{"id":"5d73345f-5631-4450-bed3-7cc824923eb3","arxiv_id":"1909.00060","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"First-principles models plus fluctuation-exchange calculations suggest the infinite-layer nickelate (Nd,Sr)NiO2 pairs electrons with d_x2-y2 symmetry like the cuprates, with a reduced Tc caused by stronger interactions and a narrower bandwidth.","lead":"This paper builds computer models of a newly discovered nickel-based superconductor that resembles the copper oxide superconductors (cuprates). It predicts that the nickelate pairs electrons in the same d-wave pattern as cuprates, but with a lower transition temperature because its electrons interact more strongly.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The load-bearing step is FLEX itself: with U_dx2-y2 ≈ 4.2 eV and a narrow Ni band, the doped nickelate sits outside the controlled weak-coupling regime, and the paper's own mother-compound caveat shows the method's limits at large U/W.","rationale":"The reader's weakest_assumption matches my own analysis: FLEX quantitative reliability is the main risk. The paper performs many useful internal consistency checks (six- versus seven-orbital, La versus Nd, Ba versus Sr, two-orbital with different U values), and these support the model construction. However, none of these checks tests the core many-body approximation. The paper's own concession in the Mother nickelate section indicates the method cannot handle the undoped strong-correlation regime; the doped case, while away from half-filling, still has U/W well above the weak-coupling range. Because the conclusion about the pairing symmetry and reduced Tc is extracted from the FLEX eigenvalue, the argument would fail if a more accurate method changed the leading pairing symmetry or reversed the λ ordering between nickelate and cuprate. I therefore flag this as the load-bearing concern. That said, the paper's language is consistently qualified — 'likely,' 'suggests,' 'possibility' — and the FLEX limitation is disclosed. The study is a well-executed computational prediction, not an overclaimed proof. For that reason the reader's ACCEPT verdict stands with moderate confidence; no verdict change is needed, though a non-perturbative cross-check would materially strengthen the central claim.","tokens_in":11970,"tokens_out":8108,"duration_ms":76095,"concrete_test":"Run the same two-orbital p=0.2 model (Ni dx2-y2/d3z2-r2, cRPA U=4.19 eV, U'=3.13 eV, J=0.73 eV, Wannier-derived hoppings) with a non-perturbative method — e.g. cellular DMFT with an exact-diagonalization impurity solver or determinant quantum Monte Carlo on a 4x4 cluster — at T=0.005 eV, and compute the leading pairing susceptibility/eigenvalue and its symmetry. If the d_x2-y2 eigenvalue is no longer the leading one, or if λ_nickelate no longer lies below λ_cuprate under the same method, the central claim weakens; if the ordering and symmetry are reproduced, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim — that dx2-y2 pairing is likely and that a larger U_dx2-y2 plus narrower bandwidth lowers Tc — is derived entirely from the FLEX approximation. FLEX is a conserving weak-coupling scheme whose accuracy degrades when U/W ≳ 1. Here U_dx2-y2(p=0.2)=4.19 eV, while the Ni dx2-y2 Wannier band is narrow (the paper explicitly contrasts it with the cuprates' wider band), so the model is in the strong-coupling regime. The authors acknowledge this for the mother compound: \"The FLEX approximation cannot treat electron correlation effects in such a regime,\" and they decline to analyze superconductivity there. The doped case is then studied with the same machinery, at even slightly larger U (4.19 vs 3.81 eV) but away from half-filling. The comparison of λ between nickelate and cuprate, and the attribution of the difference to U, therefore rests on an uncontrolled approximation. No non-perturbative benchmark (DMFT, fRG, determinant QMC) is provided to show that the FLEX eigenvalue ordering and leading d_x2-y2 symmetry survive at U/W>1. The paper is transparent and internally consistent, so the qualitative suggestion is plausible, but the quantitative 'lower Tc because of larger U' step is not settled by the evidence presented.