Paper

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.

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.

The recent discovery of superconductivity in La3Ni2O7−δ under high pressure with a transition temperature around 80 K (ref. 1) has sparked extensive experimental2–6 and theoretical efforts7–12. Several key questions regarding the pairing mechanism remain to be answered, such as the most relevant atomic orbitals and the role of atomic deficiencies. Here we develop a new, energy-filtered, multislice electron ptychography technique, assisted by electron energy-loss spectroscopy, to address these critical issues. Oxygen vacancies are directly visualized and are found to primarily occupy the inner apical sites, which have been proposed to be crucial to superconductivity13,14. We precisely determine the nanoscale stoichiometry and its correlation to the oxygen K-edge spectra, which reveals a significant inhomogeneity in the oxygen content and electronic structure within the sample. The spectroscopic results also reveal that stoichiometric La3Ni2O7 has strong charge-transfer characteristics, with holes that are self-doped from Ni sites into O sites. The ligand holes mainly reside on the inner apical O and the planar O, whereas the density on the outer apical O is negligible. As the concentration of O vacancies increases, ligand holes on both sites are simultaneously annihilated. These observations will assist in further development and understanding of superconducting nickelate materials. Our imaging technique for quantifying atomic deficiencies can also be widely applied in materials science and condensed-matter physics.

This study performed in situ high-pressure angle-dependent electrical transport measurements on Pr₄Ni₃O₁₀ single crystals using a custom diamond anvil cell rotator, confirming their superconducting anisotropy. Under a pressure of 50.2 GPa, the sample underwent a superconducting transition with a critical temperature of approximately 31 K. By measuring the upper critical fields perpendicular and parallel to the ab-plane, an anisotropy parameter γ of about 1.6 was obtained, which decreased with increasing temperature and approached 1 near the superconducting critical temperature. Fitting with the Ginzburg-Landau model yielded zero-temperature upper critical fields parallel and perpendicular to the ab-plane of 89.9 T and 57.3 T, respectively, and coherence lengths along the ab-plane and c-axis of 2.4 nm and 1.5 nm, respectively. Comparison with cuprate and iron-based superconductors revealed that the anisotropic behavior of Pr₄Ni₃O₁₀ conforms to a two-band model, where in-plane quantum confinement induces interlayer coherence, resulting in three-dimensional superconducting characteristics. This study not only confirms the existence of anisotropic superconductivity in bulk Ruddlesden-Popper nickelates but also provides critical insights into the role of dimensionality in the mechanism of high-temperature superconductivity.

Addressing the controversy over the pairing mechanism in the bilayer nickelate La₃Ni₂O₇, this work exploits the low-anisotropy nodeless full gap revealed by angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) as a constraint, and proposes the pairing gap along the Brillouin zone diagonal as a decisive probe. Symmetry analysis shows that the hybridization between the d_(x²−y²) and d_(z²) orbitals vanishes along this diagonal, so that the gaps on the γ pocket and on the α/β pockets separately encode the intrinsic pairing strength of the two orbitals. A d_(z²)-orbital-dominated hybridization-driven pairing mechanism would force gap nodes on the α/β pockets along the diagonal direction, directly contradicting the observed U-shaped dI/dV spectrum, whereas a d_(x²−y²)-orbital-dominated Hund’s-rule-driven pairing mechanism yields a uniform full gap over the entire Fermi surface, consistent with the ARPES and STM results. Weak-coupling random-phase approximation calculations, owing to the density-of-states advantage of the d_(z²) orbital, also produce nodal or near-nodal behavior near the diagonal, in conflict with experiment. This work therefore clarifies the dominant role of the d_(x²−y²) orbital in pairing and establishes the Hund’s-rule-driven pairing mechanism as the most relevant superconducting picture for La₃Ni₂O₇.