{"id":"62c4d0b9-6618-43c7-b2b7-a8794595fa8c","arxiv_id":"2607.17209","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A bilayer-specific current-induced spin response (the layer Edelstein effect) is shown by symmetry to be generic in nonmagnetic layered stacks, with DFT confirmation in TMD bilayers.","lead":"This paper predicts a new effect in two-layer materials: an electric current can make the top and bottom layers develop opposite spin magnetizations, and an out-of-plane electric field chooses which layer's spin dominates. It derives a symmetry rule that says the effect should appear in many nonmagnetic bilayer stacks, and supports it with simulations on MoSSe, MoTe2, and WTe2.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Type-II classification does not establish layer-opposite spin at fixed E: the LG_inter relation links layer L at +E to layer L' at -E, and a linear-in-E response is layer-symmetric, so the 'any 80 layer groups' universality claim is unsupported.","rationale":"The reader's weakest assumption concerns layer-resolved decomposition and interlayer hybridization. My concern is more fundamental and located in the Type-II symmetry argument: even with perfectly decoupled layers, the stated LG_inter/field-reversal reasoning does not prove layer-opposite magnetization at a fixed field; it actually implies the opposite sign for the generic linear-in-E response. If the proposed layer-resolved DFT check returns same-sign layer tensors, the strong claim that all 80 layer groups can realize the LEE is false and the paper should be rejected or drastically scaled back to Type-I inversion-stacked noncentrosymmetric monolayers. If the check returns opposite signs, the concern is resolved and the central claim is restored. Because the issue is concrete and testable, and because Type-I LEE may remain valid, the appropriate recommendation is conditional acceptance pending that verification.","tokens_in":14476,"tokens_out":23483,"duration_ms":230552,"concrete_test":"Compute layer-resolved Edelstein tensors chi^{top}_{ij}(E) and chi^{bot}_{ij}(E) for the Type-II example bilayer MoTe2 (P-6m2) at E=+0.1 eV/A using the same DFT/PAOFLOW pipeline with layer projection. If sign(chi^{top}_{xy}(E)) equals sign(chi^{bot}_{xy}(E)), Type-II LEE is refuted and the universality claim collapses. As a minimal control, solve the two-layer D3h Rashba model with t_perp=0 and finite E_z; the layer response is analytically same-sign, showing that opposite layer magnetization requires extra material-specific physics beyond the stated symmetry criterion.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that the LEE depends only on bilayer point-group symmetry and that all 80 layer-group materials can realize it. For centrosymmetric/high-symmetry monolayers this rests entirely on the Type-II mechanism. The paper argues that since a vertical field breaks all LG_inter operations and an LG_inter operation maps E to -E, components constrained by LG_inter reverse sign under field inversion, 'giving rise to opposite spin magnetizations on the two layers.' This does not follow. For g in LG_inter, g H(E) g^{-1}=H(-E) and g swaps layers, so the exact constraint is of the form chi^{L'}(E) = - g chi^L(-E) g^T (for improper g), not chi^{L'}(E)=-chi^L(E). The desired relation requires chi^L(E) to be even in E. But a component allowed by LG_intra and forbidden only by LG_inter generically has a linear-in-E term; at that order the relation gives chi^{L'}(E)=chi^L(E), i.e. same sign. Concretely, two identical D3h monolayers under the same E_z acquire identical Rashba coefficients alpha(E)=c E, so current-induced spins have the same sign in both layers; the midplane mirror only enforces alpha(-E)=-alpha(E). The MoTe2 DFT discussion reports global chi_xy=-chi_yx, a Rashba-type total tensor, not a layer-resolved comparison, so it does not confirm LEE.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces the layer Edelstein effect (LEE), a current-induced spin response in bilayers where the top and bottom layers acquire opposite spin magnetizations. Using a k·p model, symmetry analysis based on layer-group stacking, and first-principles calculations, the authors claim that the LEE is a generic symmetry-governed phenomenon: its existence depends only on the bilayer point group, and any of the 80 layer-group materials can realize it through an appropriate stacking configuration. Two mechanisms are proposed: Type-I, where interlayer-inversion symmetry enforces opposite layer-resolved Edelstein tensors; and Type-II, where an out-of-plane electric field activates the response and allegedly enforces layer-opposite magnetizations. The paper includes calculations for MoSSe, MoTe2, and WTe2 