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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.

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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.

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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.

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