Pairing Mechanism in Bilayer Nickelate La₃Ni₂O₇ Superconductors

摘要

双层镍酸盐La₃Ni₂O₇高温超导体的配对机制研究表明，基于“基因原理”和“协同费米面规则”的统一框架可自然延伸至该双层多轨道体系。通过强关联分析，识别出两个主导反铁磁超交换通道：由内顶角氧介导的层内同轨道（d_z²）最近邻交换J⊥，以及由面内氧介导的层间不同轨道（d_z²与dx²-y²）最近邻交换Jxz。由于双层成键-反键劈裂和dx²-y²轨道的B₁g对称性，两通道协同作用产生稳定的s±超导态，其特征是动量空间中镜像偶与镜像奇费米面口袋之间存在内部符号反转。两个配对通道均在β口袋上最大化超导能隙，形式因子为(coskx-cosky)²。该结果将La₃Ni₂O₇纳入非常规超导的统一框架，同时揭示了其独特的高温超导配对电子环境。

材料

• La₃Ni₂O₇

方法

• strong-correlation analysis
• functional renormalization group (FRG) calculations
• gene principle
• collaborative Fermi surface rule analysis

关键词

• s± superconducting state
• antiferromagnetic superexchange
• pairing form factor (coskx cosky)₂
• mirror even and mirror odd fermi surface pockets
• bilayer bonding antibonding splitting
• s± pairing
• antiferromagnetic exchange
• pairing form factor
• bilayer nickelate

亮点

• The unified framework based on the 'gene principle' and 'collaborative Fermi surface rule' is extended to the bilayer multi-orbital system.
• The two pairing channels maximize the superconducting gap on the β pocket with form factor (coskx-cosky)₂.
• Places La₃Ni₂O₇ within a unified framework for unconventional superconductivity, revealing a distinct electronic environment.

结论

• The pairing symmetry of bilayer La₃Ni₂O₇ is determined to be an s± state, with internal sign reversal between mirror-even and mirror-odd Fermi-surface pockets.
• Two dominant antiferromagnetic exchange channels cooperate: interlayer same-orbital (d_z2) exchange J⊥ and intralayer inter-orbital (d_z2 and dx2-y2) exchange Jxz.
• The gene principle and collaborative Fermi surface rule extend to the bilayer multi-orbital system, leading to an s± superconducting state with sign reversal between mirror-even and mirror-odd pockets.

主要论断

• Two dominant antiferromagnetic exchange channels exist in La₃Ni₂O₇: interlayer same-orbital d_z2 exchange and intralayer inter-orbital d_z2-dx2-y2 exchange.
  • 证据: 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 dx²-y²) nearest-neighbor exchange Jxz mediated by the in-plane oxygen.
• The two pairing channels cooperate to produce a stable s± superconducting state with internal sign reversal between mirror-even and mirror-odd Fermi surface pockets.
  • 证据: Due to the bilayer bonding-antibonding splitting and the B₁g symmetry of the dx²-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 beta pocket with a form factor of (coskx - cosky)₂.
  • 证据: Both pairing channels maximize the superconducting gap on the β pocket with a form factor of (coskx − cosky)².
• Two antiferromagnetic exchange channels (interlayer intra-orbital J⊥ between dz2 orbitals and intralayer inter-orbital Jxz between dz2 and dx2-y2 orbitals) provide the dominant pairing force in bilayer La₃Ni₂O₇.
  • 证据: Theoretical derivation based on strong-coupling perturbation theory.
• The two channels cooperate to produce a robust s± superconducting state with sign reversal between mirror-even and mirror-odd Fermi-surface pockets.
  • 证据: Mean-field gap equations show constructive addition on α and β pockets; FRG calculations confirm the s± state.

研究流程

• electronic structure and Fermi surface classification — Electronic structure shows bilayer bonding-antibonding splitting and two active Ni orbitals (d_z2 and dx2-y2).
  • 材料: La₃Ni₂O₇ compound
  • 方法: density functional theory (DFT); tight-binding modeling
  • 观察: identification of three Fermi pockets: alpha, beta, gamma; orbital classification by mirror symmetry and orbital phase
• identification of dominant AFM exchange interactions — Two AFM exchange channels provide the dominant pairing force.
  • 材料: La₃Ni₂O₇
  • 方法: strong-correlation analysis; perturbation theory
  • 观察: two dominant AFM channels: interlayer d_z2-d_z2 via apical oxygen (J⊥) and intralayer inter-orbital d_z2-dx2-y2 via in-plane oxygen (Jxz)
• pairing symmetry analysis — Pairing symmetry is s±, and the two channels cooperate to produce a robust superconducting state.
  • 材料: La₃Ni₂O₇
  • 方法: strong-correlation analysis; comparison with FRG
  • 观察: s± superconducting state with internal sign reversal between mirror-even and mirror-odd pockets; pairing gap maximized on beta pocket with (coskx - cosky)₂ form factor
• Electronic Structure Analysis — Fermi surface pockets are classified by mirror symmetry and orbital relative phase.
  • 材料: La₃Ni₂O₇
  • 方法: tight-binding model; band structure classification by mirror symmetry and orbital phase
  • 观察: Three Fermi pockets: α (even, in-phase), β (odd, out-of-phase), γ (even, out-of-phase)
• Derivation of Leading AFM Exchange Interactions — Two dominant AFM exchange channels: interlayer intra-orbital and intralayer inter-orbital.
  • 材料: La₃Ni₂O₇
  • 方法: strong-coupling expansion; second-order perturbation theory
  • 观察: Interlayer exchange J⊥ between dz2 orbitals via apical oxygen; intralayer inter-orbital exchange Jxz between dz2 and dx2-y2 via in-plane oxygen
• Determination of Pairing Symmetry — The two channels cooperate to produce a robust s± state with internal sign reversal.
  • 材料: La₃Ni₂O₇
  • 方法: mean-field decoupling of exchange interactions; projection onto band basis
  • 观察: Interlayer exchange gives sign change between mirror-even and mirror-odd pockets; inter-orbital exchange selects s-wave form factor (cos kx - cos ky)²
• Comparison with FRG Calculations — Strong-coupling analysis and FRG converge to the same s± state.
  • 材料: La₃Ni₂O₇
  • 方法: functional renormalization group (FRG)
  • 观察: FRG also finds s± state with similar momentum space sign changes