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Using the density matrix renormalization group method, this work systematically investigates the evolution of superconducting pairing correlations with the filling of the Ni 3d_{z²} orbital in an effective bilayer two-orbital model of pressurized bilayer nickelate La₃Ni₂O₇ on a one-dimensional minimal geometric structure. By adjusting the orbital chemical potential difference to continuously tune the 3d_{z²} orbital from 1/12 doping to near half-filling, it is found that superconducting correlations are significantly suppressed near half-filling, indicating that the itinerancy of this orbital favors pairing. Moreover, pairing correlations are enhanced in regions with larger charge fluctuations, suggesting competition between charge order and superconductivity. These results support the existing theoretical picture that interlayer antiferromagnetic superexchange provides the pairing glue, while the itinerant 3d_{z²} orbital mediates pairing and establishes long-range coherence through hybridization. The study clarifies the crucial role of the itinerancy of the 3d_{z²} orbital in superconductivity, providing important evidence for understanding the unconventional pairing mechanism in this system.

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This study establishes a correspondence between the multi-orbital Hubbard model and the bilayer Hubbard model, proposing an orbital-space bilayer model (OSBM) in which the orbital energy level difference ΔE plays a role analogous to interlayer hopping in a real-space bilayer model, and superconductivity is enhanced in the incipient-band regime. Based on this, the theory predicts that the reduced bilayer nickelate La₃Ni₂O₆, under appropriate hole doping, can serve as a candidate OSBM superconductor. A tight-binding model constructed from first principles reveals a large ΔE between the Ni d_{x²-y²} orbital and other d orbitals due to the absence of apical oxygen atoms. Using the fluctuation-exchange approximation, calculations show that in the incipient-band scenario, intersite interactions can drive s±-wave superconductivity, where the superconducting gap function changes sign between the d_{x²-y²} band and other d-orbital bands. The study also examines the energetic and dynamic stability of the crystal structure under atomic substitution and pressure. Although La₃Ni₂O₇ and La₃Ni₂O₆ share similar chemical formulas, this work suggests that the latter may realize a completely different pairing mechanism.

This study constructs a seven-orbital effective model based on first-principles calculations and employs the fluctuation exchange (FLEX) approximation to theoretically analyze the superconductivity of free-standing infinite-layer nickelate Nd₀.₈₅Sr₀.₁₅NiO₂ films under pressure. The results show that the superconducting transition temperature Tc increases monotonically with applied pressure, consistent with recent experimental observations. This enhancement is attributed to the mitigation of excessively strong electronic correlations arising from the extremely low valence state of Ni atoms, leading to a significant reduction in the effective electronic interaction parameter U, which in turn reduces quasiparticle damping and enhances spin-fluctuation-mediated d-wave pairing. Additionally, phonon calculations confirm that the crystal structure remains dynamically stable up to 90 GPa. By comparing models with different U values, the study demonstrates that only a relatively large U (approximately 5.1 eV) can reproduce the experimental trend, while smaller U values lead to premature saturation or even a dome-shaped Tc behavior, thereby supporting the mechanism whereby excessively strong correlations suppress superconductivity in infinite-layer nickelates, and pressure alleviates these correlations to enhance Tc.

This study theoretically analyzes the superconductivity of La₃Ni₂O₇ thin films under ambient pressure. A model Hamiltonian is constructed based on first-principles structure optimization, with the in-plane lattice constants fixed to those of the experimental substrates (LSAT, LAO, and SLAO), and an additional model employing experimentally determined crystal structures is used. The linearized Eliashberg equation is solved using the fluctuation exchange approximation (FLEX) with full momentum- and frequency-dependent Green’s functions and pairing interactions. The results indicate that the electronic structure, including the presence or absence of the γ Fermi pocket, depends on the adopted crystal structure and whether +U corrections are included in the band calculations, yet the s±-wave pairing symmetry remains robust. This robustness primarily arises because pairing is mediated by finite-energy spin fluctuations, which are insensitive to details of the Fermi surface topology and yield a nearly momentum-independent interlayer d_{3z²−r²} pairing gap function in the orbital representation. On the other hand, the superconducting transition temperature of the thin films (approximately 40 K) is about half that of bulk material under pressure (approximately 80 K). Within the FLEX framework, this can only be understood by adopting a model with a small interlayer hopping parameter |t⊥| derived from experimentally determined crystal structures, although other contributing factors cannot be ruled out.

