Paper

This review summarizes weak-coupling theoretical studies of superconductivity in pressurized bilayer nickelate La₃Ni₂O₇, primarily employing the random phase approximation (RPA), fluctuation exchange approximation (FLEX), and functional renormalization group (FRG), based on a bilayer two-orbital Hubbard model with Ni d_{x²-y²} and d_{3z²-r²} orbitals. Studies show that under pressure the Fermi surface consists of an electron-like α pocket and hole-like β and γ pockets; the γ pocket, dominated by the d_{3z²-r²} orbital, exhibits strong nesting with the other pockets, significantly enhancing antiferromagnetic spin fluctuations and mediating attractive pairing. Different methods generally predict the dominant pairing symmetry to be s±-wave: the superconducting gaps on the γ and α pockets have the same sign, whereas the β pocket has the opposite sign, and this pairing is closely related to the interlayer pairing channel dominated by the d_{3z²-r²} orbital. RPA efficiently describes spin and charge susceptibilities, FLEX self-consistently renormalizes quasiparticles and spin fluctuations, and FRG can treat competing orders such as superconductivity, spin density wave, and charge density wave in an unbiased manner. The review concludes that weak-coupling theory can effectively connect Fermi surface geometry with the spin-fluctuation pairing mechanism, and points out that future studies should be combined with strong-coupling pictures and more accurate first-principles parameters.

This study performed in situ high-pressure angle-dependent electrical transport measurements on Pr₄Ni₃O₁₀ single crystals using a custom diamond anvil cell rotator, confirming their superconducting anisotropy. Under a pressure of 50.2 GPa, the sample underwent a superconducting transition with a critical temperature of approximately 31 K. By measuring the upper critical fields perpendicular and parallel to the ab-plane, an anisotropy parameter γ of about 1.6 was obtained, which decreased with increasing temperature and approached 1 near the superconducting critical temperature. Fitting with the Ginzburg-Landau model yielded zero-temperature upper critical fields parallel and perpendicular to the ab-plane of 89.9 T and 57.3 T, respectively, and coherence lengths along the ab-plane and c-axis of 2.4 nm and 1.5 nm, respectively. Comparison with cuprate and iron-based superconductors revealed that the anisotropic behavior of Pr₄Ni₃O₁₀ conforms to a two-band model, where in-plane quantum confinement induces interlayer coherence, resulting in three-dimensional superconducting characteristics. This study not only confirms the existence of anisotropic superconductivity in bulk Ruddlesden-Popper nickelates but also provides critical insights into the role of dimensionality in the mechanism of high-temperature superconductivity.

Addressing the controversy over the pairing mechanism in the bilayer nickelate La₃Ni₂O₇, this work exploits the low-anisotropy nodeless full gap revealed by angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) as a constraint, and proposes the pairing gap along the Brillouin zone diagonal as a decisive probe. Symmetry analysis shows that the hybridization between the d_(x²−y²) and d_(z²) orbitals vanishes along this diagonal, so that the gaps on the γ pocket and on the α/β pockets separately encode the intrinsic pairing strength of the two orbitals. A d_(z²)-orbital-dominated hybridization-driven pairing mechanism would force gap nodes on the α/β pockets along the diagonal direction, directly contradicting the observed U-shaped dI/dV spectrum, whereas a d_(x²−y²)-orbital-dominated Hund’s-rule-driven pairing mechanism yields a uniform full gap over the entire Fermi surface, consistent with the ARPES and STM results. Weak-coupling random-phase approximation calculations, owing to the density-of-states advantage of the d_(z²) orbital, also produce nodal or near-nodal behavior near the diagonal, in conflict with experiment. This work therefore clarifies the dominant role of the d_(x²−y²) orbital in pairing and establishes the Hund’s-rule-driven pairing mechanism as the most relevant superconducting picture for La₃Ni₂O₇.