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs realistic low-energy multiorbital models for the newly discovered infinite-layer nickelate superconductor (Nd,Sr)NiO2, using LDA with maximally localized Wannier functions and cRPA for interaction parameters. The authors propose a seven-orbital model containing Ni 3d and La 5d orbitals, argue that the mother compound is self-doped and metallic because La-derived electron pockets transfer about 0.06 holes into the Ni dx2-y2 orbital, and then use the FLEX approximation on a six-orbital variant to study the doped p=0.2 compound. The central claim is that the leading superconducting instability is dx2-y2-wave pairing as in the cuprates, but with a lower transition temperature than HgBa2CuO4 because U_dx2-y2 is larger and the Ni dx2-y2 bandwidth is narrower. The paper also reports a two-orbital model comparison, a cRPA-based comparison with a five-orbital cuprate model, and a discussion of the role of the large dp level offset.","tokens_in":12141,"tokens_out":4782,"duration_ms":46013,"significance":"If the central claim holds, this is a valuable early theoretical response to the discovery of superconductivity in the nickelates: it gives a concrete first-principles-based multiorbital description, a specific pairing symmetry prediction, and a falsifiable mechanism (larger U and narrower bandwidth suppress Tc, so pressure or reduced lattice constant should enhance Tc). The paper is carefully executed in several respects: the seven-orbital and six-orbital FLEX results agree at T=0.03 eV, the La/Nd and Ba/Sr substitutions are checked against VASP band structures in the supplemental material, and the cRPA interaction parameters are reported in full tables. The authors also transparently state the limitation of FLEX in the strongly correlated regime of the mother compound. The main weakness is that the quantitative Tc-lowering mechanism is derived solely from FLEX, whose validity is not benchmarked in the large-U regime relevant to the doped nickelate.","major_comments":[{"comment":"The central quantitative conclusion—that dx2-y2 pairing is likely and that the lower Tc relative to the cuprate arises from the larger Udx2-y2 and narrower bandwidth—rests entirely on the FLEX approximation. FLEX is a weak-coupling conserving scheme whose accuracy degrades in the strong-correlation regime. With Udx2-y2 = 4.19 eV for p=0.2 (Table I) and a Ni dx2-y2 band that the paper explicitly describes as narrower than the cuprate band, the model has U/W on the order of or exceeding one. The paper itself states in the 'Mother nickelate' section that 'The FLEX approximation cannot treat electron correlation effects in such a regime,' and this caution is not limited to the undoped compound. No non-perturbative benchmark (e.g., DMFT, fRG, or determinant QMC on a minimal two-orbital or one-band model with the relevant U/t) is provided to show that the leading d-wave symmetry and the ordering of the Eliashberg eigenvalues between nickelate and cuprate survive in this regime. Consequently, the attribution of the lower Tc to the larger U is plausible but not quantitatively established. I would ask the authors either to provide such a benchmark on a reduced model or to explicitly restrict the claim to a qualitative spin-fluctuation scenario.","section":"Doped nickelate, Fig. 3 and Table I"},{"comment":"The direct comparison of the Eliashberg eigenvalue lambda between the nickelate six-orbital model (8x8x8 k-mesh, 8192 Matsubara frequencies) and the cuprate five-orbital model (32x32x2 k-mesh, 4096 Matsubara frequencies) is used to conclude that the nickelate has a smaller lambda. The numerical parameters differ substantially between the two calculations, and no convergence study with respect to k-mesh or frequency cutoff is presented for the comparison. The authors should state why this difference in numerical settings does not affect the relative ordering of lambda, or provide a check with a comparable k-mesh for the cuprate.","section":"Doped nickelate, Fig. 3"}],"minor_comments":[{"comment":"In the caption of Table S2, the orbital index list says 'Ni 3dx2-y2' for the HgBa2CuO4 model; this should read 'Cu 3dx2-y2'.","section":"Supplemental Material, Table S2"},{"comment":"The paper uses 'd9 configuration' as a starting point but later computes nNi(dx2-y2) = 0.94, so the wording 'approximately d9' would be more precise in the introduction and abstract.","section":"Mother nickelate"},{"comment":"The inset of Fig. 3(a) is described in the caption as a log-log plot of lambda vs T, but the panel itself has no axis