Correlation-renormalized spin-fluctuation pairing and the stabilization of s± superconductivity in pressurized La₃Ni₂O₇

摘要

该研究针对加压La₃Ni₂O₇中超导配对对称性尚未定论的问题，采用四轨道Wannier哈密顿量，将单格点双轨道动力学平均场理论（DMFT）的自能引入随机相近似（RPA），构建自能重整化粒子－空穴气泡以替代裸气泡，保持相同的局域Slater-Kanamori相互作用顶点。普通RPA计算显示主导配对属于B₂g的d_xy通道，而一旦包含DMFT自能，配对层级发生反转：A₁g符号改变的s_±态成为主导，B₁g d_x²-y²通道次之，原先的B₂g不稳定性被强烈抑制。口袋对分解和轨道分辨磁化率表明，该反转源于d_3z²-r²轨道的选择性重整化，它滤除了有利于d_xy配对的γ口袋散射过程，同时保留了有利于s_±的分布性口袋间散射。进一步利用双Bethe-Salpeter方程结合局域DMFT顶点计算静态自旋磁化率，得到宽广的有限动量磁响应且在Γ点附近较弱，从两粒子层面强化了s_±态的自旋涨落背景。结果表明，在La₃Ni₂O₇中强关联效应并非次要修正，恰当处理关联重整化的准粒子对于准确预测超导配对对称性至关重要。

材料

• La₃Ni₂O₇

方法

• Wannier Hamiltonian
• DMFT
• Random-phase approximation
• Self-energy-renormalized RPA
• Dual Bethe-Salpeter equation
• Continuous-time quantum Monte Carlo

关键词

• s± pairing symmetry
• orbital selective renormalization
• spin fluctuations
• superconducting gap symmetry
• correlation effects
• dxy pairing

亮点

• Combining DMFT self-energy with RPA reveals a qualitative reversal of the pairing hierarchy from dxy to s±.
• The orbital-selective renormalization of the d3z2-r2 orbital is the key mechanism behind the reversal.
• The s± state uses a distributed network of inter-pocket scattering processes, making it robust against correlation effects.
• Dual Bethe-Salpeter equation calculations confirm that the correlated spin fluctuation spectrum remains dominated by finite-momentum fluctuations, strengthening the spin-fluctuation background for s±.

结论

• In bare RPA, the leading pairing instability is of B₂g dxy symmetry.
• Including DMFT self-energy reverses the hierarchy: the A₁g s± state becomes dominant, while the B₂g channel is strongly suppressed.
• The reversal originates from orbital-selective renormalization of the d3z2-r2 orbital, which filters γ-pocket scattering processes that stabilize dxy pairing.
• The DBSE spin susceptibility confirms robust finite-momentum spin fluctuations, supporting the s± pairing scenario.
• Strong correlations are essential for reliable prediction of superconducting gap symmetry in La₃Ni₂O₇.

主要论断

• The leading superconducting instability in pressurized La₃Ni₂O₇ changes from d-wave (B₂g) to s± (A₁g) when the RPA particle-hole bubble is dressed by the DMFT self-energy.
  • 证据: Abstract: 'Once the DMFT self-energy is included, the hierarchy is reversed: the A₁g sign-changing s± state becomes dominant, the B₁g dx2-y2 channel is subleading, and the original B₂g instability is strongly suppressed.',Section III.2: 'In Fig. 2(b), the s± eigenvalue becomes the dominant one over the correlated-RPA interaction range, while the B₂g channel that led the bare calculation is pushed below both s± and B₁g.'
• The symmetry reversal is caused by orbital-selective renormalization of the d3z2-r2 orbital, which suppresses γ-pocket intra-sheet scattering that stabilizes dxy pairing while preserving distributed inter-pocket processes favorable to s±.
  • 证据: Abstract: 'Pocket-pair decomposition and orbital-resolved susceptibilities show that the reversal originates from orbital-selective renormalization of the d3z2-r2 sector, which filters the γ-pocket scattering processes that stabilize dxy pairing in bare RPA while preserving distributed inter-pocket processes favorable to s± pairing.',Section III.3: 'The DMFT-renormalized s± state has a qualitatively different structure… the large positive terms are distributed over inter-pocket channels, especially αγ and βγ… the DMFT self-energy reduces and broadens precisely that response, thereby weakening the contribution that made the dxy state dominant.'
• Strong electronic correlations are not a minor correction but are essential for accurately predicting the superconducting gap symmetry in La₃Ni₂O₇.
  • 证据: Abstract: 'Our results demonstrate that strong correlations are not a secondary correction in La₃Ni₂O₇: an appropriate treatment of correlation-renormalized quasiparticles is essential for predicting the superconducting pairing symmetry.',Conclusion: 'The prediction of the pairing symmetry in La₃Ni₂O₇ therefore requires more than an accurate Wannier Hamiltonian; it also requires a correlated quasiparticle propagator appropriate to the strongly renormalized normal state.'

