Source capture
Authors Dexi Shao, Zhiming Pan, Ming Zhang, Yupeng Li, Chen Lu
arXiv / Publisher https://arxiv.org/abs/2611.11453
PDF https://arxiv.org/pdf/2611.11453
Relevance score 4.302
Primary category cond-mat.str-el
Published 2026-11-10
Research paradigm Theoretical
Sample form Unknown

Summary

This study addresses bulk La6Ni5O12 by employing a five-layer Hubbard model and, within the random phase approximation (RPA) framework, examines the influence of electron-phonon coupling on spin-fluctuation-induced dx2-y2-wave pairing; the dominant pairing state given by this framework is dx2-y2-wave. Two phenomenological couplings inspired by oxygen breathing modes, when present alone, favor s-wave pairing, but their attractive scattering between regions where the spin-fluctuation-induced gap has opposite signs suppresses d-wave pairing. Upon inclusion of electronic charge screening, this suppression is significantly weakened; comparison of the s-wave and d-wave pairing strengths with and without screening shows that screening shifts their boundary toward the side favorable to d-wave pairing, and momentum-resolved projections further identify where the unfavorable scattering processes are weakened. Under representative electron interactions, d-wave pairing remains dominant; these results emphasize the competing roles of the momentum structure of electron-phonon coupling and charge screening in spin-fluctuation d-wave pairing.

Materials

Methods

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

Keywords

Highlights

  • 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.

Conclusions

  • A five-layer Hubbard model treated within the RPA yields a leading dx2-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.

Main claims

  • A five-layer Hubbard model within RPA yields a leading dx2-y2-wave pairing state for bulk La6Ni5O12.
    • Evidence: 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.
    • Evidence: 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.
    • Evidence: 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.
    • Evidence: 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.
    • Evidence: 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)

Workflow

  • model_construction — A five-layer Hubbard model captures the low-energy Ni dx2-y2 electronic structure of bulk La6Ni5O12.
    • Materials: bulk La6Ni5O12; five-layer NiO2 blocks; Ni dx2-y2 orbitals
    • Methods: five-layer Hubbard Hamiltonian; tight-binding matrix from Ref. [36]; five Ni-derived bands
    • Observations: 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.
    • Materials: five Ni-derived bands
    • Methods: random-phase approximation (RPA); bare susceptibility with intraband and interband particle-hole excitations; symmetrized linearized gap equation
    • Observations: 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.
    • Materials: oxygen breathing modes (mode A, mode B); in-plane oxygen distortions
    • Methods: phenomenological electron-phonon couplings with periodic momentum envelopes; frozen-phonon inputs from first-principles calculations
    • Observations: 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.
    • Materials: electron-phonon vertices; RPA charge response
    • Methods: static RPA vertex renormalization via noninteracting layer-density susceptibility; full eigenproblem solution combining phonon and spin-fluctuation interactions
    • Observations: 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.
    • Materials: phonon kernels; normalized d-wave eigenstate
    • Methods: projection of phonon kernel onto d-wave eigenstate; grouping contributions by transferred momentum
    • Observations: 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