{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-n7","topicId":"scwiki-topic-n7","code":"N7","slug":"open-questions/n7","publicationKind":"open-question","title":"Do nickelates pair with s± or d-wave symmetry?","summary":"Compare nickelate pairing evidence across families, pressure conditions and films while separating gap shape, relative phase and microscopic mechanism.","aliases":["nickelate pairing mechanism","nickelate s± versus d-wave","interband sign reversal","镍酸盐配对机制","镍酸盐s波d波","镍酸盐配对对称性"],"evidenceTypes":["theory","experiment","hypothesis"],"relatedCodes":["D5","C3","C4","N2"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-18T21:07:02.562088+00:00","review":{"checkedAt":"2026-10-19","scope":"Selected bilayer RPA and constrained-path models, final high-pressure Andreev results, directional preprint and author film spectra; bounded infinite-layer evidence and independent two-band examples.","limitations":["Complete scientific acceptance remains open.","Full supplements, raw spectral reanalysis and author-to-final comparisons remain open where stated.","Independent two-band examples are not nickelate fits or material Tc predictions.","No single pairing assignment is inferred for all nickelate families, films and pressure regimes."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"02_BATCH_2_IN_PLAN.md","sha256":"502293e5ed2fe8463b61a6c5b78a2c33bc33f3265bd36fe534fa2c469e42ff48","sourceId":"file-49326006ac2c2636"},"sourceMap":[{"startLine":1,"endLine":143,"targetSections":[],"decision":"planning-only-not-republished","note":"Other scope topics remain separately tracked."},{"startLine":144,"endLine":144,"targetSections":["scope","experimental-criteria","what-film-spectroscopy-establishes","mathematical-assumptions","why-theoretical-predictions-differ","limits-and-disputes","discovery-implications"],"decision":"new-research-for-approved-question","note":"Approved N7 question defines scope; it does not establish nickelate pairing symmetry."},{"startLine":145,"endLine":177,"targetSections":[],"decision":"planning-only-not-republished","note":"Other scope topics remain separately tracked."}],"corrections":[],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"E_{n,\\pm}=\\pm\\sqrt{\\xi_n^2+|\\Delta_n|^2}","check":"Eighteen independent decoupled BdG cases compare exact eigenvalues and electron resolvents; a fixed-hybridization counterexample demonstrates the limit."},{"targetSectionId":"mathematical-assumptions","tex":"U^{\\mathsf T}\\Delta_{\\rm layer}U=\\operatorname{diag}(\\Delta_\\perp,-\\Delta_\\perp)","check":"Direct layer-band transformation and 12 separable-kernel checks; imposed parameters, not nickelate mechanism or Tc."}],"references":[{"id":"source-35fd62b7cb3c490c","doi":"10.1038/s41586-019-1496-5","title":"Superconductivity in an infinite-layer nickelate","year":2019,"url":"https://doi.org/10.1038/s41586-019-1496-5","publicationStatus":"journal-article","verification":{"scope":"selected-final-transport-magnetic-and-methods-check","checkedAt":"2026-10-19","evidenceUrl":"https://web.stanford.edu/group/cui_group/papers/Danfeng_Cui_Hwang_NATURE_2019.pdf","note":"Final published pp624–626, online Methods PDFp5; p626 Figures3–4 visually checked. Specific sample onset14.9K maximum-curvature,midpoint13.6K,noise-floorzero9.1K; six-point contacts,two-coil response,9–11nm precursor. No extracted penetration depth or complete raw/replication audit."}},{"id":"source-df0c15d62982f853","doi":"10.1038/s41586-023-06408-7","title":"Signatures of superconductivity near 80 K in a nickelate under high pressure","year":2023,"url":"https://doi.org/10.1038/s41586-023-06408-7","publicationStatus":"journal-article","verification":{"scope":"selected-published-primary-passages-check","checkedAt":"2026-10-18","evidenceUrl":"https://iopex6.iphy.ac.cn/PDFlist/2023/Nature621%282023%29493-EX6.pdf","note":"Selected published p496 Fig3/caption and text, plus Methods PDFp7. Resistance onset, residual resistance, separate magnetic measurement, KBr and room-temperature ruby calibration retained. Raw-data/replication review remains open. On2026-10-19 finalp496Figure3 visually rechecked: run1 10microA versus run2 300microA, magnetic393Hz/50mA; upper-critical-field186T is a fit, not applied field."}},{"id":"source-7b6e19919552090c","doi":"10.1073/pnas.2427243122","title":"Evidence for nodal superconductivity in infinite-layer nickelates","year":2025,"url":"https://doi.org/10.1073/pnas.2427243122","publicationStatus":"journal-article","verification":{"checkedAt":"2026-10-19","scope":"final-abstract-and-selected-indexed-methods","evidenceUrl":"https://pubmed.ncbi.nlm.nih.gov/41296737/","note":"Online 26 November 2025; issue 2 December. Final abstract, selected indexed conclusions and mutual-inductance method checked. Full final text and raw calibration not independently audited; older 2022 preprint is not treated as the final."}},{"id":"source-14703288422dbd4c","doi":"10.1038/s41467-025-56206-0","title":"Sensitive dependence of pairing symmetry on Ni-eg crystal field splitting in the nickelate superconductor La3Ni2O7","year":2025,"url":"https://doi.org/10.1038/s41467-025-56206-0","publicationStatus":"journal-article","verification":{"checkedAt":"2026-10-19","scope":"selected-final-model-and-pairing-results","evidenceUrl":"https://www.nature.com/articles/s41467-025-56206-0.pdf","note":"Online 26 January 2025. Selected final pp. 1–4, p. 4 Figures 3–4 visually checked. Full supplementary calculations and raw model reconstruction remain open."}},{"id":"source-ae28d4e3baad051f","doi":"10.1103/1sgg-ztw8","title":"Pairing symmetry crossover from d-wave to s±-wave in a bilayer nickelate driven by Hund’s coupling and crystal field splitting","year":2026,"url":"https://doi.org/10.1103/1sgg-ztw8","publicationStatus":"journal-article","verification":{"checkedAt":"2026-10-19","scope":"selected-author-model-results-and-appendix","evidenceUrl":"https://arxiv.org/html/2510.19406v1","note":"Published 18 March 2026. Author v1 dated 22 October 2025; selected Hamiltonian, correlations, size comparisons and constrained-path appendix read. Final comparison and numerical rerun remain open; do not generalize the author appendix variational claim."}},{"id":"source-ce76c4830c64c3c7","doi":"10.1038/s41467-025-65865-y","title":"Revealing superconducting gap in La3Ni2O7−δ by Andreev reflection spectroscopy under high pressure","year":2025,"url":"https://doi.org/10.1038/s41467-025-65865-y","publicationStatus":"journal-article","verification":{"checkedAt":"2026-10-19","scope":"selected-final-spectra-contact-analysis-and-methods","evidenceUrl":"https://www.nature.com/articles/s41467-025-65865-y.pdf","note":"Published 2 December 2025. Final pp. 1–6 and p. 4 Figure 2 checked. Its larger gap is 23 meV; the 19 meV passage discusses a separate cited film experiment. Supplement, complete normalization details and raw refit remain open."}},{"id":"source-f9976c21a60be0b8","doi":"10.48550/arXiv.2509.12606","title":"Direct Observation of d-Wave Superconducting Gap Symmetry in Pressurized La3Ni2O7−δ Single Crystals","year":2025,"url":"https://doi.org/10.48550/arXiv.2509.12606","publicationStatus":"preprint","verification":{"checkedAt":"2026-10-19","scope":"selected-preprint-results-methods-and-contact-cautions","evidenceUrl":"https://arxiv.org/pdf/2509.12606v1","note":"Preprint v1, 16 September 2025; no journal reference found at this check. Selected pp. 1–8, 10–12, 14–19 read; p. 12 Figure 3 visually checked. Orientation, contact regime and tip stress need independent validation. A title claim is not settled consensus."