{"id":"a6e8ceef-01bf-452e-a760-39b053fb62c0","arxiv_id":"2512.19745","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Flat bands in 1D non-Hermitian lattices exhibit a skin effect governed by the point-gap topology of the surrounding dispersive bands, observed in a mechanical lattice.","lead":"An ideal flat band in a non-Hermitian lattice can develop a skin effect—edge-localized modes—even though the flat band itself is topologically trivial. The effect appears only when the surrounding dispersive bands enclose the flat band in complex energy, and it was observed in an active mechanical lattice.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Experimental validation is partly circular: couplings were fitted to the same flat-band responses used for comparison, and the key large-γ disappearance was measured in a 90°-rotated model rather than the original H_OBC.","rationale":"The theoretical framework of the FBSE is internally consistent and clearly formulated: the flat band remains at zero energy, and the response is governed by the point-gap topology of the dispersive bands. The Green's-function analysis, the CLS/LEV decomposition, and the GBZ/EP3 discussion all support the central mechanism. However, the experimental 'observation' is not fully independent. The parameters used to compute the theoretical response curves are extracted from the same measured responses that are then compared with those curves; this does not validate the model. The absence of error bars on the retrieved parameters further weakens the claim that the three experimental points lie in the intended parametric regions. The use of the rotated model H3 for region III is an additional layer of indirection, although the unitary equivalence is exact. A holdout test or independent parameter calibration would directly address the circularity and should be feasible with the programmable active-lattice platform. The reader's conditional verdict is appropriate: the paper is worth publishing with the requested data and analysis, not as a rejection of the theoretical result.","tokens_in":15632,"tokens_out":8377,"duration_ms":92004,"concrete_test":"Perform a holdout validation: split the measured response data into two sets—e.g., responses at different source positions or two slightly different drive frequencies. Fit the tight-binding parameters using only one set; use the fitted parameters to compute the Green's-function response for the second set. If the predicted response does not reproduce the edge localization in region II and its absence in regions I and III within the experimental noise, the FBSE observation is not independently established. Additionally, re-measure region III in the original H_OBC lattice (or report the explicit mapping of the H3 source profile to H_OBC) to confirm that the rotated-model result corresponds to the original model's response.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Fig. 3 caption states that all effective parameters were extracted by fitting experimental responses to the Green's function, and Table 1 lists retrieved (t1,t2,γ1,γ2) without uncertainties. Under these conditions, 'excellent agreement' between the measured flat-band response and the Green's-function calculation is not an independent test of the FBSE: the same data set determines both the parameters and the comparison. The central theoretical prediction—edge-localized response only when the flat band lies inside the PBC point gap of the dispersive bands—would be confirmed convincingly only if the parameters are calibrated by an independent measurement (e.g., two-site transmission or band-structure tracking) and then used to predict the response for a source configuration or frequency not used in the fit. A second, distinct concern: the disappearance of the FBSE at large non-Hermiticity (region III) is experimentally demonstrated in the unitarily rotated model H3 (End Matter), not in the original H_OBC. Although H3 is related to H_OBC by an exact unitary and its spectrum is the 90° rotation of the original, a local drive applied to a site of H3 corresponds, in H_OBC, to a nonlocal superposition of sources; the absence of edge response in H3 is therefore not automatically the same measurement as the absence of FBSE in H_OBC. The theoretical Fig. 1(b) already supports the disappearance, but the experimental support is one step removed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces and experimentally claims the flat-band skin effect (FBSE) in a one-dimensional non-Hermitian lattice. The model is a rank-defective three-band Hamiltonian with an exactly flat band at E=0 and two dispersive bands whose PBC spectra form loops in the complex-energy plane. The central theoretical claim is that FBSE appears exactly when the flat band lies inside the point gap of the dispersive bands, and disappears when the line gaps reopen at large non-Hermiticity. The theoretical analysis uses Green's functions, left/right eigenvector decomposition, the generalized Brillouin zone, and identifies order-3 