Paper

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.

本研究通过氧同位素替换（¹⁶O→¹⁸O），利用电阻率和μ子自旋旋转（μSR）实验，系统探索了双层Ruddlesden-Popper镍酸盐La₃Ni₂O₇中电荷密度波（CDW）和自旋密度波（SDW）转变的同位素效应。电阻率测量显示，CDW转变温度在¹⁸O取代后显著升高约6 K，而μSR结果则表明SDW转变温度在实验误差范围内不受影响。拉曼光谱证实了同位素替换的有效性及晶格声子模的软化。这一对比鲜明的同位素响应表明，晶格振动（即电子-声子耦合）在CDW序的形成中扮演重要角色，而SDW序主要源于电子相互作用。研究结果揭示了两种密度波序的不同微观起源，并提示电子-声子耦合可能对Ruddlesden-Popper镍酸盐的超导配对机制具有潜在关联，为理论模型提供了关键约束。

通过密度泛函理论结合动力学平均场理论（DFT+DMFT）和随机相位近似（RPA）系统研究了1313相La₃Ni₂O₇的电子结构和超导机制。DMFT计算表明，单层子系统呈近绝缘态，其中d_{z²}轨道表现出莫特物理，而三层子系统保持金属性，超导主要源于后者，且其Ni-e_g轨道相对于块体La₄Ni₃O₁₀处于空穴掺杂状态。基于DMFT导出的低能有效哈密顿量，RPA分析给出三层子系统内为s^{±}波配对对称性。与块体La₄Ni₃O₁₀相比，1313相超导转变温度显著降低的原因有两个：一是空穴掺杂减弱了配对强度；二是单层子系统作为弱连接层，将相邻的三层超导层构成S-N-S约瑟夫森结，抑制了层间相位相干，从而进一步降低全局转变温度。综合结果表明，RP相La₃Ni₂O₇家族中的高温超导应归属于2222相而非1313相。

通过密度泛函理论（DFT）和随机相位近似（RPA）计算，该研究系统分析了高压下La₅Ni₃O₁₁的电子性质与超导机制。DFT能带结构显示，这种交替堆叠双层和单层NiO₂面的材料存在两组近乎解耦的子能带，分别来自双层子系统和单层子系统。RPA分析表明，超导配对主要发生在双层子系统内，并呈现与加压La₃Ni₂O₇类似的s±波配对对称性；而单层子系统主要通过极弱的层间约瑟夫森耦合（IJC）作为桥梁，连接相邻双层以实现沿c轴的相位相干。在低压下，压力增强使IJC显著提升，从而抬升体态超导转变温度（Tc）；当压力足够高时，γ-pocket的态密度降低导致Tc逐渐下降。这一机制自然解释了实验中观测到的穹顶状Tc-压力依赖关系，并揭示了混合相与纯相镍酸盐超导体不同的压力响应。

The discovery of superconductivity (SC) with critical temperature Tc above the boiling point of liquid nitrogen in pressurized La3Ni2O7 has sparked a surge of exploration of high-Tc superconductors in the Ruddlesden-Popper (RP) phase nickelates. More recently, the RP phase nickelate La5Ni3O11, which hosts a layered structure with alternating bilayer and single-layer NiO2 planes, has been reported to accommodate SC under pressure, exhibiting a dome-shaped pressure dependence with the highest Tc ≈ 64 K, capturing a lot of interest. Here, using density functional theory (DFT) and random phase approximation (RPA) calculations, we systematically study the electronic properties and superconducting mechanism of this material. Our DFT calculations yield a band structure including two nearly decoupled sets of sub-band structures, with one set originating from the bilayer subsystem and the other from the single-layer one. RPA-based analysis demonstrates that SC in this material occurs primarily within the bilayer subsystem exhibiting an s± wave pairing symmetry similar to that observed in pressurized La3Ni2O7, while the single-layer subsystem mainly serves as a bridge facilitating the inter-bilayer phase coherence through the interlayer Josephson coupling (IJC). Since the IJC thus attained is extremely weak, it experiences a prominent enhancement under pressure, leading to the increase of the bulk Tc with pressure initially. When the pressure is high enough, the Tc gradually decreases due to the reduced density of states on the γ-pocket. In this way, the dome-shaped pressure dependence of Tc observed experimentally is naturally understood.