bilayers.","tokens_in":14884,"tokens_out":10231,"duration_ms":97357,"significance":"The concept of a layer-resolved Edelstein effect is timely and would be a valuable generalization of hidden spin polarization to current-induced phenomena. The Type-I mechanism is well grounded in standard symmetry arguments and, if validated, would provide a simple design criterion for gate-controlled layer-selective spin generation. The paper also provides first-principles calculations and a symmetry table covering all bilayer point groups. However, the Type-II mechanism, which underpins the universality claim for centrosymmetric and high-symmetry monolayers, is not rigorously established and, as argued below, the presented symmetry treatment is likely incorrect. The broad claim that all 80 layer groups can realize the LEE is therefore premature.","major_comments":[{"comment":"The derivation of Type-II LEE contains a logical error. For an operation g∈LG^inter_B, the layer-resolved tensor satisfies χ^{L'}(E) = -g χ^L(-E) g^T, not χ^{L'}(E)=-χ^L(E). If the component is odd in E, as for the field-linear Rashba term, this gives χ^{L'}(E)=+χ^L(E), i.e., the same sign. The paper's statement that 'components constrained by LG^inter_B reverse sign under field inversion' is only true for the total response after accounting for the layer swap; it does not produce opposite signs at fixed E. A concrete counterexample is two identical D3h monolayers under the same field, which acquire identical Rashba coefficients and hence identical spin polarizations. The Type-II universality claim is therefore unsupported.","section":"Symmetry rules for LEE (Type-II)"},{"comment":"The MoTe2 calculation does not validate Type-II. The reported non-zero χ_xy=-χ_yx is the global tensor of the bilayer; it is exactly the expected result if both layers have identical Rashba-type responses. The paper does not provide layer-resolved χ tensors or layer-resolved spin densities. Without these, the calculation is consistent with a uniform Edelstein effect rather than layer-opposite spins. The same applies to the WTe2 discussion in Sec. X of the SM.","section":"LEE in realistic materials (MoTe2)"},{"comment":"Because Type-II is the only mechanism available for centrosymmetric monolayers and for many point groups in Table I (e.g., Ci, C2h, D4h, D6h), the conclusion that 'any of the 80 layer-group materials can realize it' is not established. The paper should either provide a corrected derivation of Type-II (e.g., showing that a field-induced layer-dependent potential yields opposite signs) or revise the universality claim to Type-I systems only. The current presentation overstates the scope of the result.","section":"Symmetry rules for LEE (Table I and Discussion)"}],"minor_comments":[{"comment":"Table I contains duplicate point-group labels (C2, Cs, C2v, C6 appear twice). The intended orientations should be clarified.","section":"Table I"},{"comment":"Equation (2) assumes a single common relaxation time; the effect of layer-dependent relaxation times on the layer-resolved tensor is not discussed.","section":"Eq. (2)"},{"comment":"A large part of the proof, including the exhaustive enumeration of stacking configurations and the derivation of the stacking operator formalism, is deferred to the Supplemental Material and to an unpublished companion paper (Ref. 88). The manuscript would benefit from including the essential steps in the main text so that the criterion can be independently checked.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper's central claim is attractive, but the Type-II flaw is load-bearing. If the authors can supply a corrected symmetry derivation and layer-resolved first-principles validation, the paper might become publishable. Otherwise, the universality claim should be substantially narrowed. I also urge the editor to ensure that Ref. 88's content is either included in the manuscript or published in a verifiable form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the useful part. The paper gives a clean layer-resolved formulation of the Edelstein effect and a symmetry classification (Table I) for when a bilayer can support opposite layer-resolved spin magnetizations under a current. For monolayers that are already noncentrosymmetric, the Type-I mechanism is solid: an inversion-stacked bilayer forces chi^{L'} = -chi^L by symmetry, and the k.p model plus the MoSSe DFT calculation demonstrate it. That part is a real contribution and probably correct.