{"id":"db0f122b-bfa6-46c6-8e84-6ac81bc7e5f3","arxiv_id":"2607.18094","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"La5Ni3O11 superconductivity is predicted to be a two-gap s± state in the bilayer subsystem, with the T_c reduction tied to a reduced interlayer-to-intralayer hopping ratio.","lead":"A symmetry-based model of the nickelate superconductor La5Ni3O11 predicts two coexisting superconducting gaps in its bilayer subsystem, one between d_z2 orbitals across layers and one between d_x2-y2 orbitals within layers. The paper argues that the lower T_c compared with La3Ni2O7 comes from weakened interlayer hopping that suppresses the leading d_z2 pairing channel.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Feasibility sieve mixes bare-TB J with QP-renormalized kinetic terms, so the leading two-gap assignment is not yet established.","rationale":"The reader's weakest assumption focuses on the ML subsystem being Mott-insulating and irrelevant. That is a legitimate concern about model completeness. However, I find a more immediately checkable consistency issue in the quantitative selection of the pairing state. Table II's acceptance criterion compares V_i, obtained from a gap equation using H_QP (with Z-renormalized hoppings), against J ≈ 4t²/U. The J values in Table II are numerically consistent with the bare TB hoppings of Table I, not with the QP hoppings used in the BdG Hamiltonian. This mixing of energy scales matters: a narrower QP band implies a larger density of states, so a smaller V_i is sufficient to reproduce a given T_c. If the bare bandwidth were used, the required V_i would be larger, potentially exceeding J_bare. Alternatively, if the QP model is the correct low-energy theory, then J should also be renormalized, and the thresholds would be much smaller, making the fitted V_i infeasible. Either way, the feasibility sieve that selects Δ_sz2 as leading is not currently well posed. This does not necessarily overturn the paper—the authors may have a legitimate reason to treat J as a bare interaction—but it must be stated and tested before the two-gap scenario can be regarded as quantitatively established. I therefore keep the reader's CONDITIONAL verdict, with the added specification of this concrete consistency check.","tokens_in":15383,"tokens_out":15507,"duration_ms":542583,"concrete_test":"Recompute the BCS gap equation for each channel in Table II using the bare TB kinetic term (unrenormalized Table I hoppings) with the same T_c = 64 K target and the same symmetry-allowed gap matrices; if the resulting V_i increases roughly by the DOS factor (~1.5–2) and exceeds the corresponding J_bare for Δ_sz2 and/or Δ_sx2+y2, the claimed feasible two-gap state fails. As a cross-check, recompute J with the Z-renormalized QP hoppings (J_QP = 4t_QP²/U) and test whether V_i ≤ J_QP; if V_i > J_QP, the bound that selects the pairing state is violated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central two-gap claim depends on Table II's feasibility test: a pairing channel is accepted only if the interaction V_i needed to reproduce T_c = 64 K does not exceed the exchange scale J ≈ 4|t|²/U. Table I lists both bare TB and Z-renormalized QP hoppings. The BdG calculation and V_i fitting use the QP model, but the J values in Table II numerically match the bare hoppings (for Δ_sz2, 4×0.631²/4.0 ≈ 0.40 eV vs listed 0.379; for Δ_sx2+y2, 4×0.487²/4.0 ≈ 0.24 eV vs listed 0.226). If the same Z-renormalized hoppings that enter H_QP are used, J_z ≈ 4×0.230²/4.0 ≈ 0.053 eV and J_x ≈ 4×0.263²/4.0 ≈ 0.069 eV, far below the fitted V_z = 0.212 eV and V_x = 0.181 eV. Because the QP hoppings are smaller, the QP DOS is larger, so the V_i needed to hit T_c = 64 K is artificially reduced; comparing that V_i with a bare-J threshold is not an internally consistent procedure. Unless the authors specify that J is a bare interaction that is not renormalized by the same Z factors, or recompute V_i on the bare TB model, the feasibility classification—and the selection of Δ_sz2 as the leading pairing—is not demonstrated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a DFT+DMFT study of the hybrid nickelate La5Ni3O11, arguing that the monolayer subsystem is Mott-insulating/incoherent and that superconductivity is confined to the bilayer subsystem. A renormalized two-orbital quasiparticle model is constructed, and a symmetry-based BCS mean-field framework with effective pairing interactions V_i in each symmetry channel is used. By fitting V_i to reproduce the experimental Tc≈64 K and imposing a feasibility bound J≈4|t|^2/U, the authors identify a leading interlayer dz2 pairing (Δ_sz2, A1g) and a subleading intralayer dx2-y2 pairing (Δ_sx2+y2), giving a fully gapped but s±-wave projected gap. They attribute the Tc reduction relative to La3Ni2O7 to the reduced hopping ratio |t_z⊥/t_x∥| and support the s± picture with RPA susceptibility