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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.

This paper employs determinant quantum Monte Carlo to study a two-orbital model of the bilayer nickelate La3Ni2O7. With realistic dispersion and specific interaction parameters, the auxiliary-field-decoupled fermionic Hamiltonian possesses Kramers antiunitary symmetry and is therefore sign-problem-free. By tuning doping, interlayer tunneling, and Hund’s coupling, the authors find that the system can form spin-singlet layer-triplet superconductivity, whose transition temperature is affected by doping and Hund’s coupling; lower doping favors superconductivity, whereas excessive doping suppresses or even eliminates it. Interlayer tunneling plays a decisive role in the competition between superconductivity and (π,π) interlayer bond order: in the strong-interaction limit, the same symmetry also leads to a bond-order instability, which may be related to the mysterious density wave observed experimentally and is accompanied by spin-density-wave fluctuations near (π,π). The conclusion suggests that enhancing superconductivity can be achieved by strongly breaking particle-hole symmetry and weakening interlayer/subspace tunneling, the latter being consistent with the role of apical oxygen vacancies in stabilizing superconductivity.

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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.

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