labels; adding labels would improve readability.","section":"Fig. 3"},{"comment":"The statement that 'the main origin of the reduction of lambda in the six-orbital model is the large renormalization effect due to the large Udx2-y2' is supported by the two-orbital comparison, but this conclusion is phrased more strongly than the evidence allows because both the interaction strength and the orbital content change between the two-orbital and six-orbital models; a sentence qualifying the inference would be helpful.","section":"Doped nickelate"}],"recommendation":"major_revision","confidential_remarks":"The paper is timely and the model construction is carefully cross-checked, but the main physical claim is carried by FLEX in a parameter regime where the method is uncontrolled. I would be satisfied if the authors either add a non-perturbative check on a reduced model or soften the quantitative claim about the origin of the lower Tc. The paper is not fatally flawed; the issue is that the central mechanism needs either support or more explicit hedging."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou know the nickelate story; this is one of the first theory papers on the infinite-layer superconductor. The take-home: it is a careful, transparent model-construction paper that gives a plausible mechanism for cuprate-like pairing and explains the lower Tc as a consequence of larger interactions. It is not a smoking gun, but it is a solid, honest piece of work.\n\nWhat is genuinely new: they build a seven-orbital low-energy model that explicitly includes the La 5d states (not just Ni 3d), compute cRPA interactions, and show that self-doping holes out of the Ni dx2-y2 band—roughly 0.06 per cell—makes the mother compound metallic. That self-doping picture is interesting and consistent with experiment. They also carefully cross-check La vs Nd, Ba vs Sr, and six- vs seven-orbital models. The FLEX calculations use standard methods, and the comparison with cuprates uses a five-orbital HgBa2CuO4 model to keep things fair. No post-hoc fitting, no circular derivation.\n\nThe soft spot is the one they themselves admit: FLEX is a weak-coupling scheme, and the doped nickelate sits at U/W > 1 (U_dx2-y2 ≈ 4.2 eV with a narrow band). They say FLEX \"cannot treat electron correlation effects\" in the undoped regime, then use it for the doped case. The stress-test note is right that no DMFT or QMC benchmark is given. So the quantitative claim—lower Tc because of larger U—is not settled by the evidence. The qualitative direction is plausible and physically well-motivated; spin-fluctuation-mediated d-wave pairing is a reasonable hypothesis. But the eigenvalue λ does not directly give Tc, and strong correlations could in principle change the ordering. I'd like to see a non-perturbative check of the leading pairing symmetry before taking the mechanism as established.\n\nMinor points: the 0.06 self-doping is a small number and may be sensitive to the DFT functional; the cuprate comparison relies on their own earlier cRPA parameters, but that is a consistent choice. No code or data is shipped, but the methods are standard and the ecalj package is open source, so it is reproducible in principle.\n\nWho should read it: anyone working on nickelate superconductivity, both theorists and experimentalists thinking about pressure or lattice-engineering routes. It is a legitimate, serious paper. I would send it to peer review; my own verdict is that it merits publication after the authors address the FLEX-validity question with a benchmark or at least a more explicit caveat about the quantitative reliability.\n\nRecommendation: referee it, and push for a DMFT or QMC point check on the doped model during revision.","headline":"A careful, transparent first-principles model-construction paper that makes a plausible d-wave pairing prediction for the new nickelate; the FLEX-based quantitative Tc claim needs a strong-coupling benchmark before being taken as settled.","tokens_in":12796,"tokens_out":3322,"would_cite":true,"duration_ms":31278,"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":"The paper argues that the strontium-doped infinite-layer nickelate (Nd,Sr)NiO2 behaves like a cuprate superconductor, with dx2-y2-wave pairing driven by spin fluctuations, but with a lower transition temperature because the nickelate has…","keywords":["nickelate superconductor","infinite-layer