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This review systematically summarizes theoretical progress on the interlayer pairing mechanism driven by strong correlation effects in bilayer nickelate superconductors. Starting from key experimental observations, the paper extracts core physical ingredients, including the hybridized electronic structure of Ni-3d({x^2-y^2}) and 3d({z^2}) orbitals, orbital-dependent electronic correlations, Hund’s coupling, and strong interlayer magnetic coupling, and introduces fundamental theoretical frameworks such as the bilayer two-orbital Hubbard model and its (t)-(J) variants. Emphasis is placed on the strong-correlation pairing mechanism rooted in an interlayer valence bond picture in the atomic limit of half-filled d({z^2}) orbitals, with particular stress on the hybridization mechanism: local singlet pairing of d({z^2}) electrons provides condensation energy, while hybridization with itinerant d(_{x^2-y^2}) orbitals promotes superconducting phase coherence. The review further analyzes the pairing symmetry, the dependence of critical temperature on various internal and external parameters, and non-trivial normal-state behaviors including Fermi liquid, non-Fermi liquid, weak insulating, and pseudogap regimes, and discusses the effects of pressure tuning, oxygen stoichiometry, and Kondo scattering induced by oxygen vacancies. The central conclusion points to an unconventional superconductivity picture driven by the synergy between local pairing and itinerant behavior, and briefly mentions weak-coupling theories based on spin fluctuations arising from Fermi surface nesting.

High-temperature superconductivity in pressurized La3Ni2O7 has attracted considerable interest, yet the superconducting phase is rather fragile. Although bulk superconductivity can be achieved by Pr substitution for La, the underlying mechanism is still unclear. A further puzzle is the role of oxygen content: moderate oxygenation enhances superconductivity, whereas high-pressure oxygen annealing suppresses it. Here combining multislice electron ptychography and electron energy-loss spectroscopy, we show that Pr doping mitigates oxygen vacancies and stabilizes a near-stoichiometric La2PrNi2O7 structure. Strikingly, high-pressure oxygen annealing introduces interstitial oxygen atoms that arrange into a stripe-ordered superstructure, which generates excess hole carriers and alters the electronic structure, ultimately suppressing superconductivity under pressure. This contrasts sharply with cuprates, where similar oxygen ordering is known to induce superconductivity. Our findings reveal a competition between interstitial oxygen ordering and superconductivity in bilayer nickelates, providing key insights into the pairing mechanism and guiding principles for engineering more robust superconducting phases.

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Addressing the long-standing puzzle of the pairing mechanism for high-temperature superconductivity in cuprates and nickelates, this paper proposes a picture of itinerant Cooper pairs mediated by oxygen-bridged electron pairs (e⁻-O-e⁻) or metal-bridged hole pairs (h⁺-M-h⁺), based on the dominant role of ionic bonds on the order of eV, the electron affinities of O⁻ and O²⁻ (1.46 eV and -8.08 eV, respectively), and the large double ionization energies of metal atoms (approximately 15–28 eV). Such pairing forms below the pseudogap temperature T*, which is higher than Tc, and follows the relationship of chemical bond → structure → properties, being applicable to cuprates, nickelates, iron-based, and other ionic superconductors. The author verifies the correctness and universality of this mechanism through 32 independent experimental pieces of evidence, especially STM images within the CuO₂ plane and the extremely small pairing size, and points out that any sub-eV or covalent bonding pairing mechanism is unreliable. This theory reveals the missing link between ionic bonds and superconductivity, resolves a four-decade-long puzzle, and demonstrates the feasibility of achieving room-temperature carrier pairing in ionic-bond superconductors. Based on this, the author establishes a new theoretical framework centered on the strongest pairing strength and Bose–Einstein condensation, opening a new path for understanding the mechanism of high-temperature superconductivity and bringing the dream of room-temperature superconductivity closer to reality.

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This paper develops a unified itinerant electron description for the nature of spin-density wave (SDW) order and magnetic excitations in Ruddlesden-Popper nickelates. The central element is the mirror symmetry of the NiO₂ multilayer blocks, which organizes the low-energy electronic states into mirror-even and mirror-odd sectors. It is shown that the dominant interband nesting between mirror-opposite sectors drives a mirror-selective itinerant SDW instability, whose collective modes naturally reproduce the spin-wave-like spectra observed experimentally. In La₄Ni₃O₁₀, the SDW further induces a secondary mirror-even charge density wave, giving rise to intertwined spin and charge textures. These results demonstrate that magnetism in multilayer nickelates is intrinsically itinerant rather than of local-moment origin, and establish mirror-selective interband SDW order as a unifying organizational principle for magnetic correlations in these systems.

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This study systematically analyzed the electronic structure of strained La₃Ni₂O₇ thin films using density functional theory calculations, revealing that biaxial compressive strain primarily elongates the outer apical Ni–O bonds while leaving the inner apical Ni–O bonds nearly unchanged, thereby significantly enhancing the Jahn–Teller splitting energy Δ_JT, yet the interlayer d_z² orbital hopping parameter t_⊥^z exhibits only a weak variation. Given that superconductivity emerges only when the in-plane lattice constant falls below a critical value, these results identify strain-enhanced Δ_JT as a key microscopic tuning parameter. The calculated Fermi surface topology and Hall response agree well with angle-resolved photoemission spectroscopy (ARPES) and Hall measurements on LaAlO₃ and SrLaAlO₄ substrates, confirming that Jahn–Teller distortion plays a central role in optimizing superconductivity in bilayer nickelates.

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