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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.

Research on the pairing mechanism of the bilayer nickelate La₃Ni₂O₇ high-temperature superconductor demonstrates that the unified framework based on the “genesis principle” and the “synergistic Fermi surface rule” can be naturally extended to this bilayer multi-orbital system. Through strong-correlation analysis, two dominant antiferromagnetic superexchange channels are identified: the intralayer same-orbital (d_z²) nearest-neighbor exchange J⊥ mediated by the inner apical oxygen, and the interlayer different-orbital (d_z² and d_x²-y²) nearest-neighbor exchange J_xz mediated by the in-plane oxygen. Due to the bilayer bonding-antibonding splitting and the B₁g symmetry of the d_x²-y² orbital, the two channels cooperate to produce a stable s± superconducting state, characterized by internal sign reversal between the mirror-even and mirror-odd Fermi surface pockets in momentum space. Both pairing channels maximize the superconducting gap on the β pocket with a form factor of (cosk_x − cosk_y)². This result incorporates La₃Ni₂O₇ into the unified framework of unconventional superconductivity while revealing its unique electronic environment for high-temperature superconducting pairing.

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.