}},{"id":"source-a5e400bcce2d5544","doi":"10.1126/science.adw8329","title":"Nodeless superconducting gap and electron-boson coupling in (La,Pr,Sm)3Ni2O7 films","year":2026,"url":"https://doi.org/10.1126/science.adw8329","publicationStatus":"journal-article","verification":{"checkedAt":"2026-10-19","scope":"final-abstract-and-selected-author-results","evidenceUrl":"https://arxiv.org/pdf/2502.17831v2","note":"First Release 21 May 2026 verified at publisher; Science 392,1396–1400. Author v2 dated 9 July 2025 pp. 1–4 read, including temperature analysis and pseudogap limitation. Full final comparison, author figures and supplement remain open."}},{"id":"source-e78a5a3cef51e9fe","doi":"10.1038/s41567-026-03396-z","title":"Observation of superconductivity-induced leading-edge gap in a bilayer nickelate","year":2026,"url":"https://doi.org/10.1038/s41567-026-03396-z","publicationStatus":"journal-article","verification":{"checkedAt":"2026-10-19","scope":"final-identity-and-selected-author-leading-edge-results","evidenceUrl":"https://arxiv.org/pdf/2507.07409v1","note":"Online 21 July 2026, September issue verified in Crossmark. Author v1 dated 10 July 2025 selected pp. 1–7 read. Final PDF was not obtained; complete final comparison, figure and supplement checks remain open. Leading-edge shift is not equated to the full gap."}}],"materialCases":[],"claims":[{"id":"scwiki-n7-claim-scope-1","sectionId":"scope","statement":"There is no justified single pairing assignment for every nickelate. Infinite-layer nickelates and Ruddlesden–Popper bilayers have different structures and electronic settings; pressurized bulk crystals and ambient-pressure strained films also require separate treatment. The approved question about s± versus d-wave pairing therefore needs a material, composition, strain or pressure, temperature range and experimental criterion. A superconducting transition establishes neither the order-parameter symmetry nor its microscopic cause by itself.","evidenceType":"hypothesis","sourceIds":["source-35fd62b7cb3c490c","source-df0c15d62982f853"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-scope-2","sectionId":"scope","statement":"In a tetragonal single-band illustration, a d-wave gap changes sign under a quarter turn, whereas an s± state can preserve that rotation while changing sign between Fermi sheets. The two d-wave forms d(x²−y²) and dxy have different nodal directions. Real multiorbital states additionally require orbital and band transformation rules. A nodal or nodeless measurement must be compared with the actual Fermi surface and measured momentum range.","evidenceType":"hypothesis","sourceIds":["source-14703288422dbd4c","source-ae28d4e3baad051f"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"For infinite-layer La- and Pr-based films, Harvey and colleagues report low-temperature quadratic superfluid-density behavior consistent with disorder and a nodal gap. Their Nd samples have magnetic contributions that prevent a direct inference of the intrinsic nodal structure. This is evidence concerning specific infinite-layer films, not a measurement of the bilayer sign pattern. The present check covers the final abstract and selected indexed methods and conclusions; it is not a complete independent penetration-depth analysis.","evidenceType":"experiment","sourceIds":["source-7b6e19919552090c"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Guo and colleagues' final high-pressure Andreev study fits selected 23 GPa spectra with gaps near 23 and 6 meV. A dominant anisotropic s-like gap with either an s-like or a smaller d-like component describes their selected data better than the tested dominant-d alternatives. It does not measure an interband sign reversal directly. Their estimated contact radius is about 7.3 nm, versus a mean free path near 1.6 nm, and the paper discusses fragmented conducting paths. A broad resistive transition, background normalization and contact assumptions limit interpretation. Its 19 meV passage refers to a different cited film experiment, not this high-pressure gap.","evidenceType":"experiment","sourceIds":["source-ce76c4830c64c3c7"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Cao and colleagues instead interpret directional spectra in 20–22 GPa crystals as d-wave evidence. Their September 2025 preprint compares V-shaped spectra and zero-bias peaks with an anisotropic tunnelling model; it remains labelled as a preprint here. Different orientations use separate cells, and the authors describe visually aligned contacts, mechanical instability and local suppression by excessive tip pressure. These conditions need validation before treating the contrast with other spectra as a universal symmetry verdict. A zero-bias peak alone is insufficient.","evidenceType":"experiment","sourceIds":["source-f9976c21a60be0b8"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-what-film-spectroscopy-establishes-1","sectionId":"what-film-spectroscopy-establishes","statement":"Shen and colleagues' 2026 Science paper reports a nodeless gap and electron–boson coupling in (La,Pr,Sm) bilayer films. The checked author version finds a roughly 18 meV gap near the zone diagonal and uses synchrotron measurements to extend momentum coverage. It also reports spectral suppression above the resistive onset and separates that pseudogap behavior from the sharper transition-related change. Its approximately 70 meV dispersion kink does not identify the pairing mediator uniquely. The final abstract is verified, while full author-to-final and supplementary comparisons remain open.","evidenceType":"experiment","sourceIds":["source-a5e400bcce2d5544"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-what-film-spectroscopy-establishes-2","sectionId":"what-film-spectroscopy-establishes","statement":"Sun and colleagues studied Sr-doped bilayer films. Their checked author version finds leading-edge shifts of about 1–2 meV at selected momenta, including the diagonal, with an instrumental energy resolution near 5 meV. Temperature cycling and normalization checks support the reported shift, but a leading-edge displacement is not automatically the full superconducting gap. The July 2026 final publication identity is verified; its complete text has not been compared here. These different observables and film compositions must not be combined into one gap value.","evidenceType":"experiment","sourceIds":["source-e78a5a3cef51e9fe"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"Changing only the relative gap sign leaves these energies unchanged. Eighteen independent matrix cases also compare the electron spectral functions and recover the same result. This demonstrates a restricted ambiguity of magnitude measurements; it is not a statement that every spectroscopic response is insensitive to phase. A separate fixed-hybridization counterexample changes the spectrum when one gap sign flips. Real matrix elements, interband processes, disorder and interface scattering must be specified.","evidenceType":"theory","sourceIds":["source-14703288422dbd4c","source-ce76c4830c64c3c7"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-mathematical-assumptions-6","sectionId":"mathematical-assumptions","statement":"The basis change is explicitly checked. It is conditional on equivalent layers and the assumed pairing matrix; it does not establish that real films realize this state. An independent separable angular-kernel example likewise changes its leading s± or d(x²−y²) channel when imposed channel weights change. Twelve grid-and-weight cases verify the eigenvalues, including a degeneracy. These examples calculate neither a material transition temperature nor a microscopic interaction.","evidenceType":"theory","sourceIds":["source-ae28d4e3baad051f"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-why-theoretical-predictions-differ-1","sectionId":"why-theoretical-predictions-differ","statement":"Xia and colleagues show that two apparently similar bilayer band models can favor different channels in random-phase-approximation calculations. In their selected 30 GPa setting, changing the Ni-eg crystal-field splitting changes orbital weights and pairing competition even when Fermi-surface