra.","marker":"[18]"},{"why":"Provides the anatomy of skin modes and the anomalous-localization criterion the paper extends to momentum slices.","marker":"[19]"},{"why":"Defines the symmetry-protected Z2 skin effect whose distinction from the reciprocal skin effect is a central contrast.","marker":"[22]"},{"why":"Introduces topolectrical circuits and the circuit Laplacian formalism through which the tight-binding model is realized.","marker":"[32]"},{"why":"Supplies the Green's-function measurement protocol used to extract the Laplacian's eigenvalues and eigenstates.","marker":"[39]"},{"why":"Provides the prototypical non-reciprocal one-dimensional chain whose reciprocity-reversed pair frames the comparison with a doubled one-dimensional skin effect.","marker":"[41]"},{"why":"Represents the prior experimental realization of the non-reciprocal skin effect in circuits against which the passive reciprocal realization is positioned.","marker":"[44]"}],"fun_headline_variants":["Reciprocal skin effect: lossy but reciprocal lattice splits modes by momentum","Non-reciprocity not needed: skin effect from loss alone in 2D circuit","Passive circuit shows momentum-dependent edge localization without non-reciprocity","Reciprocal skin effect realized in a topolectrical circuit","Loss but no non-reciprocity: 2D skin effect in passive circuit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The experimental demonstration assumes that the assembled RLC network at the chosen drive frequency realizes the intended tight-binding Hamiltonian, including cancellation of the sublattice diagonal terms by grounding inductors and the exact mapping of the resistor term to $-ir\\begin{pmatrix}0&e^{ik_y}\\\\e^{-ik_y}&0\\end{pmatrix}$; parasitic effects and component tolerances are fixed by circuit simulation rather than by independently measuring the realized Hamiltonian, so a calibration error would change which Hamiltonian's eigenstates are observed.","fun_headline_variants_meta":{"raw":{"variants":["Reciprocal skin effect: lossy but reciprocal lattice splits modes by momentum","Non-reciprocity not needed: skin effect from loss alone in 2D circuit","Passive circuit shows momentum-dependent edge localization without non-reciprocity","Reciprocal skin effect realized in a topolectrical circuit","Loss but no non-reciprocity: 2D skin effect in passive circuit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000827,"raw_usage":{"total_tokens":3652,"prompt_tokens":1018,"completion_tokens":2634,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":634,"completion_tokens_details":{"reasoning_tokens":2531}},"tokens_in":634,"tokens_out":2634,"duration_ms":18240,"temperature":1.0,"reasoning_tokens":2531,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:36:11.864153+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Drive the circuit from two bulk sites with a $+\\pi/2$ phase difference and separately with a $-\\pi/2$ phase difference, following the protocol of Appendix F: if the $+\\pi/2$ drive does not build up a voltage concentrated at the right edge and the $-\\pi/2$ drive at the left edge, the reciprocal skin effect is not present in the realized circuit. A second check is to sweep the drive frequency away from the calibrated value and confirm that the localization direction and edge accumulation follow the sign of $\\sin(k_y)$ rather than reflecting a parasitic resonance.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the failure of bulk-boundary correspondence in non-Hermitian models, the phenomenon the reciprocal skin effect instantiates."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the anatomy of skin modes and the anomalous-localization criterion the paper extends to momentum slices."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces topolectrical circuits and the circuit Laplacian formalism through which the tight-binding model is realized."}],"review_version":1}