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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.

利用位点选择性17O-NMR对内顶端O(1)、外顶端O(2)和平面O(3,4)位点的测量研究了双层镍酸盐La3Ni2O7的自旋密度波序。在T_SDW=150 K以下，所有平面O(3,4)位点因内部磁场出现而显著展宽，而O(2)位点几乎无内部场，这与具有单自旋-无自旋（或大-小自旋）条纹的共格自旋密度波序一致；桥接NiO2平面的O(1)位点内部场几乎抵消，表明相邻平面间为反平行自旋构型。然而在T_A约115 K以下，尽管面内自旋密度波序仍保持强健，O(1)谱却消失，说明通过Ni–O(1)–Ni键的反平行自旋排列并不特别稳定。尤其与d_{3z^2-r^2}轨道强共价的O(2)位点局域自旋磁化率极小，表明桥接NiO2平面的Ni-d_{3z^2-r^2}轨道已形成良好的层间自旋单态。这些结果揭示了层间自旋单态形成及通过Ni–O(1)–Ni键合轨道的异常自旋重构，体现了该双层镍酸盐的轨道选择性本质。

本研究采用变分蒙特卡罗方法，对包含一个巡游轨道（轨道0）和一个准局域轨道（轨道1）的双带t-J模型中的超导电性进行了探索。核心发现是，系统呈现出稳健的轨道选择性d波超导态，该超导态完全起源于巡游的轨道0。通过对超交换能级层次的分析表明，准局域化的轨道1通过倾向于形成局域轨道间束缚态来与超导电性竞争，这些束缚态作为能量缺陷破坏了相位相干性。相应地，超导序参量随轨道1占据数的增加而单调下降。受镍酸盐La₃Ni₂O₇中超导电性的启发，这些结果强调了超越单带t-J框架的多轨道物理的关键作用，并为提高超导转变温度指明了具体途径：抑制源于局域d_{z²}轨道的参与。

通过构建双层两轨道哈伯德模型的全域相图，研究了双层镍酸盐La3Ni2O7中的轨道选择性电子关联。在半填充时体系发生莫特转变，在物理电子数下呈现强轨道选择性，表现为z²轨道电子形成层间自旋单重态。该效应导致能带结构显著重整化，带宽大幅收缩，而z²成键与反键带间的分裂仍维持在约1 eV。这些关联特征自然解释了ARPES实验观测到的轨道依赖有效质量增强和z²成键带下沉至费米能级以下，以及光学电导率中Drude权重急剧降低而带间峰位几乎不移动的矛盾现象。理论分析表明，层间反铁磁超交换作用在维持带分裂中起关键作用，且层内关联使z²带脱离费米面。该工作为理解多层镍酸盐的常态性质和高温超导机制提供了统一的微观图像。

针对双层镍酸盐La₃Ni₂O₇在常压下的非常规磁序，本文提出了一个忠实反映其晶体对称性的微观哈密顿量。通过大规模密度矩阵重正化群计算表明，在较大的Hund耦合JH作用下，由于隐藏的准一维性，模型中出现了(π/2,π/2)自旋条纹序，并在一定电子浓度范围内持续存在。在更对称的高压区域，当层间反铁磁耦合J⊥足够强时，模型表现出增强的层间配对倾向。该研究揭示了对角自旋条纹的微观起源，并确认Hund耦合JH和层间耦合J⊥是控制La₃Ni₂O₇磁序和配对倾向的关键要素。

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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.