Pairing Mechanism in Bilayer Nickelate La$_3$Ni$_2$O$_7$ Superconductors

Abstract: The recent discovery of superconductivity with $T_c \approx 80$~K in bilayer nickelate La$<em>3$Ni$_2$O$_7$ provides a new setting in which to test the organizing principles of unconventional high-temperature superconductivity. We show that the gene principle and the collaborative Fermi-surface rule which were previously proposed to unify unconventional high temperature superconductors, extend naturally to this bilayer, multi-orbital system. We identify that there are two antiferromagnetic exchange channels that can provide the dominant pairing force: an interlayer intra-orbital nearest-neighbour exchange $J</em>\perp$ between $d_{z<sup>2}$ orbitals mediated by the inner apical oxygen, and an intralayer inter-orbital nearest-neighbour exchange $J_{xz}$ between $d_{z<sup>2}$ and $d_{x<sup>2-y<sup>2}$ orbitals mediated by the in-plane oxygen. Owing to the bilayer bonding--antibonding splitting and the $B_{1g}$ symmetry of the $d_{x<sup>2-y<sup>2}$ orbital, these two channels cooperate to produce a robust $s<sup>\pm$ superconducting state with an internal sign reversal between 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 $(cosk_x-cosk_y)<sup>2$ in momentum space. The result places La$_3$Ni$_2$O$_7$ within a unified framework for unconventional superconductivity while revealing a distinct electronic environment for high-$T_c$ pairing.

• The paper shows that superconducting pairing in La3Ni2O7 is driven by cooperative interlayer d₍z²₎–d₍z²₎ and intralayer d₍z²₎–d₍x²-y²₎ antiferromagnetic exchanges.
• It employs a bilayer multi-orbital framework to reveal an anisotropic s± gap with internal sign reversal across distinct Fermi pockets.
• The findings extend high-Tc superconductivity principles beyond cuprates, offering strategies for material engineering in new superconductors.

Pairing Mechanism in Bilayer Nickelate La$_3$Ni$_2$O$_7$ Superconductors

Introduction

The emergence of superconductivity at $T_c \approx 80$ K in bilayer nickelate La$_3$Ni$_2$O$_7$ (henceforth Ni327) under pressure provides a key opportunity to elucidate organizing principles of unconventional high-temperature superconductivity beyond the cuprates and iron-based superconductors. This work reexamines and extends the frameworks of the "gene principle" and the "collaborative Fermi-surface rule"—both established in prior classification of unconventional superconductors [Hu2012, Hu2015prx, Hu2016]—to clarify their applicability to this bilayer, multi-orbital system. The central result is that the superconducting pairing in Ni327 is cooperatively driven by two distinct antiferromagnetic (AFM) exchange interactions: interlayer intra-orbital exchange between $d_{z^2}$ orbitals ($J_\perp$), and intralayer inter-orbital exchange between $d_{z^2}$ and $_2$0 orbitals ($_2$1), mediated by apical and in-plane oxygen, respectively. These interactions synergistically induce a robust anisotropic $_2$2 superconducting gap with internal sign reversal between Fermi pockets characterized by different mirror and orbital parities, situating Ni327 within the organizational paradigm of high-$_2$3 superconductors while revealing new multi-orbital bilayer physics.

Electronic Structure and Fermi Surface Classification

Ni327 features a layered structure where each Ni is octahedrally coordinated by oxygens, with two active $_2$4 orbitals—$_2$5 and $_2$6—dominating the low-energy electronic states. The high-pressure (tetragonal) phase is characterized by significant interlayer hopping $_2$7 (between $_2$8 states via inner apical O), intralayer hopping $_2$9 (between $_7$0), and inter-orbital hopping $_7$1. Classification of Fermi surfaces leverages mirror symmetry (layer even/odd: L$_7$2, L$_7$3) and relative orbital phase (O$_7$4, O$_7$5): the $_7$6 pocket ($_7$7-centered) is mirror-even and orbital in-phase, the $_7$8 ($_7$9-centered) is mirror-even/orbital out-of-phase, while the key $T_c \approx 80$0 pocket (large, $T_c \approx 80$1-centered) is mirror-odd and orbital out-of-phase, involving strong $T_c \approx 80$2/$T_c \approx 80$3 hybridization.

Dominant Antiferromagnetic Exchange Couplings

A defining feature of Ni327 is the nonuniform orbital filling: the $T_c \approx 80$4 bonding state on the $T_c \approx 80$5 pocket is near half-filling, supporting strong correlations, whereas the $T_c \approx 80$6 states are far from half-filling. Consequently, the primary superexchange mechanisms are as follows:

• Interlayer $T_c \approx 80$7-$T_c \approx 80$8 AFM Exchange ($T_c \approx 80$9): Mediated by apical O, leads to interlayer AFM coupling between $_3$0 orbitals on opposing layers Figure 1.

Figure 1: The local AFM exchange couplings: the interlayer AFM exchange between $_3$1 orbitals and the intralayer inter-orbital AFM exchange between $_3$2 and $_3$3 orbitals.

• Intralayer $_3$4-$_3$5 AFM Exchange ($_3$6): In-plane oxygens mediate inter-orbital AFM between $_3$7 and $_3$8 on neighboring sites within a single layer.