calculations.","tokens_in":15795,"tokens_out":9864,"duration_ms":102451,"significance":"If the conclusions hold, the paper offers a unified symmetry-based scenario for bilayer nickelates and a concrete explanation for the reduced Tc in La5Ni3O11. The two-gap structure with s±-wave projection is consistent with existing ARPES and STM observations, and the explicit parameter tables and equations in the main text allow partial checking of the calculations. The paper is also transparent that its approach is phenomenological: V_i are fitted to Tc, not derived from first principles. However, the central result is not parameter-free, and one of its load-bearing steps—the feasibility threshold used to select the leading pairing—is internally ambiguous as presented. The work is a useful contribution to the nickelate superconductivity discussion, but the main pairing assignment requires a consistency clarification before it can be fully accepted.","major_comments":[{"comment":"The feasibility threshold J≈4|t|^2/U is defined without specifying whether t and U are bare or renormalized. The BdG calculation and the V_i fit use the QP model with the hoppings in Table I (t_z⊥≈−0.230 eV, t_x∥≈−0.263 eV). Using these QP values with the cRPA U=4.0 eV gives J_z≈4×0.230²/4.0≈0.053 eV and J_x≈4×0.263²/4.0≈0.069 eV, which are far below the fitted V_z=0.212 eV and V_x=0.181 eV. The quoted J values in Table II (0.379 and 0.226 eV) match the bare TB hoppings, not the QP hoppings. If U is also renormalized by Z², the invariance J≈4t_bare²/U could justify the comparison, but the paper does not state this. Without clarification, the classification of Δ_sz2 as feasible, and hence the central two-gap assignment, is not yet demonstrated.","section":"Table II and §'Symmetry-allowed superconducting pairings'"},{"comment":"The leading-pairing identification is conditional on the fitting procedure. V_i is determined by minimizing the BCS gap equation to reproduce Tc≈64 K, and then F_BdG,i is compared for the fitted V_i. This shows which channel is most favorable among the fitted interactions, not that Δ_sz2 is the leading instability of the microscopic model. The sentence 'we identify the leading one' overstates the predictive content. A robustness scan of V_i over the physically allowed range, or a pairing calculation with the RPA vertex instead of a Tc-fitted interaction, would substantially strengthen the claim. The paper should at minimum state this caveat explicitly.","section":"§'Symmetry-allowed superconducting pairings', Eq. (4)"},{"comment":"The central scenario assumes that the ML subsystem does not participate in pairing. The authors argue that the ML d_x2-y2 orbital has Z≈0.35 but is incoherent, so it 'may not host well-defined quasiparticles near the Fermi level that can form Cooper pairs.' This is a reasonable assumption, but it is not a demonstrated conclusion. Because the ML orbital retains a nonzero quasiparticle weight, the possibility of at least partial pairing on the ML subsystem should be discussed or estimated. As written, the two-gap picture is limited to the BL subsystem, and the manuscript would be strengthened by an explicit statement of the associated uncertainty.","section":"§'Correlated electronic structure', after Fig. 2"}],"minor_comments":[{"comment":"Typos: 'an unified' should be 'a unified'; 'Base on' should be 'Based on'.","section":"Abstract"},{"comment":"The section title reads 'La5Ni3O10' but should be 'La5Ni3O11'.","section":"Section title 'Symmetry-allowed superconducting pairings'"},{"comment":"The definition of Z as 'the diagonal QP spectral weight matrix' is clear for diagonal entries, but the treatment of off-diagonal/inter-orbital Z factors in H_QP is not specified. Please clarify whether Z is assumed diagonal or how off-diagonal terms are handled.","section":"Eq. (1)"},{"comment":"The Γ-matrix notation is very compact. A table or explicit formula listing all independent pairing channels, their matrix forms and the corresponding pairing harmonics would help readers verify the group-theoretical classification.","section":"Table II"},{"comment":"For the DOS and superconducting gap sizes, please state whether thermal broadening or a finite lifetime is included, and how the gap values are extracted. For the RPA calculation, specify the numerical value of U, the code used, and whether the Z² renormalization is applied to the interaction before the RPA susceptibility is computed.","section":"Figure 3(c)-(d), Figure 4"},{"comment":"Reference [67] contains a placeholder '[link to be inserted by publisher]' for the Supplemental Material; this should be completed before publication.