双层镍酸盐La₃Ni₂O₇高温超导体的配对机制研究表明，基于“基因原理”和“协同费米面规则”的统一框架可自然延伸至该双层多轨道体系。通过强关联分析，识别出两个主导反铁磁超交换通道：由内顶角氧介导的层内同轨道（d_z²）最近邻交换J⊥，以及由面内氧介导的层间不同轨道（d_z²与d_x²-y²）最近邻交换J_xz。由于双层成键-反键劈裂和d_x²-y²轨道的B₁g对称性，两通道协同作用产生稳定的s±超导态，其特征是动量空间中镜像偶与镜像奇费米面口袋之间存在内部符号反转。两个配对通道均在β口袋上最大化超导能隙，形式因子为(cosk_x-cosk_y)²。该结果将La₃Ni₂O₇纳入非常规超导的统一框架，同时揭示了其独特的高温超导配对电子环境。

本文采用密度矩阵重正化群方法，研究了强链间耦合的三腿t-J梯子近1/3填充时的基态性质。在空穴掺杂进入1/3填充的自旋能隙态时，对关联函数呈幂律衰减，而自旋关联函数呈指数衰减；相反，电子掺杂并未显著增强对关联。进一步对比了三腿Hubbard模型，发现空穴掺杂态的对关联特性与t-J模型类似，但需足够大的自旋能隙。研究表明，空穴掺杂近1/3填充态有利于超导配对，这一非对称配对性质与弱耦合理论预测的相图不同，为理解三层镍酸盐超导体的电子特性提供了数值依据。

该研究采用重整化平均场理论，基于包含 (d_{z^2}) 和 (d_{x^2-y^2}) 轨道的双层 (t-J) 模型，系统探究了 La₃Ni₂O₇ 薄膜的超导配对对称性。通过自洽求解，揭示出由 (d_{z^2}) 轨道强层间超交换耦合驱动的 (s_\pm) 波配对，与加压块体情形一致，并成功重现了角分辨光电子能谱观测到的 (\beta) 费米面口袋上无节点超导能隙结构，计算得到的超导转变温度约 60 K 与实验吻合。轨道分辨分析表明，(\beta) 口袋的无节点特征源于 (d_{z^2}) 和 (d_{x^2-y^2}) 轨道层间配对的协同作用，同时面内 (d_{z^2}) 与 (d_{x^2-y^2}) 轨道间形成 (d) 波配对分量，可进一步增强主导的 (s_\pm) 波配对。该工作揭示了 La₃Ni₂O₇ 薄膜复杂费米面上不同配对通道间的多样协作与竞争关系，并讨论了衬底应变、氧空位等因素对配对对称性的潜在调制，为理解镍酸盐超导机理提供了重要理论依据。

本研究采用外延生长的La2.82Sr0.18Ni2O7薄膜（超导转变温度约31.6 K），通过高场输运测量（最高58 T）系统表征了上临界场及其各向异性。近转变温度附近，超导呈现厚度限制的二维特征；冷却后，面外相干长度减小至小于薄膜厚度（6 nm），表明体系向本征三维体超导转变。基于Ginzburg-Landau模型分析，测得零温下面内和面外上临界场分别为82 T和45 T，各向异性比γ≈1.34，与块材Ruddlesden-Popper镍酸盐相当。低温下面内方向上临界场因自旋顺磁对破裂效应被强烈压制，接近Pauli极限（58 T），而面外方向几乎不受影响。这种各向异性Pauli限制解释了上临界场各向异性降低的现象，并支持薄膜中超导本质上是三维体超导的结论。结果凸显了自旋顺磁效应在决定该类镍酸盐高场超导相图中的关键作用。

受垂直电场可调控Ruddlesden–Popper双层镍酸盐La₃Ni₂O₇超导性质的启发，本研究采用动力学簇量子蒙特卡洛方法求解不平衡双轨道双层Hubbard模型。通过分析未掺杂、空穴掺杂及电子掺杂情形下电场诱导的配对对称性及其演化，发现源自d_{z²}轨道的s±波配对被抑制，同时层间d_{z²}轨道失配及电子向d_{x²-y²}轨道转移驱动了从s±波到d波的配对对称性转变。有趣的是，由d_{x²-y²}轨道产生的d波配对随电场强度呈现穹顶状行为。大规模多体计算与弱耦合方法的预期一致，为理解RP镍酸盐的超导机制提供了新见解。