\n\nThe problem is Type-II, which is the basis for the claim that all 80 layer groups can realize the LEE. The paper argues that since an LG_inter operation maps the electric field to its negative, components forbidden by LG_inter are odd in E, and therefore the two layers get opposite magnetizations. This does not follow. For a component allowed by LG_intra but forbidden by LG_inter, the leading term is linear in E. The oddness under field reversal gives chi^L(-E) = -chi^L(E), but the layer-exchange relation gives chi^{L'}(E) = chi^L(E) at that order, i.e. the same sign, not opposite. Concretely, two identical D3h monolayers under a common E_z acquire identical Rashba coefficients, so the current-induced spin polarizations are parallel. The MoTe2 calculation reports a global chi_xy = -chi_yx tensor, which is just the Rashba response of the field-broken bilayer, not a layer-resolved opposite-spin signature. So Type-II does not establish LEE, and the universality claim is unsupported.\n\nThe other weaknesses are minor by comparison: Eq. (2) hides a common-relaxation-time assumption, and the exhaustive enumeration and the stacking theory are in the Supplemental Material plus an unpublished companion paper, so the proof is partly hard to verify. None of that would sink a Type-I-focused paper.\n\nVerdict: this is a valuable paper for the Type-I mechanism and the classification of when layer-opposite spins are symmetry-enforced. The Type-II section needs serious rework; either identify which components genuinely become opposite under a field, or withdraw the claim that the LEE is ubiquitously realizable in all 80 layer groups. A good referee should engage with it rather than desk-reject, because the concept is sensible and the Type-I part is solid.","headline":"The Type-I layer Edelstein effect is a real, useful result; the claim that all 80 layer groups host it rests on a Type-II argument that fails at linear order.","tokens_in":15325,"tokens_out":16292,"would_cite":true,"duration_ms":150584,"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 in-plane current drives opposite spin magnetizations on the two layers of a stacked bilayer; the effect is generic, governed only by the bilayer's point-group symmetry, and realizable in any of the 80 layer groups.","keywords":["layer Edelstein effect","current-induced spin polarization","bilayer stacking","layer group symmetry","Edelstein effect","spin-orbit coupling","electric field control","transition metal dichalcogenides"],"falsifier":"Compute the layer-resolved Edelstein tensor for an inversion-stacked MoSSe bilayer using full first-principles methods that include all interlayer hybridization, and check whether an in-plane current produces exactly opposite layer magnetizations that flip with the out-of-plane field; if the layer-opposite relation fails or the response vanishes despite the bilayer having a layer-exchanging operation, the symmetry-only criterion is incomplete.","tokens_in":14403,"feed_emoji":"⚡","tokens_out":15674,"duration_ms":109582,"temperature":0.7,"pith_summary":"The paper introduces the layer Edelstein effect (LEE), a current-induced spin phenomenon in stacked bilayers: an in-plane charge current produces spin magnetizations on the top and bottom layers that point in opposite directions, even when the bilayer as a whole is inversion-symmetric and has zero net magnetization. Using a minimal bilayer model and a general stacking theory, the authors show that the LEE is a generic, symmetry-governed response: its existence is determined solely by the bilayer point group, specifically by the presence of at least one layer-exchanging symmetry operation. This criterion makes the effect ubiquitous—any of the 80 layer-group materials can realize it through an appropriate stacking. The paper identifies two universal manifestations (explicitly symmetry-forced opposite components, and components activated by an out-of-plane electric field) and confirms both with first-principles calculations on MoSSe, MoTe2, and WTe2 bilayers. Because an electric field selects which layer carries the magnetization and reverses its sign, the LEE offers an electrical route to writing and switching layer-resolved spin states.","feed_headline":"One symmetry rule predicts layer-opposite spins in all 80 layer groups","feed_subtitle":"One layer-exchange symmetry suffices; calculations on MoSSe, MoTe2, and WTe2 confirm it.","key_machinery":"The central object is the bilayer point group LG_B, built by a stacking operator P̂ acting on a monolayer layer group LG_L; it splits into layer-preserving (LG_intra) and layer-exchanging (LG_inter) operations. The response is the layer-resolved Edelstein tensor χ, a second-rank axial tensor whose allowed components are fixed by the point group (Neumann's principle). The key move: a layer-exchanging operation forces χ^{L'}_{ij} = -χ^{L}_{ij} (Type-I), or, once an out-of-plane electric field breaks LG_inter, makes field reversal equivalent to layer exchange, yielding opposite layer magnetizations (Type-II). This