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。
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。