Symmetry-Based Microscopic Theory of the Unconventional Pairing Mechanism in La₅Ni₃O₁₁

Summary

This study systematically investigates the low-temperature physics and unconventional pairing mechanism of the hybrid nickelate La₅Ni₃O₁₁ using a symmetry-based phenomenological approach combined with charge self-consistent density functional theory and dynamical mean-field theory. The monolayer subsystem is found to be in a Mott insulating state, and superconductivity primarily originates from the Ni-e_g orbitals in the bilayer subsystem. The system exhibits a two-gap superconducting feature, with the dominant pairing arising from interlayer coupling between dz² orbitals and the secondary pairing from intralayer coupling within dx²-y² orbitals. Compared with high-pressure La₃Ni₂O₇, the reduction of the superconducting transition temperature T_c in La₅Ni₃O₁₁ can be attributed to the weakening of interlayer pairing contributions, which is directly reflected in the decreased magnitude of the hopping parameter ratio |tperp^z/tparallelx|. This unified picture provides a microscopic theoretical framework for understanding the superconducting pairing mechanism within bilayer NiO₂ planes and the role of the γ pocket.

Materials

• La₅Ni₃O₁₁
• La₃Ni₂O₇

Methods

• DFT+DMFT
• RPA
• symmetry analysis
• BCS gap equation
• group theory

Keywords

• unconventional superconductivity
• two gap superconductivity
• s± wave pairing
• interlayer pairing
• γ pocket
• hopping parameter ratio

Highlights

• A phenomenological symmetry-based approach is developed to systematically analyze the low-energy physics and pairing symmetry in nickelates.
• The monolayer subsystem of La₅Ni₃O₁₁ is demonstrated to be Mott insulating, confining superconductivity to the bilayer subsystem.
• Feasible symmetry-allowed pairing states are enumerated, revealing that sz2-wave interlayer pairing is the dominant instability, accompanied by a subdominant sx2+y2-wave intralayer pairing.
• The suppressed T_c is quantitatively linked to the diminished interlayer hopping ratio, a trend consistent across bulk, thin-film, and hybrid nickelate superconductors.
• The analysis suggests that enhancing the interlayer exchange while suppressing intralayer exchange may be an effective strategy to raise T_c.

Conclusions

• The superconductivity in La₅Ni₃O₁₁ exhibits a two-gap nature, consisting of a leading interlayer pairing between the dz2 orbitals and a subleading intralayer pairing between the dx2-y2 orbitals.
• The reduction of T_c in La₅Ni₃O₁₁ compared to pressurized bulk La₃Ni₂O₇ is attributed to the diminished contribution of the interlayer pairing, reflected by the decreased hopping parameter ratio |t⊥z/t∥x|.
• The γ pocket is pivotal in stabilizing the s±-wave state through nesting with the β and α pockets, and its absence would suppress T_c.
• The symmetry-based framework unifies the pairing mechanisms of La₅Ni₃O₁₁ and La₃Ni₂O₇, highlighting the role of the bilayer NiO₂ planes in nickelate superconductors.

Main claims

• The monolayer subsystem is Mott insulating and superconductivity originates from the bilayer subsystem.
  • Evidence: The ML subsystem resides in a Mott insulating state; consequently, the correlated Fermi surface (FS) topology is strongly renormalized, leaving the low-energy physics dominated by the Ni-e_g orbitals of the BL subsystem.,the Ni₁-dz2 orbital is fully Mott-insulated.
• Superconductivity exhibits a two-gap nature with leading interlayer sz2-wave and subleading intralayer sx2+y2-wave pairings.
  • Evidence: the superconductivity in La₅Ni₃O₁₁ exhibits a two-gap nature, consisting of a leading interlayer pairing between the dz2 orbitals and a subleading intralayer pairing between the dx2-y2 orbitals.,Our results reveal that two-gap superconductivity occurs within the BL subsystem, reminiscent of pressurized La₃Ni₂O₇.
• The reduction of T_c compared to La₃Ni₂O₇ is due to diminished contribution of interlayer pairing, reflected in the hopping ratio |t_perp^z/t_par^x|.
  • Evidence: The reduction of T_c can be attributed to the diminished contribution of the interlayer pairing, as reflected by the hopping parameter ratio |tperp^z/tparallelx|.,the suppressed T_c in La₅Ni₃O₁₁… The suppressed T_c thus reflects the diminished contribution of the interlayer pairing.

Workflow

• electronic_structure_calculation — The low-energy physics is dominated by Ni-e_g orbitals of the bilayer subsystem; the monolayer is Mott insulating.
  • Materials: DFT; DMFT; cRPA; Wannier downfolding; TRIQS; maximum entropy method
  • Methods: charge self-consistent DFT+DMFT; Slater-Kanamori interaction with cRPA parameters; tight-binding model from Wannier downfolding; renormalization of band structures by DMFT self-energy
  • Observations: monolayer subsystem becomes Mott insulating; Ni₁-dz2 orbital fully gapped; bilayer subsystem retains coherent quasiparticle features; renormalized FS shows three correlated pockets instead of five DFT pockets; interlayer hopping t_perp^z is reduced compared to La₃Ni₂O₇
• symmetry_analysis — A two-gap superconducting state with dominant interlayer sz2 pairing and subdominant intralayer sx2+y2 pairing is energetically favored.
  • Materials: group theory; p4/mmm layer group; Pauli matrices; BdG Hamiltonian
  • Methods: symmetry-allowed pairing matrix representations; classification into A₁g, B₁g, B₂g, etc.; feasibility check using V < J ≈ 4|t|2/U; BCS condensation energy minimization
  • Observations: leading pairing is A₁g interlayer sz2-wave between dz2 orbitals; subleading pairing is A₁g intralayer sx2+y2-wave between dx2-y2 orbitals; two-gap coexistence lowers condensation energy vs single gap
• superconducting_pairing_analysis — The leading sz2 pairing is stabilized by interband scattering involving the γ pocket; the subleading sx2+y2 pairing does not rely on the γ pocket.
  • Materials: RPA; linearized Eliashberg equation; BdG gap equations; projected gap functions
  • Methods: self-consistent gap equations; projected gap on FS pockets; RPA eigenvalue analysis
  • Observations: projected total gap exhibits s±-wave symmetry with accidental nodes on β pocket; V-shaped DOS consistent with tunneling spectra; RPA confirms s±-wave with nesting between γ and β/α pockets
• pairing_mechanism_interpretation — The suppression of T_c is due to diminished interlayer pairing contribution, tracked by the hopping ratio |t_perp^z/t_par^x|; enhancing Jz alone is insufficient, requires suppressing J_x.
  • Materials: comparison of hopping ratios; pressure-dependent data
  • Methods: analysis of |t_perp^z/t_par^x| as control parameter
  • Observations: reduced T_c in La₅Ni₃O₁₁ correlates with lower |t_perp^z/t_par^x|; in La₃Ni₂O₇, |t_perp^z/t_par^x| decreases with pressure, matching T_c trend