{"id":"0be7f2a9-ea1e-4986-b988-5af5ca3c4633","arxiv_id":"2607.29214","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Stacking-engineered cancellation of interlayer piezoelectric channels can suppress the linear response and expose a nearly quadratic piezoelectric response in multilayer MoS2 and NiTe2.","lead":"By sliding the atomic layers of materials like MoS2, simulations show you can switch the piezoelectric response from ordinary linear to a quadratic, frequency-doubling mode, simply by changing which stackings add or cancel each other's effects. The paper proposes this 'piezoelectric interference' as a programmable design principle for nanoscale electromechanical devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Per-gap channel decomposition behind 'piezoelectric interference' is non-unique; the design descriptor γ_e may be an artifact of the partition.","rationale":"The reader's weakest assumption correctly identifies the non-uniqueness of the per-gap channel decomposition as the most load-bearing weakness. The paper's direct DFT predictions of small e33 and finite B333 in specific stackings are internally consistent and could hold regardless of the decomposition, but the central claim that stacking-engineered 'interference' is the underlying mechanism—and the proposed γ_e descriptor for predicting new parabolic piezoelectric materials—depends on the physical faithfulness of that decomposition. Since the reader already issued a CONDITIONAL verdict on these grounds, my analysis does not change the verdict; it sharpens the test needed to validate or invalidate the mechanism. I agree with the reader's emphasis rather than raising a separate technical objection (e.g., the classical dipole method for semimetallic NiTe2) because the additivity issue directly targets the paper's explanatory core and design rule.","tokens_in":12476,"tokens_out":6049,"duration_ms":66339,"concrete_test":"Recompute the per-gap channel strengths for all 12 surveyed stackings using two independent definitions: (1) the paper's isolated-gap method, and (2) Bader charge analysis of interlayer charge transfer under uniform vertical strain, assigning each gap's contribution from the change in atomic charges across that gap. If γ_e (Eq. 9) flips sign or shifts from <0.2 to >0.5 for any material, the interference classification is not robust. As a partition-free check, compute the angle between ∇_d P_z and the relaxed strain path dd/dϵ at equilibrium for every system; if the predicted destructive-interference systems (γ_e < 0.2) do not exhibit near-orthogonality (angle within ~15° of 90°), the mechanism is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central explanatory mechanism relies on decomposing the total out-of-plane piezoelectric response into independent interlayer-gap channels e33^(i) (Eq. 5; Supplementary Note 3), and then classifying stackings as constructive/destructive via the interference factor γ_e (Eq. 9). This decomposition is a modeling choice: the total e33 is a ground-state electronic property, and assigning it to individual gaps requires a convention. The paper's isolated-gap definition (varying one gap at a time while holding others fixed) ignores collective strain relaxation and charge redistribution across gaps. If the sign or magnitude of an e33^(i) changes under an equally reasonable partition (e.g., Bader/Wannier charge decomposition of the uniform-strain response, or simultaneous gap variation), then 'interference' is not a physical mechanism but a property of the chosen bookkeeping. The direct finding of small e33 in BAAC-MoS2 and CBB-NiTe2 could survive this test, but the design principle and the γ_e descriptor used for materials screening would be unsupported. The geometric orthogonality between the relaxed strain path and the polarization gradient (Fig. 2) provides a partition-independent alternative, but it is only demonstrated for one system, not for the full 12-material map.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a stacking-engineered 'piezoelectric interference' mechanism in multilayer sliding ferroelectrics. It decomposes the out-of-plane linear piezoelectric coefficient into per-interlayer-gap channels e33^(i), argues that same-signed channels give constructive interference and opposite-signed channels give destructive interference, and uses this to design stackings with suppressed linear response but finite quadratic response. Direct DFT calculations on representative MoS2 and NiTe2 multilayer stackings show near-parabolic P_z(ε) curves for BAAC-MoS2 and CBB-NiTe2, with vertex strains reduced by factors of ~25 and ~60 relative to CBA-MoS2. The paper also presents a Ginzburg–Landau model, a 12-material materials map based on an interference factor γ_e, and predicted sliding pathways in tetralayer MoS2 that connect linear-dominated, quadratic-dominated, and sign-inverted response states.","tokens_in":12824,"tokens_out":4136,"duration_ms":47602,"significance":"If the interference mechanism is robust, the work offers a genuinely useful design principle for nonlinear piezoelectricity: instead of delicate critical tuning, stacking order would provide a reversible, layer-by-layer control of the balance between linear and quadratic electromechanical response. The direct DFT data are internally consistent, and the use of four vdW treatments with a consistent CI/DI classification