shapes remain similar. One Wannier model crosses from dxy to s± near 0.37 eV, while their other model crosses near 0.30 eV. These are model-specific boundaries, not experimentally measured universal thresholds. Neither dxy nor d(x²−y²) should be shortened to an interchangeable d label when comparing predictions.","evidenceType":"theory","sourceIds":["source-14703288422dbd4c"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-why-theoretical-predictions-differ-2","sectionId":"why-theoretical-predictions-differ","statement":"Xiong and colleagues use a constrained-path Monte Carlo treatment of a two-orbital bilayer model. In the checked author version, increasing Hund coupling or crystal-field splitting favors interlayer s± correlations over the selected intralayer d channel. The calculation retains density-density interactions while omitting spin-flip, pair-hopping and next-nearest hopping terms. Its ground-state correlations and finite-size comparisons remain conditional on that Hamiltonian and trial-state constraint. They are not an unbiased experimental determination or a finite-temperature Tc calculation; the final-version comparison remains open.","evidenceType":"theory","sourceIds":["source-ae28d4e3baad051f"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"Nodeless spectra can constrain specified d-wave models without proving s± rather than a sign-preserving s state. Conversely, a contact spectrum interpreted through one d-wave model cannot settle every film and pressure regime. Distinguish gap symmetry, intersheet phase, nodal topology and microscopic pairing interaction. Compare raw conditions, competing fit quality and uncertainties before combining evidence. Complete scientific acceptance, supplementary checks and independent experimental reanalysis remain open.","evidenceType":"hypothesis","sourceIds":["source-ce76c4830c64c3c7","source-f9976c21a60be0b8","source-a5e400bcce2d5544"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."},{"id":"scwiki-n7-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"A useful next program combines controlled disorder, phase-sensitive junctions and momentum-resolved spectroscopy on compositionally and structurally matched samples. Models should predict distinguishable observables using the same orbital parameters and conditions, and report their sensitivity to missing interactions. Preserve oxygen content, strain, thickness, pressure medium and contact geometry alongside each claim. These are proposed discriminating tests, not confirmation of one universal nickelate mechanism.","evidenceType":"hypothesis","sourceIds":["source-14703288422dbd4c","source-ae28d4e3baad051f","source-ce76c4830c64c3c7"],"conditions":"Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.","verificationScope":"Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism."}],"scopeItems":[{"id":"N7","sectionIds":["scope","experimental-criteria","what-film-spectroscopy-establishes","mathematical-assumptions","why-theoretical-predictions-differ","limits-and-disputes","discovery-implications"],"status":"scoped-check","checkedAt":"2026-10-19","scope":"Selected bilayer RPA and constrained-path models, final high-pressure Andreev results, directional preprint and author film spectra; bounded infinite-layer evidence and independent two-band examples.","limitations":["Complete scientific acceptance remains open.","Full supplements, raw spectral reanalysis and author-to-final comparisons remain open where stated.","Independent two-band examples are not nickelate fits or material Tc predictions.","No single pairing assignment is inferred for all nickelate families, films and pressure regimes."]}],"body":"## Scope\n\nThere is no justified single pairing assignment for every nickelate. Infinite-layer nickelates and Ruddlesden–Popper bilayers have different structures and electronic settings; pressurized bulk crystals and ambient-pressure strained films also require separate treatment. The approved question about s± versus d-wave pairing therefore needs a material, composition, strain or pressure, temperature range and experimental criterion. A superconducting transition establishes neither the order-parameter symmetry nor its microscopic cause by itself. [R1](#ref-source-35fd62b7cb3c490c) [R2](#ref-source-df0c15d62982f853)\n\nIn a tetragonal single-band illustration, a d-wave gap changes sign under a quarter turn, whereas an s± state can preserve that rotation while changing sign between Fermi sheets. The two d-wave forms d(x²−y²) and dxy have different nodal directions. Real multiorbital states additionally require orbital and band transformation rules. A nodal or nodeless measurement must be compared with the actual Fermi surface and measured momentum range. [R4](#ref-source-14703288422dbd4c) [R5](#ref-source-ae28d4e3baad051f)\n\n## Experimental criteria\n\nFor infinite-layer La- and Pr-based films, Harvey and colleagues report low-temperature quadratic superfluid-density behavior consistent with disorder and a nodal gap. Their Nd samples have magnetic contributions that prevent a direct inference of the intrinsic nodal structure. This is evidence concerning specific infinite-layer films, not a measurement of the bilayer sign pattern. The present check covers the final abstract and selected indexed methods and conclusions; it is not a complete independent penetration-depth analysis. [R3](#ref-source-7b6e19919552090c)\n\nGuo and colleagues' final high-pressure Andreev study fits selected 23 GPa spectra with gaps near 23 and 6 meV. A dominant anisotropic s-like gap with either an s-like or a smaller d-like component describes their selected data better than the tested dominant-d alternatives. It does not measure an interband sign reversal directly. Their estimated contact radius is about 7.3 nm, versus a mean free path near 1.6 nm, and the paper discusses fragmented conducting paths. A broad resistive transition, background normalization and contact assumptions limit interpretation. Its 19 meV passage refers to a different cited film experiment, not this high-pressure gap. [R6](#ref-source-ce76c4830c64c3c7)\n\nCao and colleagues instead interpret directional spectra in 20–22 GPa crystals as d-wave evidence. Their September 2025 preprint compares V-shaped spectra and zero-bias peaks with an anisotropic tunnelling model; it remains labelled as a preprint here. Different orientations use separate cells, and the authors describe visually aligned contacts, mechanical instability and local suppression by excessive tip pressure. These conditions need validation before treating the contrast with other spectra as a universal symmetry verdict. A zero-bias peak alone is insufficient. [R7](#ref-source-f9976c21a60be0b8)\n\n## What film spectroscopy establishes\n\nShen and colleagues' 2026 Science paper reports a nodeless gap and electron–boson coupling in (La,Pr,Sm) bilayer films. The checked author version finds a roughly 18 meV gap near the zone diagonal and uses synchrotron measurements to extend momentum coverage. It also reports spectral suppression above the resistive onset and separates that pseudogap behavior from the sharper transition-related change. Its approximately 70 meV dispersion kink does not identify the pairing mediator uniquely. The final abstract is verified, while full author-to-final and supplementary comparisons remain open. [R8](#ref-source-a5e400bcce2d5544)\n\nSun and colleagues studied Sr-doped bilayer films. Their checked author version finds leading-edge shifts of about 1–2 meV at selected momenta, including the diagonal, with an instrumental energy resolution near 5 meV. Temperature cycling and normalization checks support the reported shift, but a leading-edge displacement is not automatically the full superconducting gap. The July 2026 final publication identity is verified; its complete text has not been compared here. These different observables and film compositions must not be combined into one gap value. [R9](#ref-source-e78a5a3cef51e9fe)\n\n## Mathematical assumptions\n\nAn original clean, decoupled two-band Bogoliubov example has\n\n$$\nE_{n,\\pm}(\\mathbf k)=\\pm\\sqrt{\\xi_n(\\mathbf k)^2+|\\Delta_n(\\mathbf k)|^2}.