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Using density functional theory combined with dynamical mean-field theory (DFT+DMFT) and the random phase approximation (RPA), we systematically investigated the electronic structure and superconducting mechanism of the 1313-phase La₃Ni₂O₇. DMFT calculations reveal that the monolayer subsystem exhibits a nearly insulating state, with the d_{z²} orbital displaying Mott physics, while the trilayer subsystem remains metallic and is primarily responsible for superconductivity, with its Ni-e_g orbitals being hole-doped relative to bulk La₄Ni₃O₁₀. Based on the low-energy effective Hamiltonian derived from DMFT, RPA analysis yields an s^{±}-wave pairing symmetry within the trilayer subsystem. Compared to bulk La₄Ni₃O₁₀, the significantly reduced superconducting transition temperature in the 1313 phase arises from two factors: first, hole doping weakens the pairing strength; second, the monolayer subsystem acts as a weak-link layer, forming S-N-S Josephson junctions between adjacent trilayer superconducting layers, which suppresses interlayer phase coherence and further lowers the global transition temperature. Overall, the high-temperature superconductivity in the Ruddlesden-Popper La₃Ni₂O₇ family should be attributed to the 2222 phase rather than the 1313 phase.

Using density functional theory (DFT) and random phase approximation (RPA) calculations, this study systematically analyzes the electronic properties and superconducting mechanism of La₅Ni₃O₁₁ under high pressure. DFT band structures reveal that this material, characterized by alternating stacks of bilayer and monolayer NiO₂ planes, exhibits two nearly decoupled subbands originating from the bilayer and monolayer subsystems, respectively. RPA analysis indicates that superconducting pairing predominantly occurs within the bilayer subsystem, displaying an s±-wave pairing symmetry similar to that in pressurized La₃Ni₂O₇, while the monolayer subsystem primarily serves as a bridge connecting adjacent bilayers via extremely weak interlayer Josephson coupling (IJC) to achieve phase coherence along the c-axis. Under low pressure, increasing pressure significantly enhances IJC, thereby raising the bulk superconducting transition temperature (Tc); at sufficiently high pressures, the reduced density of states at the γ-pocket leads to a gradual decrease in Tc. This mechanism naturally explains the experimentally observed dome-shaped Tc-pressure dependence and reveals the distinct pressure response of mixed-phase compared to pure-phase nickelate superconductors.

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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