is a clear strength; the classical-dipole polarization method is also benchmarked against Berry-phase results for semiconducting references. The sliding-pathway predictions for tetralayer MoS2 are experimentally testable. However, the central explanatory claim rests on a per-gap channel decomposition that is not uniquely defined and is not yet shown to be invariant under reasonable alternative partitions. The geometric orthogonality argument in Fig. 2 provides a more partition-independent route, but it is demonstrated for only one system. Thus the significance is conditional: the numerical findings are valuable, but the 'interference' mechanism and the γ_e descriptor need additional validation before they can be accepted as a general design principle.","major_comments":[{"comment":"The central classification into constructive versus destructive interference, and the descriptor γ_e, is built on the per-gap decomposition e33^(i). This decomposition is a modeling choice and is not unique: the total e33 is a single ground-state response, and assigning it to individual vdW gaps requires a partition convention. The isolated-gap variation used in Supplementary Note 3 assumes that strain-induced charge redistribution localizes to one gap and ignores collective relaxation across gaps. If an equally reasonable partition (e.g., Bader/Wannier decomposition of the uniform-strain response, or simultaneous independent gap variations) changes the sign of any e33^(i), then 'interference' is a property of the bookkeeping rather than a physical mechanism. The authors should demonstrate sign invariance of the e33^(i) under at least one alternative partition, or reframe the claims with","section":"Results — 'Stacking-controlled piezoelectric interference'; Eq. (5), Eq. (9), Supplementary Note 3"},{"comment":"The geometric orthogonality argument (relaxation path nearly parallel to polarization contours in the (d1,d2) plane) is the most convincing, partition-independent evidence for destructive interference, but it is presented only for CBB-NiTe2. For BAAC-MoS2 — the other crucial near-parabolic system — no such landscape is shown, and the 12-material map in Fig. 3c relies on γ_e, not on direct orthogonality. To make the design principle general, the authors should either show the gradient–relaxation-path orthogonality for BAAC-MoS2 and CBAB-MoS2 as well, or provide a quantitative orthogonality criterion applied to all surveyed systems.","section":"Results — 'Geometric origin of piezoelectric interference'; Fig. 2d,e"},{"comment":"The Ginzburg–Landau model is presented as an explanatory framework, but its parameters (A_i, β_i, g_i, λ, C) are not fitted to the DFT data, and Eq. (6) is not used to compute e^(1), e^(2) from microscopic inputs. Since Eq. (5) is just the definition of the decomposition, the model can only restate the cancellation algebra; it cannot independently validate the constructive/destructive classification. The authors should either fit the GL parameters to the DFT-computed channels and show predictive agreement, or explicitly label the model as a phenomenological illustration rather than a derivation.","section":"Results — 'Ginzburg–Landau framework and materials design space'; Eq. (6), Supplementary Note 6"},{"comment":"The reported values of e33 and B333 (e.g., +24.05, +4.68, +1.07 pC/m and −218.15, −1073.83, −593.26 pC/m) are given without uncertainties, fit windows, or convergence tests. Because the central claim of 'suppressed linear response' depends on comparing these numbers to zero and to one another, the reader cannot assess whether e33 ≈ +4.68 pC/m is significantly different from zero or from the CBA value. The authors should report fitting strain ranges, standard errors from the quadratic fits, and convergence checks with respect to k-point density and strain steps.","section":"Methods and Results — reported coefficients"}],"minor_comments":[{"comment":"The text contains typographical spacing in 'V ASP' and 'DA TA A V AILABILITY'; these should be corrected to 'VASP' and 'DATA AVAILABILITY'.","section":"Methods — First-principles calculations"},{"comment":"The stacking notation (CBA, BAAC, CBB, CBAC, CBAB, ACAB, BCAB) is used without a general definition in the main text. A short convention statement or a table mapping each label to the layer stacking sequence would improve readability.","section":"Throughout"},{"comment":"For semimetallic NiTe2, the classical dipole method is used because Berry phase is ill-defined; the benchmark against Berry phase is said to be in Supplementary Note 1. A one-sentence summary of the validation for the semimetallic case in the main text would help the reader trust the NiTe2 numbers, which are central to one of the two main parabolic examples.","section":"Methods — Polarization and piezoelectricity"},{"comment":"The materials map should explicitly label axes and define the color/symbol coding in the caption; in the provided text it is not clear what the axes are or which symbol corresponds to which vdW treatment/material. If this is a rendering issue, the figure must be self-contained.","section":"Fig. 3c"}],"recommendation":"major_revision","confidential_remarks":"The direct DFT results and the specific near-parabolic stackings are likely publishable, and the paper addresses a topical and practically interesting problem. My main concern is that the central 