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope and the overall framework is coherent, but the feasibility-threshold ambiguity in Table II is a genuine obstacle to the central claim. I do not see grounds for rejection: if the authors clarify the renormalization of U in J (or recompute the thresholds on the QP model) and add the requested robustness caveats, the manuscript could be suitable for publication. The paper cites a large number of closely related preprints from 2026, including the authors' own previous work on La3Ni2O7; the novelty relative to that work should be emphasized more clearly in the final version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new thing here is a symmetry-based two-gap picture for La5Ni3O11: leading interlayer d_z2 pairing (Δ_sz2) plus subleading intralayer d_x2-y2 pairing (Δ_sx2+y2), with the T_c reduction relative to La3Ni2O7 attributed to a reduced interlayer hopping ratio. The DFT+DMFT calculation is careful, the orbital-selective Mott behavior is clearly documented, and the RPA cross-check is a nice touch. The symmetry enumeration of pairing channels is systematic and should be useful to the nickelate community.\n\nBut the central quantitative claim — that Δ_sz2 is the leading pairing — depends on a feasibility test in Table II that does not survive scrutiny. The BdG calculation and the V_i fitting use the Z-renormalized QP hoppings, yet the J ≈ 4t²/U thresholds are computed from the bare hoppings in Table I. Let's be concrete: for Δ_sz2, the bare interlayer hopping is 0.631 eV, giving J ≈ 0.38 eV; using the QP renormalized hopping 0.230 eV, J drops to about 0.05 eV, far below the fitted V = 0.212 eV. For Δ_sx2+y2 the same problem appears. So if J is renormalized consistently, every singlet channel becomes infeasible, and the selection of Δ_sz2 as leading is not demonstrated. The authors need to state which J they mean and either recompute V_i on the bare model or derive the effective J in the QP model. This is not a cosmetic issue; it is load-bearing.\n\nA second limitation: T_c is an input, not an output. The V_i are adjusted to reproduce 64 K, so the theory does not predict T_c. The explanation of the reduced T_c is inferred from V/J ratios and the hopping ratio, but no direct computation shows that the two-gap state with these parameters would lose T_c if the interlayer coupling is weakened. The comparison between the two materials remains qualitative.\n\nThe assumption that the monolayer subsystem is irrelevant is plausible given the DMFT self-energies, but it is an assumption; if the d_x2-y2 orbital with Z≈0.35 participates in pairing despite incoherence, the two-gap picture would need revision. I also note the supplemental derivations are missing from the preprint, which makes the symmetry analysis hard to verify.\n\nOverall, this is a serious paper with a legitimate qualitative scenario, but the quantitative ranking is not yet established. With the J-consistency issue fixed, it could be a meaningful contribution. I would send it to peer review, but a referee should press hard on that feasibility test and ask for a test where T_c is at least shown to be suppressed in the model as the interlayer hopping ratio decreases.","headline":"The paper's two-gap scenario for La5Ni3O11 is plausible and the symmetry framework is useful, but the quantitative ranking of the leading pairing rests on an internally inconsistent feasibility test that mixes bare and renormalized parameters.","tokens_in":16266,"tokens_out":2469,"would_cite":false,"duration_ms":28886,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.20.-z","74.70.-b","71.27.+a"],"model":"deepseek-v4-flash","headline":"Superconductivity in La5Ni3O11 is a two-gap state: interlayer dz2 pairing dominates, and a weaker intralayer dx2-y2 channel explains the reduced 64 K Tc.","keywords":["La5Ni3O11","nickelate superconductors","two-gap superconductivity","s±-wave pairing","interlayer pairing","orbital-selective correlations","DFT+DMFT","symmetry-based pairing analysis"],"falsifier":"Measure the superconducting gap on the β pocket of La5Ni3O11 with high-resolution ARPES or STM: the theory predicts a nodeless gap along Γ-M but accidental nodes on the β pocket. Also, a pressure-dependent study that tracks the interlayer hopping ratio |t⊥^z / t∥^x| should show Tc rising with this ratio if the central claim is correct.","tokens_in":15293,"feed_emoji":"🔬","tokens_out":6868,"duration_ms":64160,"temperature":0.7,"pith_summary":"La5Ni3O11, a hybrid nickelate made of alternating bilayer and monolayer blocks, superconducts at about 64 K under pressure—lower than the 80 K of the bilayer compound La3Ni2O7. The paper argues that the superconductivity lives entirely in the bilayer subsystem and is a two-gap state: a dominant interlayer pairing between nickel dz2 orbitals and a subleading intralayer pairing between dx2-y2 orbitals. The reduced transition temperature is explained by a weaker interlayer hopping ratio, which diminishes the leading pairing channel. A sympathetic reader should care because this offers a single symmetry-based mechanism that connects several nickelate