Both mechanisms are fundamentally distinct from the cuprate case, where $_3$9 is a dominant in-plane intra-orbital interaction between half-filled $_2$0 orbitals. The multi-orbital, bilayer environment in Ni327 increases the diversity and complexity of AFM exchange.

Cooperative Pairing Channels and $_2$1 Gap Structure

The superconducting gap emerges from the cooperation of the above two dominant AFM channels:

• Interlayer $_2$2: Favors an s-wave interlayer singlet, creating a sign change of the superconducting gap between even and odd mirror-symmetry Fermi pockets: $_2$3 and $_2$4 acquire one sign, $_2$5 the opposite. This is the direct bilayer analogue of the $_2$6 sign structure in iron pnictides.
• Intralayer $_2$7: Generates inter-orbital singlet pairing, with a $_2$8 ($_2$9)–imprinted form factor—projected onto the band basis, the overlap with the $_7$0 pocket is maximized, further stabilizing $_7$1 pairing.

The resulting gap function is anisotropic, with its largest amplitude on the hybridized $_7$2 pocket and an internal sign reversal between mirror-even and mirror-odd Fermi sheets. No symmetry-protected nodes are expected, but strong gap anisotropy is predicted on $_7$3.

Figure 2: The $_7$4 state: sign distribution of the superconducting order parameters on Fermi surfaces, with red/blue indicating opposite signs.

Notably, both pairing channels are constructive on the $_7$5 pocket, leading to significant gap magnitude there. The theoretical analysis rules out dominant competing $_7$6-wave channels due to negligible overlap with the Fermi pockets in a multi-orbital context.

Comparison with Established High-$_7$7 Superconductors

A critical contextualization is provided by contrasting Ni327 with cuprates and iron-based superconductors:

• Cuprates: Single orbital, in-plane nearest-neighbor AFM ($_7$8), d-wave symmetry, nodal gap.
• Iron-based: Multiple $_7$9-dominated pockets, next-nearest-neighbor AFM ($d_{z^2}$0), $d_{z^2}$1 sign structure between $d_{z^2}$2 and $d_{z^2}$3.
• Ni327: Bilayer multi-orbital ($d_{z^2}$4, $d_{z^2}$5), interlayer and inter-orbital AFM, $d_{z^2}$6 state with sign reversal linked to bilayer mirror symmetry.

This unifies Ni327 within the gene principle as a new realization: both the strong-correlation sector and the dominant exchange pathway reside in distinct orbitals, and a bilayer structure introduces a nontrivial sign structure, testable via advanced spectroscopies or quasiparticle interference analysis.

Theoretical and Practical Implications

• Robustness and Anisotropy of Gap: The work predicts a large, fully gapped, but anisotropic $d_{z^2}$7 state on the $d_{z^2}$8 pocket. Absence of symmetry-required nodes suggests enhanced phase stiffness and possible implications for raising $d_{z^2}$9 via engineering of the underlying Fermi surface or inter-orbital hybridization.
• Experimental Probes: The predicted momentum-dependent sign structure, especially the mirror-selective QPI, is an essential experimental fingerprint for the $J_\perp$0 state [ZhangQPI2025]. Mirror-odd and mirror-even impurity scattering selects inter-pocket processes connecting Fermi surfaces of opposite sign.
• Material Generality and Future Directions: The theoretical framework, emphasizing the cooperative action of interlayer and inter-orbital AFM exchange, can be readily extended to trilayer nickelates and multi-layered analogues, predicting similar $J_\perp$1 structures and guiding the search for even higher $J_\perp$2 in related compounds.
• Comparison with Functional RG and Strong-Coupling Theories: The derived gap structure and mechanisms are congruent with functional renormalization group results [Wang327prb, XWu, zhan2024cooperation], which also find robust $J_\perp$3 states, lending further credence to the physical picture and suggesting applicability across different correlation regimes.

Conclusion

This work demonstrates that superconductivity in La$J_\perp$4Ni$J_\perp$5O$J_\perp$6 arises from the interplay of two principal AFM exchange channels—interlayer $J_\perp$7-$J_\perp$8 and intralayer $J_\perp$9-$d_{z^2}$0—resulting in a unique, anisotropic $d_{z^2}$1 state with internal sign changes tied to the hybridized bilayer Fermiology. These findings generalize fundamental organizing rules for high-$d_{z^2}$2 superconductivity to a new multi-orbital context and offer measurable experimental signatures. The analysis suggests that future advances may leverage multi-orbital and multilayer engineering to design higher-$d_{z^2}$3 superconductors, with the topology of the superconducting gap tunable via control of orbital hybridization and interlayer couplings.

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References

• "Pairing Mechanism in Bilayer Nickelate La$d_{z^2}$4Ni$d_{z^2}$5O$d_{z^2}$6 Superconductors" (2604.17181)
• J. P. Hu and H. Ding, "Local antiferromagnetic exchange and collaborative Fermi surface as key ingredients of high temperature superconductors" [Hu2012]
• J. P. Hu, C. C. Le, X. X. Wu, "Predicting unconventional high-temperature superconductors in trigonal bipyramidal coordinations" [Hu2015prx]
• J. P. Hu, "Identifying the genes of unconventional high temperature superconductors" [Hu2016]
• Z. Zhang et al., "Mirror-Selective Quasiparticle Interference in Bilayer Nickelate Superconductor" [ZhangQPI2025]