Momentum-dependent phonon effects on spin-fluctuation d-wave pairing in bulk La₆Ni₅O₁₂

摘要

该研究针对块体La₆Ni₅O₁₂，采用五层Hubbard模型并在随机相近似（RPA）框架下考察电子-声子耦合对自旋涨落诱导的d_x²-y²波配对的影响；该框架给出的主导配对态为d_x²-y²波。由氧呼吸模式启发的两种唯象耦合单独存在时倾向于s波配对，但其在自旋涨落诱导能隙符号相反区域之间的吸引散射会抑制d波配对。计入电子电荷屏蔽后，这一抑制被显著削弱；比较有无屏蔽时s波与d波的配对强度可见，屏蔽将二者边界移向有利于d波的一侧，动量分辨投影进一步定位了不利散射过程被减弱的位置。在代表性电子相互作用下，d波配对仍占主导；该结果强调了电子-声子耦合的动量结构与电荷屏蔽在自旋涨落d波配对中的竞争作用。

材料

• La₆Ni₅O₁₂
• five-layer nickelates
• La₆Ni₅O₁₂ bulk

方法

• five-layer Hubbard model
• random-phase approximation (RPA)
• linearized gap equation
• frozen-phonon calculations
• static RPA charge screening
• momentum-resolved kernel projections

关键词

• spin fluctuation mediated pairing
• d wave pairing
• s wave pairing
• electron phonon coupling
• oxygen breathing modes
• charge screening
• pairing competition
• fermi surface nesting
• spin fluctuations

亮点

• Momentum-resolved projections locate the reduction of the unfavorable scattering processes by screening.
• The spin-fluctuation-induced d-wave gap carries more weight on each outer NiO₂ layer than on the central layer.
• The local ISO interaction gives the strongest s-wave pairing and vanishes in the d-wave channel.
• Screening attenuates the dominant negative contributions for both breathing modes, with magnitudes reduced by about two thirds.

结论

• A five-layer Hubbard model treated within the RPA yields a leading d_x²-y² pairing state for bulk La₆Ni₅O₁₂.
• Two phenomenological couplings motivated by oxygen breathing modes favor s-wave pairing when considered alone, while their attractive scattering between opposite-sign regions of the spin-fluctuation-induced gap suppresses d-wave pairing.
• Electronic charge screening strongly reduces this suppression and shifts the s-wave/d-wave boundary in favor of d-wave pairing.
• At the representative electronic interaction, d-wave pairing remains dominant.

主要论断

• A five-layer Hubbard model within RPA yields a leading dx2-y2-wave pairing state for bulk La₆Ni₅O₁₂.
  • 证据: largest pairing eigenvalue in dx2-y2 channel in Fig. 1(c),gap sign structure in Fig. 1(d) consistent with repulsive scattering near the susceptibility peak
• Oxygen breathing-mode electron-phonon couplings alone favor s-wave pairing.
  • 证据: all four phonon models favor s-wave pairing in Fig. 2(a,b),local ISO interaction gives strongest s-wave pairing and vanishes in d-wave channel
• Attractive phonon scattering between opposite-sign regions of the spin-fluctuation gap suppresses d-wave pairing.
  • 证据: negative projection of phonon kernels on d-wave eigenstate,momentum-resolved maps in Fig. 4 showing negative contributions
• Electronic charge screening strongly reduces the phonon suppression of d-wave pairing.
  • 证据: screening weakens phonon-induced changes in pairing strengths in Fig. 3(a,b),dominant negative contributions attenuated by about two thirds (Tab. 1)
• Screening shifts the s-wave/d-wave boundary in favor of d-wave pairing, and d-wave remains dominant at representative interaction.
  • 证据: zero crossing of pairing-strength difference moves to larger coupling in Fig. 3(d),d-wave dominance throughout studied coupling range (Sec. S3 of SM)

研究流程

• model_construction — A five-layer Hubbard model captures the low-energy Ni dx2-y2 electronic structure of bulk La₆Ni₅O₁₂.
  • 材料: bulk La₆Ni₅O₁₂; five-layer NiO₂ blocks; Ni dx2-y2 orbitals
  • 方法: five-layer Hubbard Hamiltonian; tight-binding matrix from Ref. [36]; five Ni-derived bands
  • 观察: five bands give closely spaced Fermi-surface sheets with mixed layer character; central electronlike pocket and four surrounding holelike pockets
• spin_fluctuation_pairing_calculation — Spin fluctuations within RPA yield a leading dx2-y2-wave pairing state.
  • 材料: five Ni-derived bands
  • 方法: random-phase approximation (RPA); bare susceptibility with intraband and interband particle-hole excitations; symmetrized linearized gap equation
  • 观察: largest spin susceptibility eigenvalue peaks at finite wave vector; dx2-y2 channel has largest pairing strength; gap changes sign between Fermi-surface regions connected by the peak wave vector
• electron_phonon_coupling_modeling — Oxygen breathing-mode couplings alone favor s-wave pairing and can suppress d-wave pairing.
  • 材料: oxygen breathing modes (mode A, mode B); in-plane oxygen distortions
  • 方法: phenomenological electron-phonon couplings with periodic momentum envelopes; frozen-phonon inputs from first-principles calculations
  • 观察: modes A and B alone favor s-wave pairing; local ISO interaction gives strongest s-wave pairing and vanishes in d-wave channel; phonon-induced gaps differ from spin-fluctuation-induced gap
• charge_screening_and_competition_analysis — Electronic charge screening reduces the phonon suppression of d-wave pairing and shifts the s/d boundary in favor of d-wave.
  • 材料: electron-phonon vertices; RPA charge response
  • 方法: static RPA vertex renormalization via noninteracting layer-density susceptibility; full eigenproblem solution combining phonon and spin-fluctuation interactions
  • 观察: screening weakens phonon-induced suppression of d-wave pairing; screening shifts s-wave/d-wave boundary toward larger electron-phonon coupling; d-wave pairing remains dominant throughout the studied coupling range
• momentum_resolved_projection — Momentum-resolved projections locate the scattering processes detrimental to d-wave pairing and show screening weakens them.
  • 材料: phonon kernels; normalized d-wave eigenstate
  • 方法: projection of phonon kernel onto d-wave eigenstate; grouping contributions by transferred momentum
  • 观察: largest negative contributions come from specific momentum transfers for modes A and B; screening attenuates dominant negative contributions by about two thirds; screened projections reproduce diagonalization shifts