\n$$\n\nChanging only the relative gap sign leaves these energies unchanged. Eighteen independent matrix cases also compare the electron spectral functions and recover the same result. This demonstrates a restricted ambiguity of magnitude measurements; it is not a statement that every spectroscopic response is insensitive to phase. A separate fixed-hybridization counterexample changes the spectrum when one gap sign flips. Real matrix elements, interband processes, disorder and interface scattering must be specified. [R4](#ref-source-14703288422dbd4c) [R6](#ref-source-ce76c4830c64c3c7)\n\nFor identical layers, a pure symmetric interlayer pairing matrix illustrates how opposite band signs can arise:\n\n$$\nU^{\\mathsf T}\\begin{pmatrix}0&\\Delta_\\perp\\\\\\Delta_\\perp&0\\end{pmatrix}U\n=\\begin{pmatrix}\\Delta_\\perp&0\\\\0&-\\Delta_\\perp\\end{pmatrix},\\qquad\nU=\\frac{1}{\\sqrt2}\\begin{pmatrix}1&1\\\\1&-1\\end{pmatrix}.\n$$\n\nThe basis change is explicitly checked. It is conditional on equivalent layers and the assumed pairing matrix; it does not establish that real films realize this state. An independent separable angular-kernel example likewise changes its leading s± or d(x²−y²) channel when imposed channel weights change. Twelve grid-and-weight cases verify the eigenvalues, including a degeneracy. These examples calculate neither a material transition temperature nor a microscopic interaction. [R5](#ref-source-ae28d4e3baad051f)\n\n## Why theoretical predictions differ\n\nXia and colleagues show that two apparently similar bilayer band models can favor different channels in random-phase-approximation calculations. In their selected 30 GPa setting, changing the Ni-eg crystal-field splitting changes orbital weights and pairing competition even when Fermi-surface shapes remain similar. One Wannier model crosses from dxy to s± near 0.37 eV, while their other model crosses near 0.30 eV. These are model-specific boundaries, not experimentally measured universal thresholds. Neither dxy nor d(x²−y²) should be shortened to an interchangeable d label when comparing predictions. [R4](#ref-source-14703288422dbd4c)\n\nXiong and colleagues use a constrained-path Monte Carlo treatment of a two-orbital bilayer model. In the checked author version, increasing Hund coupling or crystal-field splitting favors interlayer s± correlations over the selected intralayer d channel. The calculation retains density-density interactions while omitting spin-flip, pair-hopping and next-nearest hopping terms. Its ground-state correlations and finite-size comparisons remain conditional on that Hamiltonian and trial-state constraint. They are not an unbiased experimental determination or a finite-temperature Tc calculation; the final-version comparison remains open. [R5](#ref-source-ae28d4e3baad051f)\n\n## Limits and disputes\n\nNodeless spectra can constrain specified d-wave models without proving s± rather than a sign-preserving s state. Conversely, a contact spectrum interpreted through one d-wave model cannot settle every film and pressure regime. Distinguish gap symmetry, intersheet phase, nodal topology and microscopic pairing interaction. Compare raw conditions, competing fit quality and uncertainties before combining evidence. Complete scientific acceptance, supplementary checks and independent experimental reanalysis remain open. [R6](#ref-source-ce76c4830c64c3c7) [R7](#ref-source-f9976c21a60be0b8) [R8](#ref-source-a5e400bcce2d5544)\n\n## Discovery implications\n\nA useful next program combines controlled disorder, phase-sensitive junctions and momentum-resolved spectroscopy on compositionally and structurally matched samples. Models should predict distinguishable observables using the same orbital parameters and conditions, and report their sensitivity to missing interactions. Preserve oxygen content, strain, thickness, pressure medium and contact geometry alongside each claim. These are proposed discriminating tests, not confirmation of one universal nickelate mechanism. [R4](#ref-source-14703288422dbd4c) [R5](#ref-source-ae28d4e3baad051f) [R6](#ref-source-ce76c4830c64c3c7)\n\n## Related topics\n\nContinue with [nickelate families](/scwiki/nickelates), [d-wave pairing](/scwiki/d-wave), [dxy pairing](/scwiki/dxy-pairing), and [the unified-mechanism question](/scwiki/open-questions/n2).","revision":"d8d247e08f0c517105f1","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nThere is no justified single pairing assignment for every nickelate. Infinite-layer nickelates and Ruddlesden–Popper bilayers have different structures and electronic settings; pressurized bulk crystals and ambient-pressure strained films also require separate treatment. The approved question about s± versus d-wave pairing therefore needs a material, composition, strain or pressure, temperature range and experimental criterion. A superconducting transition establishes neither the order-parameter symmetry nor its microscopic cause by itself. [R1](#ref-source-35fd62b7cb3c490c) [R2](#ref-source-df0c15d62982f853)\n\nIn a tetragonal single-band illustration, a d-wave gap changes sign under a quarter turn, whereas an s± state can preserve that rotation while changing sign between Fermi sheets. The two d-wave forms d(x²−y²) and dxy have different nodal directions. Real multiorbital states additionally require orbital and band transformation rules. A nodal or nodeless measurement must be compared with the actual Fermi surface and measured momentum range. [R4](#ref-source-14703288422dbd4c) [R5](#ref-source-ae28d4e3baad051f)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nFor infinite-layer La- and Pr-based films, Harvey and colleagues report low-temperature quadratic superfluid-density behavior consistent with disorder and a nodal gap. Their Nd samples have magnetic contributions that prevent a direct inference of the intrinsic nodal structure. This is evidence concerning specific infinite-layer films, not a measurement of the bilayer sign pattern. The present check covers the final abstract and selected indexed methods and conclusions; it is not a complete independent penetration-depth analysis. [R3](#ref-source-7b6e19919552090c)\n\nGuo and colleagues' final high-pressure Andreev study fits selected 23 GPa spectra with gaps near 23 and 6 meV. A dominant anisotropic s-like gap with either an s-like or a smaller d-like component describes their selected data better than the tested dominant-d alternatives. It does not measure an interband sign reversal directly. Their estimated contact radius is about 7.3 nm, versus a mean free path near 1.6 nm, and the paper discusses fragmented conducting paths. A broad resistive transition, background normalization and contact assumptions limit interpretation. Its 19 meV passage refers to a different cited film experiment, not this high-pressure gap. [R6](#ref-source-ce76c4830c64c3c7)\n\nCao and colleagues instead interpret directional spectra in 20–22 GPa crystals as d-wave evidence. Their September 2025 preprint compares V-shaped spectra and zero-bias peaks with an anisotropic tunnelling model; it remains labelled as a preprint here. Different orientations use separate cells, and the authors describe visually aligned contacts, mechanical instability and local suppression by excessive tip pressure. These conditions need validation before treating the contrast with other spectra as a universal symmetry verdict. A zero-bias peak alone is insufficient. [R7](#ref-source-f9976c21a60be0b8)"},{"id":"what-film-spectroscopy-establishes","title":"What film spectroscopy establishes","markdown":"## What