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The discovery of high-temperature superconductivity in La3⁢Ni2⁢O7 at pressures above 14 GPa has spurred extensive research efforts. Yet, fundamental aspects of the superconducting phase, including the possibility of a filamentary character, are currently subjects of controversial debates. Conversely, a crystal structure with NiO6 octahedral bilayers stacked along the 𝑐-axis direction was consistently posited in initial studies on La3⁢Ni2⁢O7. Here, we reassess this structure in optical floating zone-grown La3⁢Ni2⁢O7 single crystals that show signs of filamentary superconductivity. Employing scanning transmission electron microscopy and single-crystal x-ray diffraction under high pressures, we observe multiple crystallographic phases in these crystals, with the majority phase exhibiting alternating monolayers and trilayers of NiO6 octahedra, signifying a profound deviation from the previously suggested bilayer structure. Using density functional theory, we disentangle the individual contributions of the monolayer and trilayer structural units to the electronic band structure of La3⁢Ni2⁢O7, providing a firm basis for advanced theoretical modeling and future evaluations of the potential of the monolayer-trilayer structure for hosting superconductivity.在高于 14 GPa 的压力下， La3⁢Ni2⁢O7 中高温超导性的发现激发了广泛的研究。然而，超导相的基本性质，包括其丝状特征的可能性，目前仍存在争议。相反，在对 La3⁢Ni2⁢O7 的早期研究中，人们一直假设其晶体结构为沿 𝑐 轴方向堆叠的 NiO6 八面体双层。本文中，我们重新评估了光学浮区法生长的 La3⁢Ni2⁢O7 单晶中的这种结构，这些单晶表现出丝状超导的迹象。利用扫描透射电子显微镜和高压下的单晶 X 射线衍射技术，我们观察到这些晶体中存在多种晶相，其中主要相由 NiO6 八面体的单层和三层交替构成，这表明其与先前提出的双层结构存在显著偏差。利用密度泛函理论，我们分离出单层和三层结构单元对 La3⁢Ni2⁢O7 电子能带结构的各个贡献，为高级理论建模和未来评估单层-三层结构承载超导性的潜力提供了坚实的基础。

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This study addresses the discrepancy between bulk La₃Ni₂O₇ with high transition temperatures under high pressure and its thin-film counterpart, which superconducts at ambient pressure but with a reduced Tc, by developing a symmetry-based phenomenological approach combined with DFT+U calculations and experimentally determined Tc and structural symmetries to analyze the superconducting gap structure. The results reveal that both systems exhibit s±-wave pairing symmetry and two-band superconductivity, but the dominant microscopic pairing configurations differ: in pressurized bulk, superconductivity is primarily governed by out-of-plane pairing of Ni-dz² orbitals, whereas in thin films, in-plane pairing of Ni-dx²-y² orbitals dominates. The reduction in Tc is attributed to a decreased ratio of interlayer to intralayer hopping in the film, which shifts the dominant pairing type from out-of-plane to in-plane. These findings highlight the crucial role of symmetry in unconventional superconductivity, and the developed methodology is expected to be extendable to other unconventional superconductors.

The family of nickelate superconductors have long been explored as analogs of the high temperature cuprates. Nonetheless, the recent discovery that certain stoichiometric nickelates superconduct up to high $T_c$ under pressure came as a surprise. The mechanisms underlying the superconducting state remain experimentally unclear. In addition to the practical challenges posed by working in a high pressure environment, typical samples exhibit anomalously weak diamagnetic responses, which have been conjectured to reflect inhomogeneous `filamentary’ superconducting states. We perform wide-field, high-pressure, optically detected magnetic resonance spectroscopy to image the local diamagnetic responses of as grown La$_3$Ni$_2$O$_7$ samples \emph{in situ}, using nitrogen vacancy quantum sensors embedded in the diamond anvil cell. These maps confirm significant inhomogeneity of the functional superconducting responses at the few micron scale. By spatially correlating the diamagnetic Meissner response with both the local tensorial stress environment, also imaged \emph{in situ}, and stoichiometric composition, we unravel the dominant mechanisms suppressing and enhancing superconductivity. Our wide-field technique simultaneously provides a broad view of sample behavior and excellent local sensitivity, enabling the rapid construction of multi-parameter phase diagrams from the local structure-function correlations observed at the sub-micron pixel scale.

