Do nickelates pair with s± or d-wave symmetry?

Scope

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. R1 R2

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. R4 R5

Experimental criteria

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. R3

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. R6

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. R7

What film spectroscopy establishes

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. R8

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. R9

Mathematical assumptions

An original clean, decoupled two-band Bogoliubov example has

$$E_{n,\pm}(\mathbf k)=\pm\sqrt{\xi_n(\mathbf k)^2+|\Delta_n(\mathbf k)|^2}.$$

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. R4 R6

For identical layers, a pure symmetric interlayer pairing matrix illustrates how opposite band signs can arise:

$$U^{\mathsf T}\begin{pmatrix}0&\Delta_\perp\\\Delta_\perp&0\end{pmatrix}U =\begin{pmatrix}\Delta_\perp&0\\0&-\Delta_\perp\end{pmatrix},\qquad U=\frac{1}{\sqrt2}\begin{pmatrix}1&1\\1&-1\end{pmatrix}.$$

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. R5

Why theoretical predictions differ

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. R4

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. R5

Limits and disputes

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. R6 R7 R8

Discovery implications

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. R4 R5 R6

Related topics

Continue with nickelate families, d-wave pairing, dxy pairing, and the unified-mechanism question.

Material cases

No sample-specific material records are included in this article. Model results are not experimental transition temperatures.