The evolution of pairing correlation with 3d_z2 electron filling in a bilayer two-orbital model for La₃Ni₂O₇

Summary

Using the density matrix renormalization group method, this work systematically investigates the evolution of superconducting pairing correlations with the filling of the Ni 3dz² orbital in an effective bilayer two-orbital model of pressurized bilayer nickelate La₃Ni₂O₇ on a one-dimensional minimal geometric structure. B_y adjusting the orbital chemical potential difference to continuously tune the 3dz² orbital from 1/12 doping to near half-filling, it is found that superconducting correlations are significantly suppressed near half-filling, indicating that the itinerancy of this orbital favors pairing. Moreover, pairing correlations are enhanced in regions with larger charge fluctuations, suggesting competition between charge order and superconductivity. These results support the existing theoretical picture that interlayer antiferromagnetic superexchange provides the pairing glue, while the itinerant 3dz² orbital mediates pairing and establishes long-range coherence through hybridization. The study clarifies the crucial role of the itinerancy of the 3dz² orbital in superconductivity, providing important evidence for understanding the unconventional pairing mechanism in this system.

Materials

• La₃Ni₂O₇

Methods

• DMRG

Keywords

• pairing correlation
• charge fluctuations
• charge order
• superconductivity
• itinerancy
• 3dz2 orbital

Highlights

• The study clarifies the crucial role of the itinerancy of the 3dz2 orbital in superconductivity, providing important evidence for understanding the unconventional pairing mechanism in La₃Ni₂O₇.
• The pairing correlation is enhanced at regions with large charge fluctuations, indicating a competition between charge order and superconductivity.

Conclusions

• The evolution of pairing correlation with electron filling in an effective bilayer two-orbital model for La₃Ni₂O₇ shows significant suppression when the 3dz2 orbital approaches half-filling.
• The itinerancy of the 3dz2 orbital is favorable for superconductivity in the bilayer two-orbital model.
• Pairing correlation is enhanced in regions where charge fluctuations are large, suggesting competition between charge order and superconductivity.

Main claims

• Itinerancy of the 3dz2 orbital is favorable for superconducting pairing in the bilayer two-orbital model of La₃Ni₂O₇.
  • Evidence: B_y systematically varying the 3dz2 orbital filling from 1/12 doping to half-filling, a pronounced suppression of superconducting correlations near half-filling is observed (abstract).,DMRG results show that the pairing exponent K_sc increases as the dz2 orbital approaches half-filling, indicating weaker pairing (Section III, Figs. 4-5).
• Pairing correlations are enhanced in regions where charge fluctuations are large, suggesting competition between charge order and superconductivity.
  • Evidence: Pairing correlation is enhanced around two singularity points in Fig. 2, which correspond to large charge fluctuations and changes in charge density wave patterns (Section III).,At these points, charge density wave wavelength changes or phase shifts, indicating charge order competition (abstract and supplementary figures).

Workflow

• Model construction — The model serves as a minimal model to investigate the role of dz2 orbital filling on pairing correlations.
  • Materials: Bilayer two-orbital Hamiltonian for La₃Ni₂O₇; Ni 3dx2-y2 and 3dz2 orbitals
  • Methods: Effective bilayer two-orbital model derived from DFT calculations
  • Observations: Model captures low-energy physics of pressurized La₃Ni₂O₇
• DMRG simulation — DMRG results reveal evolution of pairing correlations with dz2 orbital filling.
  • Materials: One-dimensional chain geometry; DMRG with bond dimension up to 12288 and truncation error ≈10-9
  • Methods: Density matrix renormalization group (DMRG)
  • Observations: Computed orbital-resolved charge density and spin profiles; Calculated inter-layer and intra-layer pair-pair correlation functions
• Pairing correlation analysis — Superconducting correlations are suppressed near half-filling and enhanced at charge fluctuation regions, indicating itinerancy of dz2 orbital favors pairing and competition with charge order.
  • Materials: Pair-pair correlation data for vertical (inter-layer) and intra-layer bonds
  • Methods: Power-law fit to extract pairing exponent K_sc; Finite truncation error extrapolation
  • Observations: Pairing exponent K_sc increases as dz2 filling approaches half-filling for both dz2 and dx2-y2 orbitals; Dips in K_sc at two singularity points (μ_diff ≈ 1.8 and 2.8) corresponding to large charge fluctuations