Unconventional charge and spin density-wave states are commonly observed in bilayer nickelates, drawing considerable attention due to their proximity to high-$T_c$ superconductivity in various phase diagrams. However, the nature and mechanisms of charge and spin density-waves (DWs) in nickelates remain poorly understood. Numerous experiments have reported that the charge-density-wave (CDW) transition temperature $T_{ cdw}$ and the spin-density-wave (SDW) transition temperature $T_{sdw}$ are closely related but distinct. However, in contrast to these experiments, previous mean-field-type analyses have yielded only a simple SDW phase. To resolve this key problem, this paper demonstrates that sizable CDW instabilities emerge in proportion to the SDW instability in La$3$Ni$2$O$7$.This behavior is driven by the paramagnon-interference (PMI) mechanism, which captures important electron correlations beyond mean-field theory. Therefore, (i) experimental CDW + SDW coexisting state is naturally explained. In addition, (ii) the CDW + SDW fluctuations cooperatively drive high-$T_c$ superconductivity. Notably, the predicted $s$-wave SC state is robust against the inner apical O vacancies. Furthermore, (iii) the CDW instability is highly sensitive to the size of the $d_{z^2}$-orbital hole pocket, allowing for the realization of CDW quantum criticality through carrier-doping and pressure application. We find that the coexistence of charge and spin fluctuations is essential in bilayer nickelates, with both playing a cooperative role in mediating high-$T_c$ superconductivity.

Unconventional charge- and spin-density-wave states are commonly observed in bilayer nickelates, drawing considerable attention due to their proximity to high-transition temperature ( $${T}_{{\rm{c}}}$$) superconductivity. However, the nature and origin of these density waves remain poorly understood. Experiments show that the charge-density-wave and spin-density-wave transition temperatures are closely related but distinct, while mean-field-type analyses typically have yielded only a simple spin-density-wave phase. To resolve this key problem, this paper demonstrates that sizeable charge-density-wave instabilities emerge in proportion to spin-density-wave instabilities in La3Ni2O7 due to the paramagnon-interference mechanism, which captures electron correlations beyond mean-field theories. Therefore, (i) the experimental charge- and spin-density-wave coexisting state is naturally explained, and (ii) charge- and spin-density-wave fluctuations cooperatively drive high- $${T}_{{\rm{c}}}$$superconductivity. Furthermore, the predicted s-wave superconducting state is robust against the inner-apical oxygen vacancies. We find that the coexistence of charge- and spin-fluctuations is essential in bilayer nickelates, with both playing a cooperative role in mediating high- $${T}_{{\rm{c}}}$$superconductivity.

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The discovery of pressure-induced superconductivity in two- and three-layer Ruddlesden-Popper nickelates has generated significant interest in these materials as a platform for unconventional superconductivity. While their ground state exhibits magnetism, a direct determination of their magnetic structure remains elusive. Understanding this aspect is crucial, as magnetism may play a role in the pairing mechanism of superconductivity in these compounds. We resolve the magnetic structures of the bilayer (2222) polymorphs of La3Ni2O7 and La2PrNi2O7 using neutron powder diffraction (NPD) and muon-spin rotation/relaxation (muSR). Magnetic neutron scattering appears below approximately 150 K in both compounds and is observed at the (qx, 1/2, 0) position, with qx = 0 and 1/2 for La3Ni2O7 and qx = 0 for La2PrNi2O7. Within a single layer, alternating low (0.05 - 0.075 muB) and high (0.66 muB) magnetic moment stripes form. These layers stack antiferromagnetically along the c-direction to form bilayers. The presence of two propagation vectors (qx = 0 and 1/2) in undoped La3Ni2O7 suggests the coexistence of two magnetic stacking polymorphs within a single crystallographic phase. The muSR spectra further confirm these magnetic structures. Our findings provide a detailed understanding of the magnetic ground state in bilayer nickelates, offering insights into possible precursor states that may influence the emergence of superconductivity in these materials.

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