film spectroscopy establishes\n\nShen and colleagues' 2026 Science paper reports a nodeless gap and electron–boson coupling in (La,Pr,Sm) bilayer films. The checked author version finds a roughly 18 meV gap near the zone diagonal and uses synchrotron measurements to extend momentum coverage. It also reports spectral suppression above the resistive onset and separates that pseudogap behavior from the sharper transition-related change. Its approximately 70 meV dispersion kink does not identify the pairing mediator uniquely. The final abstract is verified, while full author-to-final and supplementary comparisons remain open. [R8](#ref-source-a5e400bcce2d5544)\n\nSun and colleagues studied Sr-doped bilayer films. Their checked author version finds leading-edge shifts of about 1–2 meV at selected momenta, including the diagonal, with an instrumental energy resolution near 5 meV. Temperature cycling and normalization checks support the reported shift, but a leading-edge displacement is not automatically the full superconducting gap. The July 2026 final publication identity is verified; its complete text has not been compared here. These different observables and film compositions must not be combined into one gap value. [R9](#ref-source-e78a5a3cef51e9fe)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nAn original clean, decoupled two-band Bogoliubov example has\n\n$$\nE_{n,\\pm}(\\mathbf k)=\\pm\\sqrt{\\xi_n(\\mathbf k)^2+|\\Delta_n(\\mathbf k)|^2}.\n$$\n\nChanging only the relative gap sign leaves these energies unchanged. Eighteen independent matrix cases also compare the electron spectral functions and recover the same result. This demonstrates a restricted ambiguity of magnitude measurements; it is not a statement that every spectroscopic response is insensitive to phase. A separate fixed-hybridization counterexample changes the spectrum when one gap sign flips. Real matrix elements, interband processes, disorder and interface scattering must be specified. [R4](#ref-source-14703288422dbd4c) [R6](#ref-source-ce76c4830c64c3c7)\n\nFor identical layers, a pure symmetric interlayer pairing matrix illustrates how opposite band signs can arise:\n\n$$\nU^{\\mathsf T}\\begin{pmatrix}0&\\Delta_\\perp\\\\\\Delta_\\perp&0\\end{pmatrix}U\n=\\begin{pmatrix}\\Delta_\\perp&0\\\\0&-\\Delta_\\perp\\end{pmatrix},\\qquad\nU=\\frac{1}{\\sqrt2}\\begin{pmatrix}1&1\\\\1&-1\\end{pmatrix}.\n$$\n\nThe basis change is explicitly checked. It is conditional on equivalent layers and the assumed pairing matrix; it does not establish that real films realize this state. An independent separable angular-kernel example likewise changes its leading s± or d(x²−y²) channel when imposed channel weights change. Twelve grid-and-weight cases verify the eigenvalues, including a degeneracy. These examples calculate neither a material transition temperature nor a microscopic interaction. [R5](#ref-source-ae28d4e3baad051f)"},{"id":"why-theoretical-predictions-differ","title":"Why theoretical predictions differ","markdown":"## Why theoretical predictions differ\n\nXia and colleagues show that two apparently similar bilayer band models can favor different channels in random-phase-approximation calculations. In their selected 30 GPa setting, changing the Ni-eg crystal-field splitting changes orbital weights and pairing competition even when Fermi-surface shapes remain similar. One Wannier model crosses from dxy to s± near 0.37 eV, while their other model crosses near 0.30 eV. These are model-specific boundaries, not experimentally measured universal thresholds. Neither dxy nor d(x²−y²) should be shortened to an interchangeable d label when comparing predictions. [R4](#ref-source-14703288422dbd4c)\n\nXiong and colleagues use a constrained-path Monte Carlo treatment of a two-orbital bilayer model. In the checked author version, increasing Hund coupling or crystal-field splitting favors interlayer s± correlations over the selected intralayer d channel. The calculation retains density-density interactions while omitting spin-flip, pair-hopping and next-nearest hopping terms. Its ground-state correlations and finite-size comparisons remain conditional on that Hamiltonian and trial-state constraint. They are not an unbiased experimental determination or a finite-temperature Tc calculation; the final-version comparison remains open. [R5](#ref-source-ae28d4e3baad051f)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nNodeless spectra can constrain specified d-wave models without proving s± rather than a sign-preserving s state. Conversely, a contact spectrum interpreted through one d-wave model cannot settle every film and pressure regime. Distinguish gap symmetry, intersheet phase, nodal topology and microscopic pairing interaction. Compare raw conditions, competing fit quality and uncertainties before combining evidence. Complete scientific acceptance, supplementary checks and independent experimental reanalysis remain open. [R6](#ref-source-ce76c4830c64c3c7) [R7](#ref-source-f9976c21a60be0b8) [R8](#ref-source-a5e400bcce2d5544)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nA useful next program combines controlled disorder, phase-sensitive junctions and momentum-resolved spectroscopy on compositionally and structurally matched samples. Models should predict distinguishable observables using the same orbital parameters and conditions, and report their sensitivity to missing interactions. Preserve oxygen content, strain, thickness, pressure medium and contact geometry alongside each claim. These are proposed discriminating tests, not confirmation of one universal nickelate mechanism. [R4](#ref-source-14703288422dbd4c) [R5](#ref-source-ae28d4e3baad051f) [R6](#ref-source-ce76c4830c64c3c7)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\nContinue with [nickelate families](/scwiki/nickelates), [d-wave pairing](/scwiki/d-wave), [dxy pairing](/scwiki/dxy-pairing), and [the unified-mechanism question](/scwiki/open-questions/n2)."},{"id":"material-cases","title":"Material cases","markdown":"## Material cases\n\nNo sample-specific material records are included in this article. Model results are not experimental transition temperatures."}],"markdown":"# Do nickelates pair with s± or d-wave symmetry?\n\nCompare nickelate pairing evidence across families, pressure conditions and films while separating gap shape, relative phase and microscopic mechanism.\n\n## Scope\n\nThere is no justified single pairing assignment for every nickelate. Infinite-layer nickelates and Ruddlesden–Popper bilayers have different structures and electronic settings; pressurized bulk crystals and ambient-pressure strained films also require separate treatment. The approved question about s± versus d-wave pairing therefore needs a material, composition, strain or pressure, temperature range and experimental criterion. A superconducting transition establishes neither the order-parameter symmetry nor its microscopic cause by itself. [R1](#ref-source-35fd62b7cb3c490c) [R2](#ref-source-df0c15d62982f853)\n\nIn a tetragonal single-band illustration, a d-wave gap changes sign under a quarter turn, whereas an s± state can preserve that rotation while changing sign between Fermi sheets. The two d-wave forms d(x²−y²) and dxy have different nodal directions. Real multiorbital states additionally require orbital and band transformation rules. A nodal or nodeless measurement must be compared with the actual Fermi surface and measured momentum range. [R4](#ref-source-14703288422dbd4c) [R5](#ref-source-ae28d4e3baad051f)\n\n## Experimental criteria\n\nFor infinite-layer La- and Pr-based films, Harvey and colleagues report low-temperature quadratic superfluid-density behavior consistent with disorder and a nodal gap. Their Nd samples have magnetic contributions that prevent a direct inference of the intrinsic nodal structure. This is evidence concerning