{"id":"fba62998-4e7b-4833-8a52-546787004c86","arxiv_id":"2510.06313","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Near the relativistic Mott transition, quantum-critical fluctuations of time-reversal-even collective modes induce superconductivity in twisted WSe2 and TBG, with a rich spectrum of degenerate pairing states.","lead":"This theory paper predicts that superconductivity can appear exactly at the semimetal-insulator (Gross-Neveu) transition in twisted double-bilayer WSe2 and twisted bilayer graphene, driven by quantum-critical fluctuations of collective modes. It classifies the allowed superconducting states and links them to charged skyrmions in the neighboring insulator.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"SC claim rests on unverified η_ψ threshold from Ref. [27]; without a microscopic η_ψ, existence prediction is conditional, though pairing classification is solid.","rationale":"We agree with the reader's weakest-assumption identification: the superconducting-instability mechanism is imported from the unpublished companion, and the physical condition η_ψ > η_c^ψ is never established. This is load-bearing because the paper's headline predictions (four states in WSe2, six in TBG, T_c up to 0.4 K) are explicitly conditional on this threshold; the algebraic classification and the WZW/skyrmion correspondence are independent and remain interesting even if the threshold is not met. We did not find an internal inconsistency in Eq. (5) or the group-theoretic enumeration; the conditions appear to be applied consistently, and the time-reversal parity assignments in Table I were checked. The main gap is a physics input, not a logic error. Therefore the reader's CONDITIONAL verdict is appropriate; we do not recommend changing it. A microscopic computation of η_ψ is the decisive next step.","tokens_in":15214,"tokens_out":13770,"duration_ms":95760,"concrete_test":"Compute the fermion anomalous dimension η_ψ at the critical point of the actual 2+1D Gross-Neveu-Yukawa model relevant to double-bilayer WSe2 (N_f=4 Dirac fermions, chiral Ising/GN ordering) using large-scale determinant quantum Monte Carlo, and concurrently measure the pairing susceptibility in the A1 and B1 channels of Eqs. (9)-(10). If η_ψ is below ≈0.146 and/or the pairing susceptibility does not diverge as the critical point is approached, the paper's existence prediction for WSe2 is falsified; if η_ψ exceeds the threshold and the pairing susceptibility diverges, the concern is resolved. The same check with N_f=8 would cover TBG.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's existence claim — actual superconductivity at the relativistic Mott transitions in twisted WSe2 and TBG — rests on two unverified imports from companion Ref. [27]: the Eliashberg kernel (Eq. 2), the coupling λ_p (Eq. 3), and the threshold η_c^ψ≈0.146. The authors never compute η_ψ for either material, and footnote [45] explicitly states that the precise threshold value 'will depend on details beyond the scope of our analysis.' This is not pedantic: for 2+1D Gross-Neveu universality classes, η_ψ is typically of order 0.1 and is not guaranteed to exceed 0.146; it depends on the number of flavors and on which order parameter condenses. If the physical η_ψ falls below threshold, the system stays in the quasi-particle regime and the predicted T_c≈0.4 K does not follow, even though the algebraic classification of allowed channels (Eq. 5, Tables I–II) would remain correct. There is also an uncontrolled step between the large-N melonic SYK limit and physical systems with only n_γ=8 or 16 fermion components. The paper is transparent about this, but the central physical prediction is therefore conditional on a parameter that is neither computed nor measured.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies a generalized SYK framework, developed in the companion paper Ref. [27], to study superconductivity near Gross-Neveu (relativistic Mott) critical points in twisted double-bilayer WSe2 and twisted bilayer graphene (TBG). The central input is a critical boson–fermion model (Eq. (1)) whose pairing instability is governed by the linearized Eliashberg equation (Eq. (2)) with dimensionless pairing strength λ_p (Eq. (3)) determined solely by the fermion anomalous dimension η_ψ. The authors then derive algebraic conditions (Eq. (5)) that select the allowed pairing channels for a given collective bosonic mode: [Γ_J, α_i]=0 and Γ_J Υ_a = τ_φ Υ_a Γ_J, together with Fermi statistics. Applying these conditions to the Dirac theories of WSe2 and TBG, they find: for WSe2, all time-reversal-even gap-opening fluctuations induce pairing, but time-reversal-odd ones do not, yielding four degenerate states (Eqs. (9)–(11)); for TBG, KIVC and TIVC fluctuations each give four degenerate states (Eqs. (15), (16)), with six distinct states in total. They further show that a subset of these pairing states satisfies the additional trace condition (Eq. (18)) for a Wess-Zumino-Witten (WZW) term, linking the pairing to charge-carrying skyrmions in the proximate insulator. Using the maximal T_c from Ref. [27], they estimate T_c ≈ 0.4 K for both materials. The paper is transparent in footnote [45] that the threshold value η_c^ψ ≈ 0.146 is model-dependent, but the existence of a threshold is p","tokens_in":15547,"tokens_out":4608,"duration_ms":34947,"significance":"If the framework is valid, this work provides a concrete and experimentally testable scenario for superconductivity near relativistic Mott transitions in twisted Dirac materials, with a rich, symmetry-dictated spectrum of pairing states and a topological mechanism for pairing via skyrmions. The algebraic classification in Eq. (5) and the tables are internally consistent, checkable, and likely correct; they constitute a useful group-theoretic catalog independent of the dynamical details. The connection between the pairing conditions and the WZW-term criteria (Eq. (B1)) is elegant and is a genuinely new observation. The paper is also honest about the main caveat—that the threshold η_ψ ≥ η_c^ψ is not computed for the specific materials. However, the central existence claim (T_c ≈ 0.4 K, 'one should expect either superconductivity or strong pairing fluctuations') rests on two unverified imported ingredients from Ref. [27]: the Eliashberg kernel (Eq. (2)) and the threshold η_c^ψ, plus an uncontrolled extrapolation from the large-N melonic limit to the physical n_γ=8 or 16 systems. The classification would survive even if η_ψ falls below threshold, but the predicted superconductivity wou","major_comments":[{"comment":"The claim that superconductivity actually occurs in twisted WSe2 and TBG near the Mott transition depends entirely on whether the physical anomalous dimension η_ψ exceeds η_c^ψ ≈ 0.146. The paper never computes η_ψ for these systems; footnote [45] explicitly states that the precise threshold 'will depend on details beyond the scope of our analysis.' For 2+1D Gross-Neveu universality classes, η_ψ is typically O(0.1) and is not guaranteed to exceed 0.146; it depends on the number of fermion flavors and on which order parameter condenses. As stated, the T_c ≈ 0.4 K estimate and the abstract's claim that 'superconductivity can emerge' are therefore conditional on a parameter that is neither computed nor measured. This is load-bearing: if η_ψ < η_c^ψ, the algebraic classification (Eq. (5), Tables I–II) remains correct but the central physical prediction fails. The authors should either comput","section":"Eq. (2), footnote [45], and 'To estimate T_c'"},{"comment":"The kernel (Eq. (2)) and λ_p (Eq. (3)) are derived in a generalized SYK model with random couplings among N fermion flavors, in a melonic large-N limit. The physical systems have only n_γ=8 (WSe2) or n_γ=16 (TBG) components. The paper does not discuss whether 1/N corrections are small for these values, nor does it test the robustness of the result to the random-coupling assumption. This is an uncontrolled step between the controlled large-N limit and the physical Dirac theories. The authors should provide at least a rough estimate of the corrections for N=8,16, or otherwise justify why the melonic result applies to these small representations.","section":"SYK large-N limit"},{"comment":"In the main text, the authors state 'we find in total 56 such partner states' for TBG, but Appendix B counts 336 triples before restricting to order parameters that all transform the same under time reversal; only 56 survive that restriction. The phrase 'in total' is misleading and the reader may infer fewer states than actually satisfy the WZW condition. Please clarify the counting and the restriction in the main text.","section":"WZW partner-state counting"}],"minor_comments":[{"comment":"Typo in title: 'T wisted' should be 'Twisted'.","section":"Title"},{"comment":"There are missing spaces in phrases such as 'atfilling𝜈=2' and 'theDirac point is right at the Fermi level' (intro). Please run a spell/format check.","section":"Various"},{"comment":"The caption's explanation of the +− and ++ labels for 𝜇_z and 𝜇_0 is cryptic; please spell out the convention more clearly.","section":"Figure 2 caption"},{"comment":"The phrase 'in total 56 such partner states' should be clarified to indicate that this is the count after restricting to triples whose components transform the same under time reversal, not the total number of triples satisfying Eq. (18).","section":"Appendix B / main text"}],"recommendation":"major_revision","confidential_remarks":"The paper leans very heavily on the companion manuscript Ref. [27] for the central dynamical input (Eqs. (2), (3), and η_c^ψ). Editors may wish to ensure that the companion is available and has passed review, since the validity of the existence claim depends on it. The symmetry-based classification is self-contained and valuable; the revision should focus on either computing η_ψ for the relevant GN transitions or clearly reframing the paper as a conditional classification plus a threshold conjecture."