Paper

This study employs the variational Monte Carlo method to investigate superconductivity in a two-band t-J model consisting of an itinerant orbital (orbital 0) and a quasi-localized orbital (orbital 1). The key finding is the emergence of a robust orbital-selective d-wave superconducting state, which originates entirely from the itinerant orbital 0. Analysis of the superexchange energy hierarchy reveals that the quasi-localized orbital 1 competes with superconductivity by favoring the formation of local inter-orbital bound states, which act as energy defects that disrupt phase coherence. Consequently, the superconducting order parameter decreases monotonically with increasing occupation of orbital 1. Inspired by superconductivity in the nickelate La₃Ni₂O₇, these results highlight the crucial role of multiorbital physics beyond the single-band t-J framework and identify a concrete pathway for enhancing the superconducting transition temperature: suppressing the involvement of the localized d_{z²} orbital.

By constructing the global phase diagram of a bilayer two-orbital Hubbard model, we investigate the orbital-selective electron correlations in the bilayer nickelate La3Ni2O7. At half-filling the system undergoes a Mott transition, and at the physical electron filling it exhibits strong orbital selectivity, manifested as interlayer spin singlet formation among z²-orbital electrons. This effect leads to significant band-structure renormalization with dramatic bandwidth narrowing, while the splitting between the z² bonding and antibonding bands remains at about 1 eV. These correlation features naturally explain the orbital-dependent effective mass enhancement and the sinking of the z² bonding band below the Fermi level observed in ARPES experiments, as well as the puzzling contrast in optical conductivity where the Drude weight drops sharply yet the interband peak position barely shifts. Theoretical analysis reveals that interlayer antiferromagnetic superexchange plays a key role in maintaining the band splitting, and intralayer correlations drive the z² band away from the Fermi surface. This work provides a unified microscopic picture for understanding the normal-state properties and the mechanism of high-temperature superconductivity in multilayer nickelates.

This paper proposes a microscopic Hamiltonian that faithfully reflects the crystal symmetry of the bilayer nickelate La₃Ni₂O₇ under ambient pressure, addressing its unconventional magnetic order. Large-scale density matrix renormalization group calculations reveal that under a large Hund coupling (J_H), a ((\pi/2, \pi/2)) spin stripe order emerges due to hidden quasi-one-dimensionality and persists over a range of electron concentrations. In the more symmetric high-pressure regime, when the interlayer antiferromagnetic coupling (J_\perp) is sufficiently strong, the model exhibits an enhanced tendency for interlayer pairing. This study unveils the microscopic origin of the diagonal spin stripe order and identifies both the Hund coupling (J_H) and the interlayer coupling (J_\perp) as key factors controlling the magnetic order and pairing tendency in La₃Ni₂O₇.

The recent discovery of superconductivity in pressurized bilayer nickelate La3Ni2O7 has triggered tremendous research interest. However, the experimentally observed oxygen deficiency implies that obtaining perfect stoichiometric single crystals is still challenging. The influence of oxygen deficiency on physical properties remains unexplained. Here, we construct a chemical potential phase diagram to characterize the stability of La3Ni2O7. The narrow stable region explains the difficulty of synthesizing pure samples. First, oxygen defect studies reveal that the interlayer apical oxygen vacancy has the highest defect concentrations and is responsible for oxygen deficiency. Second, unfolding band structures show as the oxygen-deficient variant increases, Ni $$3d_{\;z^{2}}$$bands shift toward a lower energy position under the Fermi level at Γ point, which is adverse to the metallization of Ni $$3d_{\;z^{2}}$$bands. Third, high-pressure calculations indicate that oxygen vacancy would destroy the hybridization of interlayer Ni $$3d_{\;z^{2}}$$orbitals, and the larger the oxygen deficiency, the higher the pressure needed to metalize the Ni $$3d_{\;z^{2}}$$bands. Thus, the oxygen deficiency would suppress the emergence of superconductivity in La3Ni2O7−δ. Our results elucidate the mechanism of oxygen deficiency for superconductivity in La3Ni2O7−δ and provide instructive guidance to the experimental research.

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.

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.