'interference' mechanism and the γ_e descriptor are defined through a non-unique per-gap decomposition; this needs to be addressed head-on with partition-robustness tests. The geometric orthogonality argument is a strong alternative but is currently only shown for one system. I am not recommending rejection because the numerical findings stand independently of the decomposition, but the manuscript's central claim is not yet supported to the standard required for the journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my read. The paper has a real idea: treat each vdW gap as a local piezoelectric channel and use stacking order to make channels cancel, exposing the quadratic term. The DFT for BAAC-MoS2 and CBB-NiTe2 shows genuinely small e33 with finite B333, and the four vdW treatments agree on the classification. The geometric argument in Fig. 2 (relaxed strain path nearly orthogonal to the polarization gradient) is the strongest part, because it does not depend on any particular channel decomposition. I'd take the two near-parabolic examples as a solid computational result.\n\nThe soft spot is the one the stress-test flags. The per-gap channel decomposition (Eq. 5, SI Note 3) is a bookkeeping choice. e33^(i) is not observable, and the isolated-gap variation ignores collective relaxation. If a different partition changes the signs of the channels, the 'interference' language and the gamma_e descriptor lose their predictive meaning. The paper partially guards against this by showing the geometric orthogonality for CBB-NiTe2, but only for one system; the materials map (gamma_e vs eps_v) is built from the same fitted channels, so it inherits the arbitrariness. This is not fatal to the direct results, but it is a real gap between the data and the design principle.\n\nOther issues are more routine: GL parameters are ad hoc and not tied to the DFT; the fitted e33 and B333 come without uncertainties or stated strain windows; no data/code deposit; no experiment (paper is upfront about that). These are fixable in revision.\n\nOverall: this deserves a serious referee. The referee should push for a test of the decomposition's uniqueness — e.g., an alternative charge partition or a two-gap simultaneous variation — and for the geometric argument extended across the survey. If that holds, the gamma_e descriptor becomes credible. If not, the paper still stands as a set of well-calculated examples, but the screening claim weakens.\n\nI'd send it to review. I'd cite it if I worked on sliding ferroelectrics. I'd not bring it to reading group as a methods showcase, maybe as a discussion of what counts as an explanation in computational materials.","headline":"Genuinely interesting design principle with solid DFT for the two showcase stackings, but the interference mechanism and gamma_e descriptor rest on a non-unique channel partition that needs a robustness test.","tokens_in":13259,"tokens_out":3264,"would_cite":true,"duration_ms":35081,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["77.65.-j","77.80.-e"],"model":"deepseek-v4-flash","headline":"Stacking order in multilayer sliding ferroelectrics can cancel the linear piezoelectric response and expose a purely quadratic one, offering a programmable route to nonlinear electromechanics.","keywords":["sliding ferroelectrics","piezoelectric interference","nonlinear piezoelectricity","quadratic piezoelectric response","stacking engineering","interlayer channels","MoS2","NiTe2"],"falsifier":"Measure the polarization–strain curve of a ferrielectric CBAB-stacked tetralayer MoS2 sample; if it is not close to parabolic (i.e., if e33 is not strongly suppressed), the predicted destructive interference is not realized. Alternatively, compute e33 and B333 of BAAC-MoS2 using a method that does not rely on per-gap partitioning (e.g., direct Berry-phase strain derivative); if e33 remains large, the interference explanation collapses.","tokens_in":12382,"feed_emoji":"⚡","tokens_out":3566,"duration_ms":36857,"temperature":0.7,"pith_summary":"This paper tries to establish that the out-of-plane piezoelectric response of multilayer sliding ferroelectrics is not a single material property but a sum of stacking-dependent contributions from each interlayer gap. When these contributions have the same sign, they reinforce to give a large linear response; when they have opposite signs, they cancel the linear coefficient while leaving a finite quadratic coefficient, producing a nearly parabolic polarization–strain curve. The authors show this mechanism in BAAC-stacked MoS2 and CBB-stacked NiTe2, and predict that sliding a tetralayer MoS2 sample can switch it between linear, quadratic, and sign-inverted response states. A sympathetic reader would care because it offers a general, reconfigurable design principle for nonlinear piezoelectricity, avoiding the delicate strain or phase-instability tuning previously required.","feed_headline":"Sliding atomic layers exposes a purely quadratic piezoelectric response","feed_subtitle":"Opposite-signed interlayer gaps cancel the linear term in MoS2 and NiTe2 stacks, yielding near-parabolic strain-response curves.","key_machinery":"The central object is the interface-resolved channel decomposition: the total out-of-plane piezoelectric coefficient e33 is written as the sum of per-gap coefficients e33^(i), each associated with a specific interlayer gap and