specific infinite-layer films, not a measurement of the bilayer sign pattern. The present check covers the final abstract and selected indexed methods and conclusions; it is not a complete independent penetration-depth analysis. [R3](#ref-source-7b6e19919552090c)\n\nGuo and colleagues' final high-pressure Andreev study fits selected 23 GPa spectra with gaps near 23 and 6 meV. A dominant anisotropic s-like gap with either an s-like or a smaller d-like component describes their selected data better than the tested dominant-d alternatives. It does not measure an interband sign reversal directly. Their estimated contact radius is about 7.3 nm, versus a mean free path near 1.6 nm, and the paper discusses fragmented conducting paths. A broad resistive transition, background normalization and contact assumptions limit interpretation. Its 19 meV passage refers to a different cited film experiment, not this high-pressure gap. [R6](#ref-source-ce76c4830c64c3c7)\n\nCao and colleagues instead interpret directional spectra in 20–22 GPa crystals as d-wave evidence. Their September 2025 preprint compares V-shaped spectra and zero-bias peaks with an anisotropic tunnelling model; it remains labelled as a preprint here. Different orientations use separate cells, and the authors describe visually aligned contacts, mechanical instability and local suppression by excessive tip pressure. These conditions need validation before treating the contrast with other spectra as a universal symmetry verdict. A zero-bias peak alone is insufficient. [R7](#ref-source-f9976c21a60be0b8)\n\n## What film spectroscopy establishes\n\nShen and colleagues' 2026 Science paper reports a nodeless gap and electron–boson coupling in (La,Pr,Sm) bilayer films. The checked author version finds a roughly 18 meV gap near the zone diagonal and uses synchrotron measurements to extend momentum coverage. It also reports spectral suppression above the resistive onset and separates that pseudogap behavior from the sharper transition-related change. Its approximately 70 meV dispersion kink does not identify the pairing mediator uniquely. The final abstract is verified, while full author-to-final and supplementary comparisons remain open. [R8](#ref-source-a5e400bcce2d5544)\n\nSun and colleagues studied Sr-doped bilayer films. Their checked author version finds leading-edge shifts of about 1–2 meV at selected momenta, including the diagonal, with an instrumental energy resolution near 5 meV. Temperature cycling and normalization checks support the reported shift, but a leading-edge displacement is not automatically the full superconducting gap. The July 2026 final publication identity is verified; its complete text has not been compared here. These different observables and film compositions must not be combined into one gap value. [R9](#ref-source-e78a5a3cef51e9fe)\n\n## Mathematical assumptions\n\nAn original clean, decoupled two-band Bogoliubov example has\n\n$$\nE_{n,\\pm}(\\mathbf k)=\\pm\\sqrt{\\xi_n(\\mathbf k)^2+|\\Delta_n(\\mathbf k)|^2}.\n$$\n\nChanging only the relative gap sign leaves these energies unchanged. Eighteen independent matrix cases also compare the electron spectral functions and recover the same result. This demonstrates a restricted ambiguity of magnitude measurements; it is not a statement that every spectroscopic response is insensitive to phase. A separate fixed-hybridization counterexample changes the spectrum when one gap sign flips. Real matrix elements, interband processes, disorder and interface scattering must be specified. [R4](#ref-source-14703288422dbd4c) [R6](#ref-source-ce76c4830c64c3c7)\n\nFor identical layers, a pure symmetric interlayer pairing matrix illustrates how opposite band signs can arise:\n\n$$\nU^{\\mathsf T}\\begin{pmatrix}0&\\Delta_\\perp\\\\\\Delta_\\perp&0\\end{pmatrix}U\n=\\begin{pmatrix}\\Delta_\\perp&0\\\\0&-\\Delta_\\perp\\end{pmatrix},\\qquad\nU=\\frac{1}{\\sqrt2}\\begin{pmatrix}1&1\\\\1&-1\\end{pmatrix}.\n$$\n\nThe basis change is explicitly checked. It is conditional on equivalent layers and the assumed pairing matrix; it does not establish that real films realize this state. An independent separable angular-kernel example likewise changes its leading s± or d(x²−y²) channel when imposed channel weights change. Twelve grid-and-weight cases verify the eigenvalues, including a degeneracy. These examples calculate neither a material transition temperature nor a microscopic interaction. [R5](#ref-source-ae28d4e3baad051f)\n\n## Why theoretical predictions differ\n\nXia and colleagues show that two apparently similar bilayer band models can favor different channels in random-phase-approximation calculations. In their selected 30 GPa setting, changing the Ni-eg crystal-field splitting changes orbital weights and pairing competition even when Fermi-surface shapes remain similar. One Wannier model crosses from dxy to s± near 0.37 eV, while their other model crosses near 0.30 eV. These are model-specific boundaries, not experimentally measured universal thresholds. Neither dxy nor d(x²−y²) should be shortened to an interchangeable d label when comparing predictions. [R4](#ref-source-14703288422dbd4c)\n\nXiong and colleagues use a constrained-path Monte Carlo treatment of a two-orbital bilayer model. In the checked author version, increasing Hund coupling or crystal-field splitting favors interlayer s± correlations over the selected intralayer d channel. The calculation retains density-density interactions while omitting spin-flip, pair-hopping and next-nearest hopping terms. Its ground-state correlations and finite-size comparisons remain conditional on that Hamiltonian and trial-state constraint. They are not an unbiased experimental determination or a finite-temperature Tc calculation; the final-version comparison remains open. [R5](#ref-source-ae28d4e3baad051f)\n\n## Limits and disputes\n\nNodeless spectra can constrain specified d-wave models without proving s± rather than a sign-preserving s state. Conversely, a contact spectrum interpreted through one d-wave model cannot settle every film and pressure regime. Distinguish gap symmetry, intersheet phase, nodal topology and microscopic pairing interaction. Compare raw conditions, competing fit quality and uncertainties before combining evidence. Complete scientific acceptance, supplementary checks and independent experimental reanalysis remain open. [R6](#ref-source-ce76c4830c64c3c7) [R7](#ref-source-f9976c21a60be0b8) [R8](#ref-source-a5e400bcce2d5544)\n\n## Discovery implications\n\nA useful next program combines controlled disorder, phase-sensitive junctions and momentum-resolved spectroscopy on compositionally and structurally matched samples. Models should predict distinguishable observables using the same orbital parameters and conditions, and report their sensitivity to missing interactions. Preserve oxygen content, strain, thickness, pressure medium and contact geometry alongside each claim. These are proposed discriminating tests, not confirmation of one universal nickelate mechanism. [R4](#ref-source-14703288422dbd4c) [R5](#ref-source-ae28d4e3baad051f) [R6](#ref-source-ce76c4830c64c3c7)\n\n## Related topics\n\nContinue with [nickelate families](/scwiki/nickelates), [d-wave pairing](/scwiki/d-wave), [dxy pairing](/scwiki/dxy-pairing), and [the unified-mechanism question](/scwiki/open-questions/n2).\n\n## Material cases\n\nNo sample-specific material records are included in this article. Model results are not experimental transition temperatures.\n\n## Sources\n\n### Ref source-35fd62b7cb3c490c\n\n[R1] Superconductivity in an infinite-layer nickelate (2019). [DOI 10.1038/s41586-019-1496-5](https://doi.org/10.1038/s41586-019-1496-5). Publication: journal-article. Check: selected-final-transport-magnetic-and-methods-check. Checked: 2026-10-19. Final published pp624–626, online Methods PDFp5; p626 Figures3–4 visually checked. Specific sample onset14.9K maximum-curvature,midpoint13.6K,noise-floorzero9.1K; six-point contacts,two-coil response,9–11nm precursor. No extracted penetration depth or complete raw/replication audit.