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: what's genuinely new here is the classification. The authors take the pairing mechanism from their companion paper [27] and work out the allowed superconducting channels for twisted double-bilayer WSe2 and TBG using the algebraic conditions of Eq. (5). That classification, including the degeneracies and the 56 WZW/skyrmion partner states for TBG, is a useful addition and appears internally consistent. The paper is also refreshingly transparent: footnote 45 and the discussion around Fig. 1 are upfront about the load-bearing assumptions.\n\nThe soft spot is the existence claim — the 'T_c ≈ 0.4 K' and the assertion that superconductivity actually appears at these transitions. That comes from the generalized SYK framework of Ref. [27]: the Eliashberg kernel, the pairing strength λ_p, and the threshold η_c^ψ ≈ 0.146 are all imported, and the authors never compute η_ψ for either material. In 2+1D Gross-Neveu universality classes η_ψ is typically around 0.1 and is not guaranteed to exceed 0.146; it depends on flavor number and the order-parameter channel. The paper does not bridge the large-N melonic limit to the physical n_γ = 8 or 16. So the prediction is conditional in a real sense, not just a formal one. But this is not circular, and the authors don't hide it. The classification would survive even if η_ψ falls below threshold.\n\nWhat I'd want before taking the 0.4 K prediction to the bank: the companion paper [27] out, and either a microscopic computation of η_ψ for these systems or a clear argument about why the large-N estimate transfers. The WZW/skyrmion connection is a nice extra, and the list in Appendix B is useful in its own right.\n\nBottom line: this deserves a serious referee. The classification is solid and worth having even if the existence claim is eventually weakened. I'd send it out, with the companion paper made available. For my own work, I'd cite the classification tables but not the T_c estimate.","headline":"A solid group-theoretic classification of pairing channels in twisted WSe2 and TBG, with an honest but conditional superconductivity existence claim resting on an uncomputed anomalous dimension.","tokens_in":16027,"tokens_out":2140,"would_cite":true,"duration_ms":18184,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Near the relativistic Mott transition in twisted double-bilayer WSe2 and twisted bilayer graphene, quantum-critical fluctuations of gap-opening collective modes can bind strongly incoherent electrons into superconductivity, with the allowed","keywords":["twisted bilayer graphene","twisted double-bilayer WSe2","Gross-Neveu transition","quantum criticality","superconductivity without quasiparticles","skyrmions","Dirac semimetal","large-N random-coupling theory"],"falsifier":"A numerical determination of the fermion anomalous dimension η_ψ at the Gross-Neveu critical point in a microscopic lattice model of twisted double-bilayer WSe2 or twisted bilayer graphene that yields η_ψ below ≈0.146 would falsify the claim that these materials superconduct through this mechanism, while leaving the algebraic classification of allowed pairing states intact.","tokens_in":15133,"feed_emoji":"🌀","tokens_out":8935,"duration_ms":59066,"temperature":0.7,"pith_summary":"This paper argues that superconductivity can appear at the exact twist angle where twisted Dirac materials turn into insulators, driven by the same critical fluctuations that make electrons incoherent. It identifies which collective modes promote pairing in two concrete systems. In twisted double-bilayer WSe2, only time-reversal-even modes do, yielding four nearly degenerate pairing states. In twisted bilayer graphene, fluctuations of inter-valley-coherent order produce six degenerate or nearly degenerate superconducting states, some with finite momentum. The paper also shows that these same conditions are precisely those for charged skyrmions in the insulator, linking the superconducting and topological sectors.","feed_headline":"Incoherent electrons can superconduct at twisted Dirac Mott transition","feed_subtitle":"Quantum-critical fluctuations of gap-opening order predict superconductivity near 0.4 K in WSe2 and TBG.","key_machinery":"The paper's strong-coupling framework is a generalized large-N random-coupling theory in which melonic diagrams dominate and give universal power laws for the critical fermion and boson propagators, characterized by the fermion anomalous dimension η_ψ. The Eliashberg equation for the anomalous self-energy has a kernel that is universal at the Gross-Neveu critical point, with a dimensionless pairing strength λ_p that grows with η_ψ; superconductivity requires η_ψ ≥ η_c^ψ ≈ 0.146. The central algebraic selection rule is Eq. (5): a pairing matrix Γ_J must commute with the Dirac matrices and satisfy Γ_J Υ_a = τ_φ Υ_a Γ_J, which together with Fermi statistics fixes which pairing states each