Using angle-resolved photoemission spectroscopy, the electronic structure of the Ruddlesden-Popper phase nickelate heterostructure La₂PrNi₂O₇/NdAlO₃ was investigated, and for the first time a superconducting gap opening at Tc was observed in the absence of a pseudogap, accompanied by pronounced coherent peaks, directly yielding a nodeless superconducting order parameter of approximately 16 meV. By reconstructing the electronic density of states from momentum-integrated spectra, a sharp drop and an electronic specific heat jump near Tc were revealed, providing the previously missing thermodynamic evidence for the superconducting phase transition in nickelates. The Fermi surface consists of three multiorbital pockets, α, β, and γ; while the γ pocket persists under various epitaxial strains and thus shows no one-to-one correspondence with superconductivity, its steep dispersion and the significant changes of the β pocket suggest a link between Fermi surface topology and the onset of superconductivity. These results establish a nodeless pairing symmetry (supporting s-wave rather than d-wave) and clarify the interplay among Fermi surface topology, strain, and superconductivity, offering direct experimental insight into the mechanism of high-temperature superconductivity in RP nickelates.

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By employing a low-temperature ultrahigh-vacuum dark-box transfer technique to preserve sample surface quality, this study systematically resolves the three-dimensional electronic band structure of superconducting (La,Pr,Sm)₃Ni₂O₇/SrLaAlO₄ thin films using angle-resolved photoemission spectroscopy (ARPES) with multiple photon energies. The experiments reveal orbital-dependent dimensionality: the dx²-y²-dominated band exhibits quasi-two-dimensional character, while the dz²-dominated γ band displays clear kz dispersion. Finite gaps are observed along high-symmetry directions for all detected bands, with temperature-dependent analysis of the γ band indicating a superconducting gap of approximately 18 meV and a ratio 2Δ/kBTc ~ 8, far exceeding the weak-coupling BCS limit. Moreover, suppression of spectral weight near the Fermi level persists above the superconducting transition temperature, and ubiquitous waterfall-like spectral features are observed, indicating a significant influence of electron correlations. These findings underscore the critical role of the third dimension and the dz² orbital in the nickelate superconducting mechanism, imposing important constraints on theoretical models.

This paper points out that Li et al. made three errors in calculating the superconducting volume fraction from zero-field-cooled (ZFC) and field-cooled (FC) magnetization measurements on single crystals of the high-pressure nickelate superconductor La₂SmNi₂O₇. First, due to the paramagnetic Meissner effect (Wohlleben effect), the magnetic moment in FC mode can be either positive or negative, and thus cannot be used to calculate the superconducting volume fraction. Second, reanalysis of Li et al.’s ZFC data reveals that, according to their own calculation method, the superconducting volume fraction should be 22.8%, not the reported 62.1%—a discrepancy of about a factor of three, primarily arising from differences in the demagnetization factor (Li et al. used 0.849, while the authors calculated 0.81548 using Brandt’s formula). Third, even if the ZFC magnetic moment value is correctly calculated, it cannot be directly used to determine the superconducting volume fraction, because there are infinitely many shapes and distributions of superconducting regions smaller than the actual sample size that can produce the same measured magnetic moment. The authors emphasize that they agree with Li et al.’s experimental confirmation of bulk superconductivity in pressurized nickelates, but argue that these calculation errors need to be corrected to avoid misleading future research.