exceptional points on the non-Bloch wavevector plane. The experimental part reports steady-state mechanical-lattice responses for three parameter regimes, claiming edge-localized response in the FBSE regime and its absence outside, including in the large-non-Hermiticity regime using a unitarily rotated model.","tokens_in":16004,"tokens_out":4217,"duration_ms":44246,"significance":"If the central claim is correct, it identifies a genuinely new mechanism for non-Hermitian skin effects: a topologically trivial flat band acquires skin-like response through the point-gap topology of surrounding dispersive bands, with a tunable, re-entrant parameter window. The theoretical framework is largely self-contained and parameter-free: the flat band is exact by construction, the FBSE criterion is derived from PBC spectra, and the CLS decomposition is given explicitly. The extension to AB-cage, ladder, and Lieb models in the Supplemental Material strengthens the generality of the criterion. The experimental platform is appropriate and capable of realizing the required non-reciprocal couplings. However, the experimental validation as reported is not independent: parameters are extracted from the same response data used for comparison, no uncertainties are given, and the key disappearance regime is measured in a rotated model rather than in the original OBC model. These issues are load-bearing for the experimental 'observation' claim.","major_comments":[{"comment":"The caption states that 'all effective parameters were extracted by fitting experimental responses to the Green’s function.' Therefore the excellent agreement between the measured flat-band responses and the Green’s-function calculations in Fig. 3(c1-c3) is partly tautological: the same data determine both the model parameters and the comparison. Table 1 lists retrieved t1, t2, γ1, γ2 without uncertainties. To establish the FBSE observation convincingly, the parameters should be calibrated by an independent measurement (e.g., two-site transmission, band-structure tracking, or a source configuration not used in the fit) and then used to predict the response out of sample. Without this, the experimental confirmation of the central phase diagram is not independent.","section":"Fig. 3 caption and Table 1"},{"comment":"The disappearance of FBSE in region III is experimentally demonstrated in the rotated Hamiltonian H3, obtained from H_OBC by H1 = i H_OBC and a subsequent unitary embedding, not in the original OBC model Eq. (2). While H3 is related by exact unitary transformations, a local single-site drive in H3 corresponds, in the original lattice, to a nonlocal superposition of sources. Thus the measured absence of edge response in H3 does not automatically establish the absence of FBSE for a local drive in H_OBC. The theoretical Fig. 1(b) already predicts the disappearance, but the experimental support is one step removed. The authors should specify the source mapping and show that the relevant response observable is preserved, or measure the original model with a scheme that isolates the flat band from the gain modes.","section":"End Matter, Eqs. (5)-(6) and Fig. 3(b3)"},{"comment":"No raw data, noise floor, or repeated-measurement statistics are reported. The experimental profiles in Fig. 3(b1-b3) are single normalized traces without error bars, and Table 1 gives no uncertainties in the fitted parameters. Since the mechanical lattice is active and feedback-controlled, systematic uncertainties in γ1 and γ2 are especially relevant for locating the regimes in Fig. 1(b). At minimum, the authors should report measurement uncertainties and demonstrate that the three regimes are separated by more than the experimental resolution in parameter space.","section":"Fig. 3 and Table 1"}],"minor_comments":[{"comment":"The definition of χ as written omits the normalization denominator. It should be χ = Σ_n n |R_n|^2 / Σ_n |R_n|^2 (or equivalently state that |R⟩ is normalized). As printed, the quantity is not a center-of-mass measure.","section":"Eq. (3)"},{"comment":"The caption describes the REVs as 'CLS' in panels (a,c), while the main text states that the orthogonalized REVs are 'still not exactly CLS.' The caption should be reconciled with the main text to avoid confusion.","section":"Fig. 2 caption"},{"comment":"References [54] and [69] appear to be explanatory footnotes embedded in the reference list rather than standard citations. These should be moved into the main text or footnotes and formatted consistently.","section":"References [54] and [69]"}],"recommendation":"major_revision","confidential_remarks":"The theoretical core is strong and likely publishable, but the experimental 'observation' claim needs substantial strengthening: independent parameter calibration, uncertainty reporting, and a direct or carefully mapped measurement of the region-III disappearance in the original model. I recommend major revision rather than rejection because the required fixes are within the scope of the manuscript and the theoretical contribution