colle","core_discovery":"The paper establishes that, for a generic two-dimensional Dirac system at its Gross-Neveu (relativistic Mott) critical point, the superconducting instability is governed entirely by the algebraic relations between the pairing matrices and the collective-mode coupling matrices: [Γ_J, α_i]=0 and Γ_J Υ_a = τ_φ Υ_a Γ_J. Applying this to AB-BA stacked twisted double-bilayer WSe2 at filling ν=2, it finds that all time-reversal-even, gap-opening bosons promote pairing — producing four degenerate states, most typically an s-wave state — while time-reversal-odd modes (Haldane, spin-Hall, Kekulé loop-current variants) do not. In a Dirac model of twisted bilayer graphene with the mini-valley flavor inc","pith_inferences":["If the threshold η_c is a general feature, the same mechanism could apply to other twisted Dirac systems, suggesting that superconductivity near correlation-driven gap openings may be more widespread than currently suspected.","The degeneracy among the four WSe2 states is an artifact of the continuum Dirac theory; lattice corrections will lift it. A natural next step is to compute which specific state survives — the paper leaves that hierarchy open.","The coincidence with the skyrmion/WZW conditions suggests the predicted superconducting states may have topological signatures (e.g., chiral or helical Cooper pair wavefunctions) even though the paper does not establish topology explicitly.","A microscopic calculation or measurement of η_ψ at the transition in each material would turn the qualitative prediction into a quantitative one; experiments could look for a dome of T_c peaking at the critical twist angle."],"forward_implications":["At the critical twist angle where twisted double-bilayer WSe2 becomes insulating, superconductivity or at least strong pairing fluctuations are predicted; the dominant instability is one of four degenerate pairing states, with an s-wave (A1) state the most common outcome.","In twisted bilayer graphene, both KIVC and TIVC fluctuations at the onset of inter-valley-coherent order promote pairing, yielding six distinct degenerate or nearly degenerate superconducting states, some with finite center-of-mass momentum.","The mechanism only works when electrons are strongly incoherent — well-defined quasiparticles would not pair this way — and the richer the Dirac structure (16-component in TBG vs 8-component in WSe2), the more readily pairs form.","The algebraic conditions that select pairing states coincide with the conditions for a Wess-Zumino-Witten term, so insulators with charged skyrmions are a subset of the pairing states; skyrmions carry charge 2e in WSe2 and 4e in TBG.","With a Dirac cutoff of about 20 meV, the optimal transition temperature is about 0.4 K."],"fun_headline_variants":["Incoherent electrons superconduct at twisted Dirac Mott transition","Superconductivity from incoherent electrons at twisted Dirac Mott transition","Twisted Dirac Mott transition: pairing from incoherent electrons","Twisted Dirac Mott transition leads to superconductivity of incoherent electrons","Relativistic Mott transition in twisted Dirac materials enables incoherent pairing"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The superconductivity result rests on adopting the companion paper's Eliashberg kernel and on the assumption that the Gross-Neveu transitions in twisted WSe2 and TBG are in the generalized large-N limit with a fermion anomalous dimension above the universal threshold (about 0.146); the paper does not compute this anomalous dimension from a microscopic model, and the authors explicitly say the precise threshold value is not their key prediction.","fun_headline_variants_meta":{"raw":{"variants":["Incoherent electrons superconduct at twisted Dirac Mott transition","Superconductivity from incoherent electrons at twisted Dirac Mott transition","Twisted Dirac Mott transition: pairing from incoherent electrons","Twisted Dirac Mott transition leads to superconductivity of incoherent electrons","Relativistic Mott transition in twisted Dirac materials enables incoherent pairing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000725,"raw_usage":{"total_tokens":3069,"prompt_tokens":708,"completion_tokens":2361,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":452,"completion_tokens_details":{"reasoning_tokens":2276}},"tokens_in":452,"tokens_out":2361,"duration_ms":14467,"temperature":1.0,"reasoning_tokens":2276,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T11:11:00.779978+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A numerical determination of the fermion anomalous dimension η_ψ at the Gross-Neveu critical point in a microscopic lattice model of twisted double-bilayer WSe2 or twisted bilayer graphene that yields η_ψ below ≈0.146 would falsify the claim that these materials superconduct through this mechanism, while leaving the algebraic classification of allowed pairing states intact.","supporting_citations":[],"review_version":1}