研究流程

• model_construction — The low-energy electronic structure is well captured by the four-orbital Wannier model.
  • 材料: Four-orbital Wannier Hamiltonian from Xia et al. for La₃Ni₂O₇; Dense momentum mesh (≈300×300)
  • 方法: Bloch Hamiltonian construction; Wannier interpolation of band structure and Fermi velocities
  • 观察: Fermi surface consists of three sheets (α, β, γ) with orbital character mainly from Ni d3z2−r2 and dx2−y2
• dmft_self_energy — The DMFT self-energy produces orbital-selective mass renormalization, with the d3z2−r2 orbital being more correlated.
  • 材料: TRIQS framework; Continuous-time quantum Monte Carlo impurity solver
  • 方法: Single-site two-orbital dynamical mean-field theory (DMFT) for the d3z2−r2 and dx2−y2 orbitals; Density-density Kanamori interaction with on-site U and J; Held double-counting correction
  • 观察: Quasiparticle weights: Zγ ≈ 0.5 for the d3z2−r2 orbital, Zδ ≈ 0.7 for the dx2−y2 orbital; Stronger correlation and lifetime broadening in the d3z2−r2 sector
• renormalized_rpa_pairing — Including the DMFT self-energy reverses the pairing hierarchy, making the sign-changing s± state dominant over the previously leading dxy state.
  • 材料: DMFT Green’s function G_DMFT; Slater–Kanamori interaction matrices (spin and charge channels)
  • 方法: Self-energy-renormalized RPA: replace bare bubble G₀G₀ with G_DMFT G_DMFT; Compute static irreducible susceptibility, spin/charge RPA susceptibilities, and pairing vertex; Solve symmetry-resolved linearized gap equation on Fermi surface patches; Tune interaction to keep Stoner factor ≈ 0.95 for both bare and DMFT-dressed calculations
  • 观察: Bare RPA: leading eigenvalue in B₂g (dxy) channel, followed byA₁g (s±) and B₁g (dx2−y2); DMFT-dressed RPA: A₁g (s±) becomes leading, B₁g subleading, B₂g strongly suppressed
• pairing_mechanism_analysis — The reversal originates from orbital-selective renormalization: DMFT filters γ-pocket scattering that stabilizes dxy in bare RPA, while preserving inter-pocket processes conducive to s±.
  • 材料: Fermi-surface patch kernel; Gap eigenvectors
  • 方法: Pocket-pair decomposition of pairing eigenvalues; Comparison of bare and DMFT-dressed irreducible magnetic susceptibilities along high-symmetry paths
  • 观察: Bare RPA dxy instability dominated by γγ intra-pocket scattering; DMFT-dressed s± draws strength from inter-pocket processes (αγ, βγ) and distributed off-diagonal contributions; DMFT self-energy suppresses the coherent γ-sheet response, filtering the processes that favored dxy
• dbse_spin_susceptibility_validation — The correlated spin fluctuation spectrum remains dominated by finite-momentum magnetic fluctuations, consistent with the mechanism for s± pairing.
  • 材料: Dual Bethe–Salpeter equation (DBSE) implementation in TPRF library of TRIQS; Local two-particle DMFT vertex
  • 方法: Static spin susceptibility calculation using DBSE with local DMFT particle-hole vertex; Evaluate χ_s(q, ω=0) on a momentum mesh
  • 观察: Broad finite-momentum spin response with minima near Γ; Enhanced antiferromagnetic fluctuations near zone boundary