determined by local stacking. This decomposition, combined with the interference factor γe that measures constructive versus destructive addition, carries the argument. The paper supports it with an energy–polarization landscape in interlayer-distance space (d1, d2), where the linear response is governed by the projection of the strain-relaxation path onto the polarization gradient; near-orthogonality between the two suppresses e33. A generalized Ginzburg–Landau free e","core_discovery":"The central claim is that each van der Waals gap in a multilayer sliding ferroelectric acts as an independent piezoelectric channel whose sign and magnitude are set by the local stacking environment, so the total out-of-plane linear coefficient is the algebraic sum of channel coefficients. Constructive interference of same-signed channels gives a linear-dominated response, while destructive interference of opposite-signed channels suppresses the linear coefficient without extinguishing the quadratic coefficient. Quantitative first-principles results show BAAC-MoS2 with e33 ≈ +4.68 pC/m and B333 ≈ −1073.83 pC/m, and CBB-NiTe2 with e33 ≈ +1.07 pC/m and B333 ≈ −593.26 pC/m, both approaching the","pith_inferences":["The same interference logic could apply to other stacking-dependent order parameters beyond polarization—for instance, nonlinear optical susceptibilities or spin–orbit-coupled responses—where per-gap sign cancellation might tune higher-order coefficients while suppressing the leading term.","Because the quadratic-dominated state is reached at zero strain, the vertex strain itself becomes a stack-tunable engineering parameter: one could design a material whose harmonic output peaks at zero bias, potentially useful for energy harvesting or mechanical logic where amplitude is not the distinguishing feature.","An experimental test could use artificially assembled heterostructures with one chemically modified gap (e.g., an intercalant): if the per-gap channel decomposition is faithful, the modified gap's contribution should add linearly to the rest, allowing direct measurement of individual channel coefficients.","If sliding-programmable quadratic response is confirmed, it suggests a mechanical 'frequency-doubling switch' that could be toggled by a lateral field, which would be a new functionality for van der Waals devices beyond simple polarization reversal."],"forward_implications":["Stacking order alone can suppress the linear piezoelectric coefficient without requiring critical strain or material-specific instability, making nonlinear piezoelectricity designable rather than accidental.","The interference factor γe serves as a compact descriptor: systems with γe < 0.2 exhibit vertex strains of only a few percent, enabling screening for near-parabolic piezoelectric candidates.","In a single tetralayer MoS2 sample, lateral sliding is predicted to connect linear-dominated, quadratic-dominated, and sign-inverted response states, providing a non-volatile, reconfigurable electromechanical element.","The quadratic-dominated state offers a route to frequency doubling: a sinusoidal vertical ac field would produce an output at twice the frequency, extending beyond ordinary ferroelectric polarization reversal.","The mechanism naturally generalizes to other layered systems with multiple comparable interfacial polar units, such as moiré superlattices and oxide heterostructures, though the present demonstration is in transition-metal dichalcogenides."],"fun_headline_variants":["Stacking gaps cancel linear piezo, boost quadratic","Interference in sliding stacks yields quadratic piezo","Engineered stacking silences linear piezoelectricity","Quadratic piezoelectricity via stacking interference","Sliding layers tune piezo from linear to quadratic"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The macroscopic piezoelectric response factorizes cleanly into independent per-gap channels e33^(i), so that the total linear coefficient is an algebraic sum of these local channel coefficients—a partition of charge redistribution that is a modeling choice rather than a directly measurable quantity.","fun_headline_variants_meta":{"raw":{"variants":["Stacking gaps cancel linear piezo, boost quadratic","Interference in sliding stacks yields quadratic piezo","Engineered stacking silences linear piezoelectricity","Quadratic piezoelectricity via stacking interference","Sliding layers tune piezo from linear to quadratic"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00049,"raw_usage":{"total_tokens":2249,"prompt_tokens":744,"completion_tokens":1505,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":488,"completion_tokens_details":{"reasoning_tokens":1449}},"tokens_in":488,"tokens_out":1505,"duration_ms":11558,"temperature":1.0,"reasoning_tokens":1449,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T11:29:07.603225+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the polarization–strain curve of a ferrielectric CBAB-stacked tetralayer MoS2 sample; if it is not close to parabolic (i.e., if e33 is not strongly suppressed), the predicted destructive interference is not realized. Alternatively, compute e33 and B333 of BAAC-MoS2 using a method that does not rely on per-gap partitioning (e.g., direct Berry-phase strain derivative); if e33 remains large, the interference explanation collapses.","supporting_citations":[],"review_version":1}