nickelate","cuprate analogue","d9 electron configuration","multiorbital model","constrained RPA","fluctuation exchange approximation","d-wave pairing"],"falsifier":"Measure the superconducting gap symmetry in Nd0.8Sr0.2NiO2 thin films: if a phase-sensitive or low-temperature penetration-depth experiment shows the gap is not dx2-y2 (for instance, fully gapped s-wave), the paper's central prediction is wrong.","tokens_in":11694,"feed_emoji":"⚡","tokens_out":7680,"duration_ms":62764,"temperature":0.7,"pith_summary":"This paper tries to establish that the newly discovered nickelate superconductor (Nd,Sr)NiO2 pairs electrons in the same way the cuprates do, but with a lower transition temperature because the nickelate's electrons interact more strongly and move in a narrower band. To reach that conclusion, the authors build effective low-energy models from first principles, including not just the nickel orbitals but also the lanthanum orbitals that cross the Fermi level. A fluctuation-exchange calculation on those models returns a leading instability with dx2-y2 (d-wave) pairing symmetry, as in the cuprates, and an Eliashberg eigenvalue that grows as temperature falls. A sympathetic reader should care because this gives a concrete microscopic picture of a material class that could be tuned toward higher Tc, and it explains why the undoped mother compound is a self-doped metal rather than a Mott insulator.","feed_headline":"Nickelate superconductor likely pairs like the cuprates","feed_subtitle":"First-principles models show larger interactions and narrower bands than in cuprates, explaining the lower Tc.","key_machinery":"The load-bearing object is a seven-orbital tight-binding model built from maximally localized Wannier functions, containing Ni 3dx2-y2, 3d3z2-r2, 3dxz, 3dyz, 3dxy, and La 5dxy and 5d3z2-r2 orbitals, with on-site Coulomb interactions computed by constrained RPA. For the pairing analysis the fully occupied Ni dxy orbital is removed to give a six-orbital model, and the interactions are fed into the fluctuation-exchange approximation (FLEX), where the spin-fluctuation-mediated pairing vertex is used in a linearized Eliashberg equation. The key quantity is the eigenvalue lambda of that equation: its leading eigenfunction determines the pairing symmetry, and its growth toward lambda = 1 with decreasing temperature measures the tendency toward superconductivity. The comparison to the cuprates is made with an analogous five-orbital HgBa2CuO4 model, so that the larger U and narrower bandwidth claimed for the nickelate are quantitative.","core_discovery":"On the paper's own terms, the central discovery is that the infinite-layer nickelate's low-energy physics is governed by a Ni 3dx2-y2 band analogous to the cuprate Cu dx2-y2 band, but with two decisive differences: the on-site Coulomb interaction U on that orbital is significantly larger (4.19 eV vs 2.60 eV in a five-orbital HgBa2CuO4 model), and the bandwidth is narrower. Because lanthanum-derived bands sit at the Fermi level, the nominal d9 mother compound is self-doped with about 0.06 holes per unit cell in the Ni orbital, which prevents a Mott insulating state and weakens magnetic nesting. For 20% strontium doping, the FLEX calculation for a six-orbital model (with the fully occupied Ni dxy removed) yields a largest Eliashberg eigenvalue that always has dx2-y2 pairing symmetry, and the eigenvalue is smaller than in the cuprate comparison, consistent with a lower Tc. The paper attributes the smaller eigenvalue to the larger intra-orbital interaction and narrower bandwidth, and traces both back to a larger d-p level offset in the nickelate.","pith_inferences":["A testable extension is that phase-sensitive or penetration-depth experiments on Nd0.8Sr0.2NiO2 films should show line nodes in the gap if the d-wave prediction holds.","The same parameter relation, larger U and smaller bandwidth, may explain why Tc in nickelates stays below about 15 K even at optimal doping, and suggests searching for higher Tc in nickelates with stronger Ni-O hybridization, for instance by epitaxial strain or different rare-earth spacers.","One could extend the FLEX analysis to include self-energy effects on the La pocket or to compute superfluid stiffness; if the pocket contributes substantially, the observed Tc may be set by phase fluctuations rather than by the pairing eigenvalue