Paper

This paper theoretically analyzes scanning tunneling microscopy spectra of superconducting bilayer nickelate films using a two-orbital bilayer model based on first-principles Wannier functions and the continuous Green’s function method. The study finds that the multi-orbital character and the spatial anisotropy of Wannier functions render the local density of states highly sensitive to the tip position: as the tip height increases, the relative weights of coherence peaks from different bands change significantly, thereby enabling distance-dependent measurements to distinguish the orbital origins of the controversial γ-band and β-band coherence peaks. Furthermore, in impurity-containing systems, quasiparticle interference patterns can clearly resolve the symmetry of s-wave and d-wave superconducting order parameters. This work provides explicit theoretical guidance for experimentally identifying the band attribution of superconducting gaps and the pairing symmetry.

This study investigates a quarter-hole-filled two-orbital bilayer Hubbard model inspired by transition metal bilayer systems. By explicitly treating the strong interlayer bonding of the dz2 orbital in a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel-Khomskii Hamiltonian that describes the coupling between electron spins and layer pseudospins. Combining Weiss mean-field theory with generalized flavor-wave theory, we reveal a rich ground-state phase diagram, including ferromagnetic and antiferromagnetic phases accompanied by layer-staggered charge-density order, a layer-coherent phase with spontaneous interlayer quantum coherence, and a novel maximal spin-layer entangled phase. This entangled phase arises from an emergent O(4) symmetry that is spontaneously broken to O(3), and its excitation spectrum features three gapless Goldstone modes that are entangled. The results suggest a geometry-driven mechanism for realizing composite entanglement in strongly correlated bilayer systems, and provide a concrete theoretical framework for understanding bilayer nickelate superconductors and other multi-component correlated materials.

By fabricating periodic nanohole arrays to construct infinite-layer nickelate superconducting thin films (Nd₀.₈Sr₀.₂NiO₂) into Josephson junction arrays, researchers systematically enhanced the phase fluctuations of the system. In the nanopatterned films, the weakening of macroscopic phase coherence drives the superconducting transition to exhibit a two-stage characteristic and ultimately tends toward an anomalous metallic ground state with saturated resistance. The emergence of charge-2e quantum oscillations indicates inter-array coherence, while the anomalous zero-field magnetoresistance peak marks the persistence of extreme quantum phase fluctuations down to very low temperatures. Notably, through the synergistic enhancement of nanopatterning and magnetic fields, a reversal of superconducting anisotropy is observed in Nd-nickelates, where the in-plane critical field becomes lower than the out-of-plane critical field. The evolution of this anisotropy may reveal an intrinsic exchange Zeeman field coupled to collective electronic states. These results elucidate how superconductivity evolves in response to phase fluctuations and establish nanopatterning as an effective paradigm for unveiling hidden intertwined orders in strongly correlated systems.

Combining first-principles calculations with fluctuation exchange-Migdal-Eliashberg theory, this study investigates the interplay between electron correlations and electron-phonon coupling in infinite-layer nickelate superconductors. The results show that spin fluctuations drive robust d-wave superconductivity in the Ni d_{x^2-y^2} orbital, while electron-phonon coupling induces s-wave pairing in interstitial orbitals, and their synergy gives rise to a mixed s+id superconducting state. The emergence of the s-wave component strongly depends on carrier density: a moderate electron-phonon coupling strength (λ=0.4) stabilizes the mixed state only at an electron density n=0.9, but not at n=0.8. In the thermodynamic limit, the critical coupling required to stabilize the s-wave component is about 0.6, but it can be reduced to 0.4 in finite-size systems. These results reveal that local oxygen defects, by modulating the local electron density, can form finite-size domains with distinct pairing symmetries, thereby providing a microscopic explanation for the spatially inhomogeneous superconducting gaps observed experimentally, and highlight the crucial influence of the cooperative effect of electron correlations and electron-phonon coupling on the pairing symmetry in nickelate superconductors.

Using first-principles calculations and large-scale dynamic cluster quantum Monte Carlo simulations, this work systematically investigates the effect of electron doping on the superconducting properties of two-orbital bilayer models for three representative systems: bulk La₃Ni₂O₇ under ambient pressure and at 15 GPa, as well as the La₃Ni₂O₇:La₃Al₂O₇ heterostructure. The results show that electron doping universally enhances s±-wave pairing superconductivity, with the heterostructure exhibiting the highest superconducting transition temperature in the underdoped region, even exceeding that of bulk samples under 15 GPa pressure. Further analysis reveals an inter-orbital synergistic mechanism: pairing on the d_{z²} orbital induces pairing on the d_{x²-y²} orbital, which gradually dominates at low temperatures, forming a two-orbital collaborative superconducting instability. This conclusion is validated by simulations with two different cluster sizes. This study provides a theoretical prediction for enhanced superconductivity in electron-doped Ruddlesden-Popper phase nickelates and proposes the heterostructure as a feasible experimental pathway, awaiting future experimental verification.

Polycrystalline samples of La₃₋ₓNaₓNi₂O₇₊δ with various sodium doping concentrations were synthesized via a solid-state method, and their structural, thermal, magnetic, and electrical transport properties were systematically investigated using X-ray diffraction, thermogravimetric analysis, and measurements of magnetic susceptibility and electrical resistivity. X-ray diffraction analysis revealed that when the sodium doping level x ≥ 0.075, the samples undergo a structural transition from the ‘327’ Amam phase to the ‘4310’ Bmab phase, accompanied by gradual lattice expansion. Resistivity measurements indicated that sodium doping significantly enhances metallicity while slightly suppressing the density wave transition temperature; applying external pressure further suppresses the density wave transition, yet the low-temperature insulating behavior remains insensitive to pressure. These findings demonstrate that hole doping introduced by substituting sodium for lanthanum effectively modulates competing electronic phases in layered nickelates, providing crucial experimental evidence for understanding the roles of elemental substitution and carrier doping in stabilizing high-pressure superconducting phases.

Evidence for charge and spin density waves in single crystals of La₃Ni₂O₇ and La₃Ni₂O₆

Using ultrafast terahertz spectroscopy, we performed optical-pump terahertz-probe experiments on an infinite-layer samarium nickel oxide thin film with Tc = 20 K to measure the temperature-dependent photoconductivity. Under weak excitation, the photoinduced destruction of the superfluid density is proportional to the equilibrium superfluid density and decreases linearly with increasing temperature, consistent with clean-limit d-wave pairing. From this linear relationship, the superconducting gap was extracted to be 2.5 meV, yielding 2Δ/kTc ≈ 3, indicating the system is in the weak coupling regime. Furthermore, independent estimates of the ratio of the mean free path to the coherence length (l/ξ) give approximately 1.5, further confirming clean-limit behavior. These results demonstrate that nickel oxide superconductors can realize a clean superconducting state and reveal a close similarity in pairing mechanism to cuprate high-temperature superconductors.

The recently discovered superconductivity with critical temperature 𝑇𝑐 up to 80 K in the double-layer Nickelate La3⁢Ni2⁢O7−𝛿 under pressure has drawn great attention. Here, we report the positive muon spin relaxation (𝜇+⁢SR) study of polycrystalline La3⁢Ni2⁢O6.92 under ambient pressure. Zero-field 𝜇+⁢SR experiments reveal the existence of magnetic order in La3⁢Ni2⁢O6.92 with 𝑇𝑁=154 K. The weak transverse field 𝜇+⁢SR measurements reveal the bulk nature of magnetism. In addition, a small quantity of oxygen deficiencies can greatly broaden the internal magnetic field distribution sensed by muons.

Evidence of Spin Density Waves in La₃Ni₂O₇−δ