Paper

Using resonant X-ray scattering and spectroscopy, we investigate the relationship between spin-density wave (SDW) order and superconductivity in bilayer nickelate La₂PrNi₂O₇ thin films. Superconductivity is found to emerge only in regions without SDW and with complete oxygen stoichiometry, whereas oxygen deficiency promotes SDW order, indicating phase separation between the two. Further Ni-L₃ and O-K edge spectroscopy reveal that the superconducting phase exhibits a metallic ground state dominated by Ni d⁸ and oxygen ligand-hole character; oxygen deficiency induces electron localization and the appearance of low-energy excitations. Combined with theoretical analysis, we propose that ligand holes primarily reside on the interlayer apical oxygen sites, forming stable interlayer five-spin polaron states as the ground state of superconducting bilayer nickelates. This study demonstrates that oxygen stoichiometry is a key parameter controlling interlayer coupling and electronic structure, and that SDW order is not the intrinsic parent state of superconductivity.

By stabilizing bilayer nickelate (La,Pr)₃Ni₂O₇ superconducting thin films with a protective capping layer and employing X-ray absorption and resonant inelastic X-ray scattering spectroscopy, this study directly probes the evolution of electronic structures across insulating, superconducting, and metallic states. Experimental and theoretical analyses reveal that the in-plane d_{x²-y²} states constitute an itinerant electron backbone, whereas superconductivity emerges only when the out-of-plane d_{z²}-p_z-d_{z²} interlayer hybridization becomes coherent, accompanied by suppression of static spin order and the appearance of strongly damped spin excitations. Oxygen stoichiometry and epitaxial strain jointly regulate this interlayer channel, confining the superconducting phase to a narrow window of interlayer coherence and correlation strength. These findings elucidate the microscopic prerequisites for superconductivity in bilayer nickelates and provide a multi-orbital framework to describe its emergent mechanism.

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.

Motivated by the unresolved question of whether d-wave or s±-wave pairing dominates in the bilayer nickelate La3Ni2O7 and by the unclear connection between its spin order, magnetic excitations, and pairing mechanism, the authors use finite-temperature determinant quantum Monte Carlo simulations of a single-orbital bilayer Hubbard model to study pairing competition under conditions of relatively strong interlayer coupling and comparable intra- and interlayer antiferromagnetic correlation strengths. The results show that with increasing hole doping, spin stripes form spontaneously, accompanied by a crossover of the dominant pairing symmetry from d-wave to s±-wave; this crossover tracks changes in the relative strengths of the two types of spin correlation, with interlayer correlations exceeding intralayer correlations in magnitude. The odd channel of the dynamical spin structure factor further exhibits momentum-dependent reorganization of magnetic excitations, consistent with a fluctuating spin-stripe picture. On this basis, the authors argue that the spin-fluctuation structure is a key link connecting spin stripes and pairing competition and offers a minimal-model perspective for understanding La3Ni2O7; this is a prediction from model calculations rather than an established experimental mechanism.

Based on a bilayer two-orbital Hubbard model, this study employs the ground-state constrained path integral quantum Monte Carlo method to investigate the regulatory mechanisms of vertical electric fields (interlayer potential differences) and electron correlations on the competition between interlayer $s^{\pm}$ and intralayer $d$-wave pairing in bilayer nickelates. The results indicate that increasing the interlayer potential difference typically enhances the $d$-wave pairing vertex contribution and suppresses $s^{\pm}$ pairing, thereby shifting the pairing preference toward the $d$-wave channel; conversely, increasing the crystal field splitting enhances the relative competitiveness of $s^{\pm}$ pairing, while increasing the Hund coupling favors $s^{\pm}$ pairing under weak bias but enhances $d$-wave pairing under large bias. Microscopic analysis reveals that the electric field primarily induces interlayer charge redistribution within each orbital sector, accompanied by enhancements in the antiferromagnetic spin structure factor and local interorbital parallel spin correlations induced by Hund coupling. These findings elucidate the potential connections among charge redistribution, magnetic correlations, and pairing competition, providing a theoretical basis for understanding how layer polarization and multi-orbital interactions influence the relative pairing tendencies in bilayer nickelates.

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.

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.

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.

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.

This study employs $^{139}$La nuclear quadrupole resonance (NQR) spectroscopy to re-examine the crystal structure and spin density wave (SDW) state of ambient-pressure bilayer nickelate La$_3$Ni$_2$O$_7$. The experimental observation of two distinct La(2) sites is naturally explained within the low-symmetry $Am2m$ structural framework, whereas previous defect models based on the $Amam$ structure fail to provide a self-consistent description. Within the $Am2m$ structure, the SDW spin configuration is re-identified as a “large-small” spin stripe structure, arising from the distinct large and small magnetic moments associated with two inequivalent Ni sites. Based on DFT+U calculations and NQR parameter analysis, the study confirms the itinerant nature of this SDW order, indicating that it is driven by Fermi surface nesting rather than local magnetic moment mechanisms, thereby providing a foundation for understanding the origin of high-$T_c$ superconductivity in this material under high pressure.