alone."],"forward_implications":["If the claim is right, the infinite-layer nickelates are a genuine cuprate-like family: their superconductivity is driven by spin fluctuations and has dx2-y2 gap symmetry on the Ni Fermi surface.","The mother compound NdNiO2 should be a self-doped, nonmagnetic metal in its ideal stoichiometry, so the absence of Mott magnetism is not a puzzle but a prediction of the band structure.","Reducing the in-plane lattice constant, which widens the Ni 3dx2-y2 band and lowers U, should raise Tc; this is offered as a route to find superconductivity in related nickelates and as a reason NdNiO2 works better than LaNiO2.","The nearly gapless lanthanum electron pocket carries low-energy quasiparticles even in the superconducting state, so the pocket should show up in low-temperature thermodynamics.","Multiorbital models that omit the La orbitals are quantitatively unreliable for pairing strength; the interactions must include the metallic screening from the La bands."],"supporting_citations":[{"why":"Reports the experimental discovery of 9-15 K superconductivity in Nd0.8Sr0.2NiO2, the material the models are built to explain.","marker":"[21]"},{"why":"First-principles analysis establishing the low-spin d9 state of LaNiO2, the starting point for the cuprate analogy.","marker":"[19]"},{"why":"Earlier LDA study of LaNiO2 whose bands and Fermi surface are the reference for the present model.","marker":"[20]"},{"why":"Introduces the constrained RPA scheme used to derive the effective screened on-site interactions.","marker":"[27]"},{"why":"Introduces the fluctuation-exchange approximation used here to compute the spin-fluctuation pairing vertex and Eliashberg eigenvalue.","marker":"[31]"},{"why":"Provides the HgBa2CuO4 crystal structure used for the quantitative cuprate comparison.","marker":"[39]"},{"why":"Earlier cRPA-based estimates of cuprate on-site interactions against which the nickelate values are contrasted.","marker":"[40]"}],"fun_headline_variants":["Nickelate pairs like cuprate but with lower Tc","d9 nickelate: stronger U, narrower band, lower Tc","Cuprate-like pairing predicted in new nickelate","Nickelate superconductor: larger interactions, weaker pairing"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central claim rests on the assumption that FLEX, fed with cRPA on-site interactions, gives a trustworthy estimate of the pairing tendency in a strongly correlated multiorbital nickelate, even though the same approximation is conceded to fail for the undoped mother compound.","fun_headline_variants_meta":{"raw":{"variants":["Nickelate pairs like cuprate but with lower Tc","d9 nickelate: stronger U, narrower band, lower Tc","Cuprate-like pairing predicted in new nickelate","Nickelate superconductor: larger interactions, weaker pairing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000167,"raw_usage":{"total_tokens":1240,"prompt_tokens":910,"completion_tokens":330,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":526,"completion_tokens_details":{"reasoning_tokens":260}},"tokens_in":526,"tokens_out":330,"duration_ms":3507,"temperature":1.0,"reasoning_tokens":260,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:03:04.458381+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the superconducting gap symmetry in Nd0.8Sr0.2NiO2 thin films: if a phase-sensitive or low-temperature penetration-depth experiment shows the gap is not dx2-y2 (for instance, fully gapped s-wave), the paper's central prediction is wrong.","supporting_citations":[{"cited_title":"Ikeda, Y","cited_arxiv_id":null,"evidence_quote":"First-principles analysis establishing the low-spin d9 state of LaNiO2, the starting point for the cuprate analogy."},{"cited_title":"Onozuka, A","cited_arxiv_id":null,"evidence_quote":"Earlier LDA study of LaNiO2 whose bands and Fermi surface are the reference for the present model."},{"cited_title":"Kotani, J","cited_arxiv_id":null,"evidence_quote":"Introduces the fluctuation-exchange approximation used here to compute the spin-fluctuation pairing vertex and Eliashberg eigenvalue."},{"cited_title":"Still, if we compare the results for the six- and seven-orbital models at lower temperatures taking the same number of Mat- subara frequencies, the results are almost identical","cited_arxiv_id":null,"evidence_quote":"Provides the HgBa2CuO4 crystal structure used for the quantitative cuprate comparison."}],"review_version":1}