\n### Ref source-df0c15d62982f853\n\n[R2] Signatures of superconductivity near 80 K in a nickelate under high pressure (2023). [DOI 10.1038/s41586-023-06408-7](https://doi.org/10.1038/s41586-023-06408-7). Publication: journal-article. Check: selected-published-primary-passages-check. Checked: 2026-10-18. Selected published p496 Fig3/caption and text, plus Methods PDFp7. Resistance onset, residual resistance, separate magnetic measurement, KBr and room-temperature ruby calibration retained. Raw-data/replication review remains open. On2026-10-19 finalp496Figure3 visually rechecked: run1 10microA versus run2 300microA, magnetic393Hz/50mA; upper-critical-field186T is a fit, not applied field.\n### Ref source-7b6e19919552090c\n\n[R3] Evidence for nodal superconductivity in infinite-layer nickelates (2025). [DOI 10.1073/pnas.2427243122](https://doi.org/10.1073/pnas.2427243122). Publication: journal-article. Check: final-abstract-and-selected-indexed-methods. Checked: 2026-10-19. Online 26 November 2025; issue 2 December. Final abstract, selected indexed conclusions and mutual-inductance method checked. Full final text and raw calibration not independently audited; older 2022 preprint is not treated as the final.\n### Ref source-14703288422dbd4c\n\n[R4] Sensitive dependence of pairing symmetry on Ni-eg crystal field splitting in the nickelate superconductor La3Ni2O7 (2025). [DOI 10.1038/s41467-025-56206-0](https://doi.org/10.1038/s41467-025-56206-0). Publication: journal-article. Check: selected-final-model-and-pairing-results. Checked: 2026-10-19. Online 26 January 2025. Selected final pp. 1–4, p. 4 Figures 3–4 visually checked. Full supplementary calculations and raw model reconstruction remain open.\n### Ref source-ae28d4e3baad051f\n\n[R5] Pairing symmetry crossover from d-wave to s±-wave in a bilayer nickelate driven by Hund’s coupling and crystal field splitting (2026). [DOI 10.1103/1sgg-ztw8](https://doi.org/10.1103/1sgg-ztw8). Publication: journal-article. Check: selected-author-model-results-and-appendix. Checked: 2026-10-19. Published 18 March 2026. Author v1 dated 22 October 2025; selected Hamiltonian, correlations, size comparisons and constrained-path appendix read. Final comparison and numerical rerun remain open; do not generalize the author appendix variational claim.\n### Ref source-ce76c4830c64c3c7\n\n[R6] Revealing superconducting gap in La3Ni2O7−δ by Andreev reflection spectroscopy under high pressure (2025). [DOI 10.1038/s41467-025-65865-y](https://doi.org/10.1038/s41467-025-65865-y). Publication: journal-article. Check: selected-final-spectra-contact-analysis-and-methods. Checked: 2026-10-19. Published 2 December 2025. Final pp. 1–6 and p. 4 Figure 2 checked. Its larger gap is 23 meV; the 19 meV passage discusses a separate cited film experiment. Supplement, complete normalization details and raw refit remain open.\n### Ref source-f9976c21a60be0b8\n\n[R7] Direct Observation of d-Wave Superconducting Gap Symmetry in Pressurized La3Ni2O7−δ Single Crystals (2025). [DOI 10.48550/arXiv.2509.12606](https://doi.org/10.48550/arXiv.2509.12606). Publication: preprint. Check: selected-preprint-results-methods-and-contact-cautions. Checked: 2026-10-19. Preprint v1, 16 September 2025; no journal reference found at this check. Selected pp. 1–8, 10–12, 14–19 read; p. 12 Figure 3 visually checked. Orientation, contact regime and tip stress need independent validation. A title claim is not settled consensus.\n### Ref source-a5e400bcce2d5544\n\n[R8] Nodeless superconducting gap and electron-boson coupling in (La,Pr,Sm)3Ni2O7 films (2026). [DOI 10.1126/science.adw8329](https://doi.org/10.1126/science.adw8329). Publication: journal-article. Check: final-abstract-and-selected-author-results. Checked: 2026-10-19. First Release 21 May 2026 verified at publisher; Science 392,1396–1400. Author v2 dated 9 July 2025 pp. 1–4 read, including temperature analysis and pseudogap limitation. Full final comparison, author figures and supplement remain open.\n### Ref source-e78a5a3cef51e9fe\n\n[R9] Observation of superconductivity-induced leading-edge gap in a bilayer nickelate (2026). [DOI 10.1038/s41567-026-03396-z](https://doi.org/10.1038/s41567-026-03396-z). Publication: journal-article. Check: final-identity-and-selected-author-leading-edge-results. Checked: 2026-10-19. Online 21 July 2026, September issue verified in Crossmark. Author v1 dated 10 July 2025 selected pp. 1–7 read. Final PDF was not obtained; complete final comparison, figure and supplement checks remain open. Leading-edge shift is not equated to the full gap.\n\n## Claim evidence and conditions\n\n### scwiki-n7-claim-scope-1\n\nThere is no justified single pairing assignment for every nickelate. Infinite-layer nickelates and Ruddlesden–Popper bilayers have different structures and electronic settings; pressurized bulk crystals and ambient-pressure strained films also require separate treatment. The approved question about s± versus d-wave pairing therefore needs a material, composition, strain or pressure, temperature range and experimental criterion. A superconducting transition establishes neither the order-parameter symmetry nor its microscopic cause by itself.\n\nEvidence: hypothesis. Sources: source-35fd62b7cb3c490c, source-df0c15d62982f853.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-scope-2\n\nIn a tetragonal single-band illustration, a d-wave gap changes sign under a quarter turn, whereas an s± state can preserve that rotation while changing sign between Fermi sheets. The two d-wave forms d(x²−y²) and dxy have different nodal directions. Real multiorbital states additionally require orbital and band transformation rules. A nodal or nodeless measurement must be compared with the actual Fermi surface and measured momentum range.\n\nEvidence: hypothesis. Sources: source-14703288422dbd4c, source-ae28d4e3baad051f.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-experimental-criteria-1\n\nFor infinite-layer La- and Pr-based films, Harvey and colleagues report low-temperature quadratic superfluid-density behavior consistent with disorder and a nodal gap. Their Nd samples have magnetic contributions that prevent a direct inference of the intrinsic nodal structure. This is evidence concerning specific infinite-layer films, not a measurement of the bilayer sign pattern. The present check covers the final abstract and selected indexed methods and conclusions; it is not a complete independent penetration-depth analysis.\n\nEvidence: experiment. Sources: source-7b6e19919552090c.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-experimental-criteria-2\n\nGuo and colleagues' final high-pressure Andreev study fits selected 23 GPa spectra with gaps near 23 and 6 meV. A dominant anisotropic s-like gap with either an s-like or a smaller d-like component describes their selected data better than the tested dominant-d alternatives. It does not measure an interband sign reversal directly. Their estimated contact radius is about 7.3 nm, versus a mean free path near 1.6 nm, and the paper discusses fragmented conducting paths. A broad resistive transition, background normalization and contact assumptions limit interpretation. Its 19 meV passage refers to a different cited film experiment, not this high-pressure gap.\n\nEvidence: experiment. Sources: source-ce76c4830c64c3c7.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-experimental-criteria-3\n\nCao and colleagues instead interpret directional spectra in 20–22 GPa crystals as d-wave evidence. Their September 2025 preprint compares V-shaped spectra and zero-bias peaks with an anisotropic tunnelling model; it remains labelled as a preprint here. Different orientations use separate cells, and the authors describe visually aligned contacts, mechanical instability and local suppression by excessive tip pressure. These conditions need validation before treating the contrast with other spectra as a universal symmetry verdict. A zero-bias peak alone is insufficient.