superconductors, with a concrete control parameter for Tc.","feed_headline":"Two-gap state explains La5Ni3O11's 64 K superconductivity","feed_subtitle":"A weaker interlayer dz2 pairing channel, traced to a reduced hopping ratio, accounts for the drop from 80 K to 64 K.","key_machinery":"The central object is a renormalized quasiparticle Hamiltonian for the bilayer subsystem, built from orbital-selective quasiparticle weights Z derived from DFT+DMFT self-energies. On top of this, the paper defines a symmetry-based pairing analysis: all symmetry-allowed pairing matrices compatible with the p4/mmm layer group, time-reversal, and particle-hole symmetry are written down, and each is solved self-consistently at the mean-field level to reproduce Tc ≈ 64 K. The decisive comparison is the BCS condensation energy of each candidate, which selects the Δ_sz2 + Δ_sx2+y2 two-gap state. The mechanism connecting structure to Tc is the hopping ratio |t⊥^z / t∥^x|, which tracks the relative s","core_discovery":"Using charge self-consistent DFT+DMFT, the authors find that in La5Ni3O11 the monolayer subsystem is a Mott insulator (with the dx2-y2 orbital too incoherent to form quasiparticles), leaving the bilayer subsystem as the only source of Cooper pairs. Enumerating all pairing symmetries allowed by the p4/mmm layer group and comparing their BCS condensation energies, they identify the leading instability as an A1g interlayer pairing between Ni dz2 orbitals (Δ_sz2), coexisting with a subleading A1g intralayer pairing between Ni dx2-y2 orbitals (Δ_sx2+y2). The combined state is fully gapped along high-symmetry directions but is s±-wave on the Fermi surface, with accidental nodes on the β pocket; it","pith_inferences":["The authors do not explore, but the same symmetry-based logic would predict stacking-dependent Tc across other hybrid nickelates, controlled by the same interlayer-to-intralayer hopping ratio.","The strongest testable extension is materials engineering: selectively increasing interlayer dz2 hopping while leaving intralayer dx2-y2 hopping fixed should push Tc upward in La5Ni3O11, a prediction the paper implies but does not state.","If the monolayer dx2-y2 orbital ever gains coherence (e.g., under different pressure or doping), the two-gap scenario would need a third gap, so the paper's scope is tied to the Mott-insulating assignment."],"forward_implications":["If correct, La5Ni3O11 and pressurized La3Ni2O7 share a common two-gap mechanism, differing only in the relative strength of the interlayer channel.","The predicted fully gapped but sign-changing s±-wave gap with accidental nodes on the β pocket gives a concrete, testable spectral fingerprint.","The theory explains why thin-film La3Ni2O7 (Tc ≈ 40 K) favors the intralayer channel and why in-plane, not out-of-plane, strain raises Tc.","It implies that raising Tc requires simultaneously enhancing the interlayer exchange interaction and suppressing the intralayer exchange interaction.","The ratio |t⊥^z / t∥^x| becomes a control parameter for Tc across bilayer-containing nickelates."],"fun_headline_variants":["Mott monolayer shuts down, bilayer dz2 pairs alone in La5Ni3O11","Two-gap model: weak dz2 interlayer hopping drops Tc to 64 K","La5Ni3O11's superconductivity: interlayer dz2 dominates, dx2y2 assists","Symmetry rules pinpoint why La5Ni3O11 is a 64 K superconductor","How La5Ni3O11 loses 16 K: Mott monolayer and hopping ratio"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the monolayer subsystem cannot host Cooper pairs because it is Mott-insulating and incoherent; if its dx2-y2 orbital turns out to contribute coherent quasiparticles or pairing, the two-gap scenario is incomplete.","fun_headline_variants_meta":{"raw":{"variants":["Mott monolayer shuts down, bilayer dz2 pairs alone in La5Ni3O11","Two-gap model: weak dz2 interlayer hopping drops Tc to 64 K","La5Ni3O11's superconductivity: interlayer dz2 dominates, dx2y2 assists","Symmetry rules pinpoint why La5Ni3O11 is a 64 K superconductor","How La5Ni3O11 loses 16 K: Mott monolayer and hopping ratio"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000529,"raw_usage":{"total_tokens":2464,"prompt_tokens":901,"completion_tokens":1563,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":645,"completion_tokens_details":{"reasoning_tokens":1444}},"tokens_in":645,"tokens_out":1563,"duration_ms":15095,"temperature":1.0,"reasoning_tokens":1444,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T16:00:24.377048+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the superconducting gap on the β pocket of La5Ni3O11 with high-resolution ARPES or STM: the theory predicts a nodeless gap along Γ-M but accidental nodes on the β pocket. Also, a pressure-dependent study that tracks the interlayer hopping ratio |t⊥^z / t∥^x| should show Tc rising with this ratio if the central claim is correct.","supporting_citations":[],"review_version":1}