turns the LEE into a table-lookup classification over the 80 layer groups.","core_discovery":"The central claim is that the layer Edelstein effect is a universal symmetry-governed response of nonmagnetic bilayers—whether a stacked bilayer shows opposite current-induced spin magnetizations on its two layers is fixed entirely by its point-group symmetry, and the decisive condition is the presence of at least one layer-exchanging operation. Inversion symmetry does not forbid it. The paper derives this criterion by combining a minimal bilayer band model with an enumeration of all 80 layer groups under a general stacking-operator framework, and verifies the response in first-principles calculations on bilayer MoSSe, MoTe2, and WTe2. Two mechanisms emerge: Type-I, where the monolayer's Ede","pith_inferences":["A likely extension is the layer-resolved orbital Edelstein effect: the same layer-group decomposition should apply to orbital magnetization, yielding an analogous orbital LEE with Type-I/II classifications.","Because sliding one layer changes the stacking operator and therefore the bilayer point group, sliding ferroelectricity could act as a mechanical switch to toggle the LEE on and off—a natural mechanical analogue to the electric-field switch studied here.","The layer-opposite relation may blur if interlayer hybridization is strong; a testable prediction is that the LEE magnitude and layer contrast should decrease as interlayer spacing shrinks, which could be checked by first-principles calculations at varying distances.","The Table I enumeration suggests a high-throughput screening recipe: for any pair of monolayers with known layer groups, enumerate stacking operators and look up the permitted point group to predict which stacks show LEE, potentially mapping the entire space of van der Waals heterostructures."],"forward_implications":["Any of the 80 layer-group materials can exhibit the LEE in some stacking configuration, so materials discovery reduces to reading off the bilayer point group from Table I.","An out-of-plane electric field (as in a dual-gated device) selects which layer hosts the induced magnetization and reverses the sign of the response, providing an electrical on/off and sign switch.","Because inversion symmetry does not forbid the LEE, centrosymmetric bilayers—usually dismissed for Edelstein-type responses—become viable candidates for current-induced spin generation.","In Type-II systems the electric field is necessary, not just a fine-tuner: the layer-opposite spin response appears only under a field and flips when the field reverses, a clean switch.","First-principles calculations on bilayer MoSSe, MoTe2, and WTe2 indicate the predicted LEE magnitudes are observable, including at finite temperature in realistic van der Waals devices."],"fun_headline_variants":["One symmetry rule predicts layer-opposite spins in bilayers","Layer Edelstein effect: symmetry alone dictates spin orientation per layer","Opposite spins on each layer: a universal bilayer response","Layer-exchange symmetry enables current-induced spin separation"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The symmetry argument treats the bilayer as two independent layers whose spin magnetizations add up, which presumes that interlayer hybridization is weak enough not to mix the layer-resolved spin responses; the paper only states that interlayer tunneling 'can be substantially suppressed' without giving quantitative conditions in the main text.","fun_headline_variants_meta":{"raw":{"variants":["One symmetry rule predicts layer-opposite spins in bilayers","Layer Edelstein effect: symmetry alone dictates spin orientation per layer","Opposite spins on each layer: a universal bilayer response","Layer-exchange symmetry enables current-induced spin separation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000308,"raw_usage":{"total_tokens":1603,"prompt_tokens":756,"completion_tokens":847,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":500,"completion_tokens_details":{"reasoning_tokens":792}},"tokens_in":500,"tokens_out":847,"duration_ms":8387,"temperature":1.0,"reasoning_tokens":792,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T18:41:40.363089+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the layer-resolved Edelstein tensor for an inversion-stacked MoSSe bilayer using full first-principles methods that include all interlayer hybridization, and check whether an in-plane current produces exactly opposite layer magnetizations that flip with the out-of-plane field; if the layer-opposite relation fails or the response vanishes despite the bilayer having a layer-exchanging operation, the symmetry-only criterion is incomplete.","supporting_citations":[],"review_version":1}