\n\nEvidence: experiment. Sources: source-f9976c21a60be0b8.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-what-film-spectroscopy-establishes-1\n\nShen and colleagues' 2026 Science paper reports a nodeless gap and electron–boson coupling in (La,Pr,Sm) bilayer films. The checked author version finds a roughly 18 meV gap near the zone diagonal and uses synchrotron measurements to extend momentum coverage. It also reports spectral suppression above the resistive onset and separates that pseudogap behavior from the sharper transition-related change. Its approximately 70 meV dispersion kink does not identify the pairing mediator uniquely. The final abstract is verified, while full author-to-final and supplementary comparisons remain open.\n\nEvidence: experiment. Sources: source-a5e400bcce2d5544.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-what-film-spectroscopy-establishes-2\n\nSun and colleagues studied Sr-doped bilayer films. Their checked author version finds leading-edge shifts of about 1–2 meV at selected momenta, including the diagonal, with an instrumental energy resolution near 5 meV. Temperature cycling and normalization checks support the reported shift, but a leading-edge displacement is not automatically the full superconducting gap. The July 2026 final publication identity is verified; its complete text has not been compared here. These different observables and film compositions must not be combined into one gap value.\n\nEvidence: experiment. Sources: source-e78a5a3cef51e9fe.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-mathematical-assumptions-3\n\nChanging only the relative gap sign leaves these energies unchanged. Eighteen independent matrix cases also compare the electron spectral functions and recover the same result. This demonstrates a restricted ambiguity of magnitude measurements; it is not a statement that every spectroscopic response is insensitive to phase. A separate fixed-hybridization counterexample changes the spectrum when one gap sign flips. Real matrix elements, interband processes, disorder and interface scattering must be specified.\n\nEvidence: theory. Sources: source-14703288422dbd4c, source-ce76c4830c64c3c7.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-mathematical-assumptions-6\n\nThe basis change is explicitly checked. It is conditional on equivalent layers and the assumed pairing matrix; it does not establish that real films realize this state. An independent separable angular-kernel example likewise changes its leading s± or d(x²−y²) channel when imposed channel weights change. Twelve grid-and-weight cases verify the eigenvalues, including a degeneracy. These examples calculate neither a material transition temperature nor a microscopic interaction.\n\nEvidence: theory. Sources: source-ae28d4e3baad051f.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-why-theoretical-predictions-differ-1\n\nXia and colleagues show that two apparently similar bilayer band models can favor different channels in random-phase-approximation calculations. In their selected 30 GPa setting, changing the Ni-eg crystal-field splitting changes orbital weights and pairing competition even when Fermi-surface shapes remain similar. One Wannier model crosses from dxy to s± near 0.37 eV, while their other model crosses near 0.30 eV. These are model-specific boundaries, not experimentally measured universal thresholds. Neither dxy nor d(x²−y²) should be shortened to an interchangeable d label when comparing predictions.\n\nEvidence: theory. Sources: source-14703288422dbd4c.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-why-theoretical-predictions-differ-2\n\nXiong and colleagues use a constrained-path Monte Carlo treatment of a two-orbital bilayer model. In the checked author version, increasing Hund coupling or crystal-field splitting favors interlayer s± correlations over the selected intralayer d channel. The calculation retains density-density interactions while omitting spin-flip, pair-hopping and next-nearest hopping terms. Its ground-state correlations and finite-size comparisons remain conditional on that Hamiltonian and trial-state constraint. They are not an unbiased experimental determination or a finite-temperature Tc calculation; the final-version comparison remains open.\n\nEvidence: theory. Sources: source-ae28d4e3baad051f.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-limits-and-disputes-1\n\nNodeless spectra can constrain specified d-wave models without proving s± rather than a sign-preserving s state. Conversely, a contact spectrum interpreted through one d-wave model cannot settle every film and pressure regime. Distinguish gap symmetry, intersheet phase, nodal topology and microscopic pairing interaction. Compare raw conditions, competing fit quality and uncertainties before combining evidence. Complete scientific acceptance, supplementary checks and independent experimental reanalysis remain open.\n\nEvidence: hypothesis. Sources: source-ce76c4830c64c3c7, source-f9976c21a60be0b8, source-a5e400bcce2d5544.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n### scwiki-n7-claim-discovery-implications-1\n\nA useful next program combines controlled disorder, phase-sensitive junctions and momentum-resolved spectroscopy on compositionally and structurally matched samples. Models should predict distinguishable observables using the same orbital parameters and conditions, and report their sensitivity to missing interactions. Preserve oxygen content, strain, thickness, pressure medium and contact geometry alongside each claim. These are proposed discriminating tests, not confirmation of one universal nickelate mechanism.\n\nEvidence: hypothesis. Sources: source-14703288422dbd4c, source-ae28d4e3baad051f, source-ce76c4830c64c3c7.\n\nConditions: Preserve nickelate family, sample, pressure/strain, momentum coverage, gap estimator, model basis and publication version.\n\nVerification scope: Selected primary evidence and independent restricted examples; no complete raw-data refit or settled material-wide mechanism.\n\n## Approved scope items\n\nN7. Checked: 2026-10-19. Selected bilayer RPA and constrained-path models, final high-pressure Andreev results, directional preprint and author film spectra; bounded infinite-layer evidence and independent two-band examples.\n\n- Complete scientific acceptance remains open.\n- Full supplements, raw spectral reanalysis and author-to-final comparisons remain open where stated.\n- Independent two-band examples are not nickelate fits or material Tc predictions.\n- No single pairing assignment is inferred for all nickelate families, films and pressure regimes.\n\n## Revision and review\n\nArticle ID: scwiki-n7. Revision: d8d247e08f0c517105f1. Updated: 2026-10-18T21:07:02.562088+00:00.\n\nReview scope: Selected bilayer RPA and constrained-path models, final high-pressure Andreev results, directional preprint and author film spectra; bounded infinite-layer evidence and independent two-band examples.\n\n- Complete scientific acceptance remains open.\n- Full supplements, raw spectral reanalysis and author-to-final comparisons remain open where stated.\n- Independent two-band examples are not nickelate fits or material Tc predictions.\n- No single pairing assignment is inferred for all nickelate families, films and pressure regimes.\n\nSource: [02_BATCH_2_IN_PLAN.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/02_BATCH_2_IN_PLAN.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 502293e5ed2fe8463b61a6c5b78a2c33bc33f3265bd36fe534fa2c469e42ff48.\n","wordCount":1074}}