is valuable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know before anything else: the theoretical result is the meat of this paper, and it is solid. The authors show that an ideal flat band can develop a non-Hermitian skin effect, and that the effect is governed by the point-gap topology of the two dispersive bands that enclose the flat band on the complex-energy plane — not by the flat band's own (trivial) spectral topology. The criterion is parameter-free: FBSE appears when the flat band sits inside the PBC point gap, and it disappears at large non-Hermiticity when the line gap reopens. The analytic dispersion, the χ phase map, and the LEV-based explanation are internally consistent. The supplemental extension to AB cage, ladder, and Lieb lattices supports the claim that this is a generic mechanism. The Green's function scaling with lattice size in the FBSE regime is a clean signature. The EP3 analysis on the GBZ and the quantum distance discontinuity are interesting, though secondary.\n\nNow the soft spots, in proportion. The experimental validation is not as independent as it looks. The caption of Fig. 3 states that all effective parameters were extracted by fitting the experimental responses to the Green's function. That means the 'excellent agreement' in Fig. 3 is partly tautological: the same data set supplies both the fitted parameters and the comparison. Raw data and error bars are absent, and Table 1 lists retrieved couplings without uncertainties. That is enough to make the experimental claim conditional rather than fully demonstrated. The vanishing of FBSE in region III is also measured in a 90°-rotated model H3 rather than the original H_OBC. The rotation is exact and the spectrum is preserved, but a local drive in H3 corresponds to a nonlocal superposition of sources in H_OBC, so that particular measurement is one step removed from the original model. It corroborates the theory, but it is not the same measurement.\n\nNone of this undermines the central theoretical claim, which stands on its own equations. But it means the experimental observation should be viewed as supporting evidence, not independent confirmation.\n\nWho should read this: anyone working on non-Hermitian skin effects, flat-band physics, or topological mechanical metamaterials. The theoretical result is new and clearly argued, and the paper deserves a serious referee. If I were the editor, I'd send it out and ask for raw data, error analysis, and an independent parameter calibration before acceptance. That is a revision, not a rejection.","headline":"The flat-band skin effect is a real and well-argued theoretical result; the experiment confirms it but is not fully independent because the same response data were used to extract the model parameters.","tokens_in":16413,"tokens_out":2782,"would_cite":true,"duration_ms":28066,"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":"An ideal flat band can host a non-Hermitian skin effect, one that appears only when the surrounding dispersive bands enclose it in a point gap and disappears again at large non-Hermiticity.","keywords":["flat-band skin effect","non-Hermitian skin effect","compact localized states","point-gap topology","order-3 exceptional points","biorthogonal eigenvectors","active mechanical lattice"],"falsifier":"Measure the flat-band steady-state response in the original (unrotated) lattice for parameters in region III while suppressing the dispersive gain modes (e.g., by using a narrow probe or time-gating); if the response still localizes at the edge, the FBSE does not disappear, contradicting the central re-entrant claim. Alternatively, sweep gamma_2 across the predicted boundary in Fig. 1(b) and check that the center-of-mass chi jumps sharply at the PBC gap-closing curve; a shift or absence of the jump would falsify the point-gap mechanism.","tokens_in":15583,"feed_emoji":"🌀","tokens_out":5428,"duration_ms":56164,"temperature":0.7,"pith_summary":"This paper tries to establish a new phenomenon: the non-Hermitian skin effect, normally reserved for dispersive bands with nontrivial point-gap topology, also appears on a symmetry-protected ideal flat band. The flat band itself always sits at zero energy and is topologically trivial, so the skin effect is instead inherited from the dispersive bands: when their periodic-boundary spectra form a closed loop around the flat band on the complex-energy plane, the flat band's steady-state response localizes at the open boundary. This leads to two surprising consequences: the effect only exists in a finite parameter window, and it counterintuitively vanishes when non-Hermiticity is made very large. The authors confirm the prediction in a 12-cell active mechanical lattice and show that the gaps between the flat and dispersive bands close at order-3 exceptional points, where the flat-band wavefunctions are singular. If right, this extends non-Hermitian spectral topology to flat-band systems and gives a new handle on edge localization.","feed_headline":"Flat bands show a skin