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The report of superconductivity (SC) with Tc~80 K in bilayer Ruddlesden-Popper (RP) nickelate La3Ni2O7-delta have sparked considerable investigations on its normal state properties and SC mechanism under pressure and at low temperature. It is believed that the density wave (DW) at ~150 K plays an important role in SC emergence, but its nature remains largely underexplored. Here, we utilized temperature-dependent in-situ Ni K-edge X-ray Absorption Near-edge Spectroscopy (XANES) to probe the Ni-3d/4p electronic states of La3Ni2O7-delta and La2PrNi2O7-delta samples down to 4.8 K, enabling us to witness the evolution of both in-plane d_(x^2-y^2)/p_x (p_y) and out-of-plane d_(3z^2-r^2)/p_z orbitals of NiO6 octahedron across the DW transition. Main edge energy associated with Ni 4p orbital shows an anomalous decline near DW transition, signifying the occurrence of lattice distortions as a hallmark of charge density wave. Below DW transition, the enlarged crystal field splitting (CFS) indicates an enhanced NiO6 octahedral distortion. Intriguingly, magnetic Pr substituents could activate the mutual interplay of d_(x^2-y^2) and d_(3z^2-r^2) orbitals. We discussed its relevance to the favored bulk SC in the pressurized polycrystalline La2PrNi2O7-delta than pristine.

Site-selective (^{17})O-NMR measurements of the inner apical O(1), outer apical O(2), and planar O(3,4) sites were used to investigate the spin density wave order in the bilayer nickelate La(3)Ni(2)O(7). Below (T{\rm SDW}=150) K, all planar O(3,4) sites broaden significantly due to the appearance of internal magnetic fields, while the O(2) sites show almost no internal field, consistent with coherent spin density wave order with single-spin–no-spin (or large–small spin) stripes; the internal field at the O(1) sites bridging the NiO(2) planes nearly cancels, indicating an antiparallel spin configuration between adjacent planes. Below (T{\rm A}\sim 115) K, however, although the in-plane spin density wave order remains robust, the O(1) spectrum disappears, indicating that the antiparallel spin arrangement through the Ni–O(1)–Ni bonds is not particularly stable. In particular, the O(2) sites, which are strongly covalently bonded to the (d{3z^2-r^2}) orbitals, exhibit extremely small local spin susceptibility, suggesting that the Ni-(d{3z^2-r^2}) orbitals bridging the NiO(_2) planes already form a well-developed interlayer spin singlet. These results reveal interlayer spin singlet formation and an anomalous spin reconstruction through the Ni–O(1)–Ni bonding orbitals, reflecting the orbital-selective nature of this bilayer nickelate.

This study employs the variational Monte Carlo method to investigate superconductivity in a two-band t-J model consisting of an itinerant orbital (orbital 0) and a quasi-localized orbital (orbital 1). The key finding is the emergence of a robust orbital-selective d-wave superconducting state, which originates entirely from the itinerant orbital 0. Analysis of the superexchange energy hierarchy reveals that the quasi-localized orbital 1 competes with superconductivity by favoring the formation of local inter-orbital bound states, which act as energy defects that disrupt phase coherence. Consequently, the superconducting order parameter decreases monotonically with increasing occupation of orbital 1. Inspired by superconductivity in the nickelate La₃Ni₂O₇, these results highlight the crucial role of multiorbital physics beyond the single-band t-J framework and identify a concrete pathway for enhancing the superconducting transition temperature: suppressing the involvement of the localized d_{z²} orbital.

By constructing the global phase diagram of a bilayer two-orbital Hubbard model, we investigate the orbital-selective electron correlations in the bilayer nickelate La3Ni2O7. At half-filling the system undergoes a Mott transition, and at the physical electron filling it exhibits strong orbital selectivity, manifested as interlayer spin singlet formation among z²-orbital electrons. This effect leads to significant band-structure renormalization with dramatic bandwidth narrowing, while the splitting between the z² bonding and antibonding bands remains at about 1 eV. These correlation features naturally explain the orbital-dependent effective mass enhancement and the sinking of the z² bonding band below the Fermi level observed in ARPES experiments, as well as the puzzling contrast in optical conductivity where the Drude weight drops sharply yet the interband peak position barely shifts. Theoretical analysis reveals that interlayer antiferromagnetic superexchange plays a key role in maintaining the band splitting, and intralayer correlations drive the z² band away from the Fermi surface. This work provides a unified microscopic picture for understanding the normal-state properties and the mechanism of high-temperature superconductivity in multilayer nickelates.

This paper proposes a microscopic Hamiltonian that faithfully reflects the crystal symmetry of the bilayer nickelate La₃Ni₂O₇ under ambient pressure, addressing its unconventional magnetic order. Large-scale density matrix renormalization group calculations reveal that under a large Hund coupling (J_H), a ((\pi/2, \pi/2)) spin stripe order emerges due to hidden quasi-one-dimensionality and persists over a range of electron concentrations. In the more symmetric high-pressure regime, when the interlayer antiferromagnetic coupling (J_\perp) is sufficiently strong, the model exhibits an enhanced tendency for interlayer pairing. This study unveils the microscopic origin of the diagonal spin stripe order and identifies both the Hund coupling (J_H) and the interlayer coupling (J_\perp) as key factors controlling the magnetic order and pairing tendency in La₃Ni₂O₇.

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The recent discovery of superconductivity in pressurized bilayer nickelate La3Ni2O7 has triggered tremendous research interest. However, the experimentally observed oxygen deficiency implies that obtaining perfect stoichiometric single crystals is still challenging. The influence of oxygen deficiency on physical properties remains unexplained. Here, we construct a chemical potential phase diagram to characterize the stability of La3Ni2O7. The narrow stable region explains the difficulty of synthesizing pure samples. First, oxygen defect studies reveal that the interlayer apical oxygen vacancy has the highest defect concentrations and is responsible for oxygen deficiency. Second, unfolding band structures show as the oxygen-deficient variant increases, Ni $$3d_{\;z^{2}}$$bands shift toward a lower energy position under the Fermi level at Γ point, which is adverse to the metallization of Ni $$3d_{\;z^{2}}$$bands. Third, high-pressure calculations indicate that oxygen vacancy would destroy the hybridization of interlayer Ni $$3d_{\;z^{2}}$$orbitals, and the larger the oxygen deficiency, the higher the pressure needed to metalize the Ni $$3d_{\;z^{2}}$$bands. Thus, the oxygen deficiency would suppress the emergence of superconductivity in La3Ni2O7−δ. Our results elucidate the mechanism of oxygen deficiency for superconductivity in La3Ni2O7−δ and provide instructive guidance to the experimental research.