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This study systematically explores the isotope effects on the charge density wave (CDW) and spin density wave (SDW) transitions in the bilayer Ruddlesden-Popper nickelate La₃Ni₂O₇ through oxygen isotope substitution (¹⁶O→¹⁸O) using resistivity and muon spin rotation (μSR) experiments. Resistivity measurements reveal a significant increase in the CDW transition temperature by approximately 6 K after ¹⁸O substitution, while μSR results indicate that the SDW transition temperature remains unaffected within experimental error. Raman spectroscopy confirms the effectiveness of the isotope substitution and the softening of lattice phonon modes. This contrasting isotope response suggests that lattice vibrations, i.e., electron-phonon coupling, play a crucial role in the formation of the CDW order, whereas the SDW order primarily originates from electronic interactions. The findings unveil distinct microscopic origins of the two density wave orders and hint at the potential relevance of electron-phonon coupling to the superconducting pairing mechanism in Ruddlesden-Popper nickelates, providing key constraints for theoretical models.

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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.