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

Summary

To resolve the unsettled superconducting pairing symmetry in pressurized La₃Ni₂O₇, this study employs a four-orbital Wannier Hamiltonian and incorporates the self-energy from single-site two-orbital dynamical mean-field theory (DMFT) into the random phase approximation (RPA), constructing self-energy-renormalized particle–hole bubbles to replace the bare bubbles while retaining the same local Slater-Kanamori interaction vertices. Conventional RPA calculations reveal that the dominant pairing belongs to the B₂g d_xy channel, but once the DMFT self-energy is included, the pairing hierarchy is reversed: the sign-changing A₁g s_± state becomes dominant, the B₁g d_x²-y² channel takes the second place, and the original B₂g instability is strongly suppressed. Pocket-resolved decomposition and orbital-resolved susceptibility analyses show that this reversal originates from the selective renormalization of the d_3z²-r² orbital, which filters out γ-pocket scattering processes that favor d_xy pairing while preserving distributed inter-pocket scattering conducive to s_±. Further employing the dual Bethe-Salpeter equation with local DMFT vertices to compute the static spin susceptibility yields a broad finite-momentum magnetic response that is weak near the Γ point, reinforcing the spin-fluctuation background for the s_± state at the two-particle level. These results demonstrate that strong correlation effects in La₃Ni₂O₇ are not minor corrections; properly treating correlation-renormalized quasiparticles is essential for accurately predicting the superconducting pairing symmetry.

Materials

• La₃Ni₂O₇

Methods

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

Keywords

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

Highlights

• 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±.

Conclusions

• 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.

Main claims

• 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.
  • Evidence: 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±.
  • Evidence: 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.
  • Evidence: 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.'

Workflow

• model_construction — The low-energy electronic structure is well captured by the four-orbital Wannier model.
  • Materials: Four-orbital Wannier Hamiltonian from Xia et al. for La₃Ni₂O₇; Dense momentum mesh (≈300×300)
  • Methods: Bloch Hamiltonian construction; Wannier interpolation of band structure and Fermi velocities
  • Observations: 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.
  • Materials: TRIQS framework; Continuous-time quantum Monte Carlo impurity solver
  • Methods: 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
  • Observations: 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.
  • Materials: DMFT Green’s function G_DMFT; Slater–Kanamori interaction matrices (spin and charge channels)
  • Methods: 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
  • Observations: 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±.
  • Materials: Fermi-surface patch kernel; Gap eigenvectors
  • Methods: Pocket-pair decomposition of pairing eigenvalues; Comparison of bare and DMFT-dressed irreducible magnetic susceptibilities along high-symmetry paths
  • Observations: 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.
  • Materials: Dual Bethe–Salpeter equation (DBSE) implementation in TPRF library of TRIQS; Local two-particle DMFT vertex
  • Methods: Static spin susceptibility calculation using DBSE with local DMFT particle-hole vertex; Evaluate χ_s(q, ω=0) on a momentum mesh
  • Observations: Broad finite-momentum spin response with minima near Γ; Enhanced antiferromagnetic fluctuations near zone boundary