effect, then lose it","feed_subtitle":"Flat-band modes localize at edges only while other bands loop around them in complex energy; strong non-Hermiticity flips it off.","key_machinery":"The Green's function G(E) = (E - H_OBC)^{-1} evaluated infinitesimally close to the flat-band energy, together with the Lehmann (biorthogonal) spectral representation. The flat band is enforced by a rank-2 Hamiltonian structure, giving an exactly degenerate zero-energy subspace spanned by compact localized states; the Green's function response is determined by the left eigenvectors, which in the FBSE regime are exponentially localized at the boundary opposite to where the right (CLS) modes sit. The point-gap topology of the dispersive bands, not of the flat band, selects the parameter region where this happens.","core_discovery":"The central claim is that a flat-band skin effect (FBSE) occurs when the flat band lies inside the point gap of the dispersive bands under periodic boundary conditions. Although the flat band's own open-boundary eigenvectors (compact localized states) remain spread across the bulk, a source at the flat-band frequency produces a response exponentially localized at one edge because some left eigenvectors become localized at the opposite boundary with very large magnitudes. The mechanism is biorthogonal: the Green's function at zero energy is a sum over flat-band modes, and the extreme non-normality of the flat-band subspace, rather than any winding of the flat band itself, produces the skin re","pith_inferences":["If FBSE is tied to the point-gap enclosure, similar effects should appear in higher-dimensional flat-band systems where the dispersive bands form point-gap loops; a 2D test would be a natural next step.","The biorthogonal mechanism implies the skin response is sensitive to the source's overlap with the localized left eigenvectors; pumping schemes that excite different flat-band superpositions could control the edge on demand.","The 'disappearance at large non-Hermiticity' might be masked in the original model by dispersive gain modes with near-zero real frequency; the paper's spectral-rotation argument needs an independent check that isolates the flat band in the unrotated lattice."],"forward_implications":["FBSE should be generic across flat-band models: the authors show it in AB cage, ladder, and Lieb lattices as well.","The effect is re-entrant: it can be switched off by increasing non-Hermiticity, unlike standard skin effects.","The gap-closing points are order-3 exceptional points under both periodic and open boundary conditions, and the flat-band quantum distance is discontinuous there.","An active mechanical lattice reproduces the predicted responses, including the disappearance in region III when viewed through a spectrally rotated model.","The response center-of-mass chi provides a basis-invariant diagnostic for FBSE, avoiding ambiguities from the degenerate flat-band subspace."],"fun_headline_variants":["Flat-band skin effect appears and disappears with non-Hermiticity","Flat bands get skin effect only when dispersive bands wrap them","Flat-band skin effect: a transient edge localization","Skin effect for flat bands: it's all about the surrounding bands","Mechanical lattice shows flat-band skin effect"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole experiment assumes the measured steady-state response is produced by the ideal tight-binding model with couplings fitted from the same responses, and that the spectral-rotation trick used at large non-Hermiticity does not change the response physics; if either fails, the claimed observation is not established.","fun_headline_variants_meta":{"raw":{"variants":["Flat-band skin effect appears and disappears with non-Hermiticity","Flat bands get skin effect only when dispersive bands wrap them","Flat-band skin effect: a transient edge localization","Skin effect for flat bands: it's all about the surrounding bands","Mechanical lattice shows flat-band skin effect"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001429,"raw_usage":{"total_tokens":5610,"prompt_tokens":759,"completion_tokens":4851,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":503,"completion_tokens_details":{"reasoning_tokens":4770}},"tokens_in":503,"tokens_out":4851,"duration_ms":33738,"temperature":1.0,"reasoning_tokens":4770,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T15:36:28.084250+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the flat-band steady-state response in the original (unrotated) lattice for parameters in region III while suppressing the dispersive gain modes (e.g., by using a narrow probe or time-gating); if the response still localizes at the edge, the FBSE does not disappear, contradicting the central re-entrant claim. Alternatively, sweep gamma_2 across the predicted boundary in Fig. 1(b) and check that the center-of-mass chi jumps sharply at the PBC gap-closing curve; a shift or absence of the jump would falsify the point-gap mechanism.","supporting_citations":[],"review_version":1}