REVIEW 2 major objections 4 minor 1 cited by
Model construction and a possibility of cuprate-like pairing in a new d9 nickelate superconductor (Nd,Sr)NiO2
T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash
Pith's one-line read 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…
desk verdict 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. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
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.
What would settle it
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.
Extended reading notes
Core claim
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.
Load-bearing premise
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.
Editorial extensions
If this is right
- 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.
Reading between the lines
- 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.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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.
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 (2)
- [Doped nickelate, Fig. 3 and Table I] 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.
- [Doped nickelate, Fig. 3] 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.
minor comments (4)
- [Supplemental Material, Table S2] In the caption of Table S2, the orbital index list says 'Ni 3dx2-y2' for the HgBa2CuO4 model; this should read 'Cu 3dx2-y2'.
- [Mother nickelate] 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.
- [Fig. 3] 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.
- [Doped nickelate] 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.
Circularity Check
No significant circularity: the model parameters are computed from first principles and the FLEX pairing eigenvalue is an independent output, not a fitted or renamed input.
full rationale
The paper's derivation chain is self-contained. The effective models are built from LDA band structures and Wannier functions, and the many-body interactions are computed with cRPA (Table I). The cuprate comparison is not imported from prior self-citations: the authors explicitly construct a five-orbital model for HgBa2CuO4 in this work, stating 'here we construct, to make a fair comparison with the nickelate, a five-orbital model', and report newly calculated cRPA values. Earlier two-orbital estimates are only cited for context, not as the load-bearing numbers. The FLEX calculation produces the Eliashberg eigenvalue lambda and Stoner factor alpha_S as genuine outputs; the d_x2-y2 symmetry is found as the leading eigenfunction rather than imposed by an ansatz. The claim that larger U_dx2-y2 and narrower bandwidth lower Tc is inferred from the computed lambda-vs-temperature curves in Fig. 3, not from a parameter fitted to the experimental Tc. The mother-compound caveat ('The FLEX approximation cannot treat electron correlation effects in such a regime') is an acknowledged limitation that prevents an analysis there, not a circular step; it does not redefine an output as an input. The self-doping claim follows from the computed orbital-resolved densities and Fermi-surface topology. No equation or parameter reduces by construction to another, and no load-bearing step depends on an unverified self-citation. The result is therefore not circular; its quantitative reliability is a separate correctness concern about FLEX in a strongly correlated regime, not a circularity issue.
Assumptions & free parameters
assumptions (5)
- domain assumption LDA/DFT band structure provides a reliable starting point for the correlated nickelate.
- domain assumption cRPA gives accurate effective on-site interactions for the low-energy model.
- domain assumption FLEX with on-site interactions and the linearized Eliashberg equation captures the superconducting pairing tendency.
- domain assumption Virtual crystal approximation with Ba in place of Sr is valid for the doped nickelate.
- domain assumption The Hartree double-counting subtraction, subtracting the self-energy at omega = 0, is appropriate.
Cite this review
Pith. "Pith review of Model construction and a possibility of cuprate-like pairing in a new d9 nickelate superconductor (Nd,Sr)NiO2." pith.science (2026). https://pith.science/paper/KUVBVJEZ
@misc{pith2026190900060,
author = {Pith},
title = {Pith review of: Model construction and a possibility of cuprate-like pairing in a new d9 nickelate superconductor (Nd,Sr)NiO2},
year = {2026},
howpublished = {\url{https://pith.science/paper/KUVBVJEZ}},
note = {Machine review of arXiv:1909.00060}
}
read the original abstract
Effective models are constructed for a newly discovered superconductor (Nd,Sr)NiO2, which has been considered as a possible nickelate analogue of the cuprates owing to the d9 electron configuration. Estimation of the effective interaction, which turns out to require a multiorbital model that takes account of all the orbitals involved on the Fermi surface, shows that the effective interactions are significantly larger than in the cuprates. A fluctuation exchange study for the model indicates that dx2-y2-wave superconductivity is likely to occur as in the cuprates, where the transition temperature in the nickelate can be lower from the cuprates due to the larger interaction and narrower bandwidth.
Figures
Forward citations
Cited by 1 Pith paper
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The critical nature of the Ni spin state in doped NdNiO$_2$
An impurity exact-diagonalization model places NdNiO2's NiO2 layers at a singlet-triplet crossover, with a cuprate-like singlet hole state and superexchange about ten times smaller than in cuprates.
Reference graph
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94, nNid3z2− r2 = 1. 83, nNidxy = 1. 97, nNidxz+dyz = 3. 89, nLad3z2− r2 = 0 . 12, and nLadxy = 0 . 25. If it were not for the bands having the La character, the d9 configuration would give nNidx2− y2 = 1 . 0. The present result shows that about 0.06 holes per unit cell exist in the Ni 3 dx2− y2 orbital that are self-doped from the La electron pockets. It ...
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C. Weber, K. Haule, and G. Kotliar, Phys. Rev. B 82, 125107 (2010). arXiv:1909.00060v2 [cond-mat.supr-con] 4 Sep 2019 Supplemental material: Model construction and a possibili ty of cuprate-like pairing in a new d9 nickelate superconductor (Nd,Sr)NiO 2 Hirofumi Sakakibara,1, 2...
2010 arXiv
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