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This paper employs the density matrix renormalization group method to study the ground-state properties of a three-leg t-J ladder with strong interchain coupling near 1/3 filling. When holes are doped into the spin-gapped state at 1/3 filling, the pairing correlation function exhibits power-law decay while the spin correlation function decays exponentially; in contrast, electron doping does not significantly enhance pairing correlations. Further comparison with the three-leg Hubbard model shows that the pairing correlation properties of the hole-doped state are similar to those of the t-J model, but require a sufficiently large spin gap. The study indicates that hole doping near 1/3 filling favors superconducting pairing, and this asymmetric pairing property differs from the phase diagram predicted by weak-coupling theory, providing numerical evidence for understanding the electronic properties of tri-layer nickelate superconductors.

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Using renormalized mean-field theory based on a bilayer (t-J) model incorporating (d_{z^2}) and (d_{x^2-y^2}) orbitals, this study systematically investigates the superconducting pairing symmetry of La₃Ni₂O₇ thin films. Self-consistent solutions reveal (s_\pm)-wave pairing driven by strong interlayer superexchange coupling of the (d_{z^2}) orbital, consistent with the pressurized bulk case, and successfully reproduce the nodeless superconducting gap structure on the (\beta) Fermi surface pocket observed by angle-resolved photoemission spectroscopy, yielding a calculated superconducting transition temperature of approximately 60 K in agreement with experiments. Orbital-resolved analysis demonstrates that the nodeless character of the (\beta) pocket arises from the cooperative interlayer pairing of (d_{z^2}) and (d_{x^2-y^2}) orbitals, while in-plane pairing between these orbitals generates a (d)-wave component that further enhances the dominant (s_\pm)-wave order. The work elucidates the diverse cooperative and competitive relationships among different pairing channels on the complex Fermi surfaces of La₃Ni₂O₇ films and discusses the potential modulation of pairing symmetry by factors such as substrate strain and oxygen vacancies, providing a crucial theoretical basis for understanding the superconducting mechanism in nickelates.

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This study employs epitaxial La2.82Sr0.18Ni2O7 thin films (with a superconducting transition temperature of approximately 31.6 K) to systematically characterize the upper critical field and its anisotropy via high-field transport measurements up to 58 T. Near the transition temperature, superconductivity exhibits thickness-limited two-dimensional characteristics; upon cooling, the out-of-plane coherence length decreases to below the film thickness (6 nm), indicating a transition to intrinsic three-dimensional bulk superconductivity. Based on the Ginzburg-Landau model, the zero-temperature in-plane and out-of-plane upper critical fields are determined to be 82 T and 45 T, respectively, yielding an anisotropy ratio γ≈1.34, comparable to that of bulk Ruddlesden-Popper nickelates. At low temperatures, the in-plane upper critical field is strongly suppressed by the spin paramagnetic pair-breaking effect, approaching the Pauli limit (58 T), while the out-of-plane direction remains largely unaffected. This anisotropic Pauli limiting explains the reduced anisotropy of the upper critical field and supports the conclusion that superconductivity in the films is inherently three-dimensional bulk superconductivity. The results highlight the critical role of spin paramagnetic effects in determining the high-field superconducting phase diagram of these nickelates.

Inspired by the vertically electric-field-tunable superconducting properties of Ruddlesden–Popper bilayer nickelate La₃Ni₂O₇, this study employs the dynamic cluster quantum Monte Carlo method to solve the imbalanced two-orbital bilayer Hubbard model. By analyzing the electric-field-induced pairing symmetry and its evolution under undoped, hole-doped, and electron-doped conditions, we find that the s±-wave pairing originating from the d_{z²} orbital is suppressed, while the interlayer mismatch of the d_{z²} orbital and the transfer of electrons to the d_{x²-y²} orbital drive a pairing symmetry transition from s±-wave to d-wave. Interestingly, the d-wave pairing arising from the d_{x²-y²} orbital exhibits a dome-shaped behavior as a function of electric field strength. The large-scale many-body calculations are consistent with the predictions of weak-coupling methods, providing new insights into the superconducting mechanism of RP nickelates.

This study systematically investigates the strain effect in trilayer nickelate La₄Ni₃O₁₀ thin films through atomically precise synthesis, electrical transport measurements, picometer-resolution electron microscopy, and synchrotron X-ray diffraction. While compressive epitaxial strain effectively suppresses the parent density-wave order and enhances crystal symmetry (e.g., eliminating out-of-plane octahedral rotations), no superconductivity is observed even under the maximum compressive strain of -2.8%. Critical structural characterization reveals that compressive strain fails to completely eliminate the characteristic in-plane octahedral rotations in the thin films, which exhibit interlayer inequivalence between the inner and outer layers of each trilayer unit and persist robustly. Synchrotron X-ray diffraction shows that the amplitude of in-plane rotations decreases monotonically with compressive strain but does not vanish entirely. In contrast, in the bilayer system La₃Ni₂O₇, compressive strain fully suppresses all octahedral rotations, thereby inducing superconductivity. These results uncover a key difference between trilayer and bilayer systems, indicating that ambient-pressure superconductivity in trilayer nickelates cannot be achieved solely through epitaxial strain engineering, and alternative tuning methods need to be explored.

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