What Does the Single-Particle Spectrum Imply on the Pairing Nature and Pairing Mechanism in La₃Ni₂O₇?

Summary

Addressing the controversy over the pairing mechanism in the bilayer nickelate La₃Ni₂O₇, this work exploits the low-anisotropy nodeless full gap revealed by angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) as a constraint, and proposes the pairing gap along the Brillouin zone diagonal as a decisive probe. Symmetry analysis shows that the hybridization between the d_(x²−y²) and d_(z²) orbitals vanishes along this diagonal, so that the gaps on the γ pocket and on the α/β pockets separately encode the intrinsic pairing strength of the two orbitals. A d_(z²)-orbital-dominated hybridization-driven pairing mechanism would force gap nodes on the α/β pockets along the diagonal direction, directly contradicting the observed U-shaped dI/dV spectrum, whereas a d_(x²−y²)-orbital-dominated Hund’s-rule-driven pairing mechanism yields a uniform full gap over the entire Fermi surface, consistent with the ARPES and STM results. Weak-coupling random-phase approximation calculations, owing to the density-of-states advantage of the d_(z²) orbital, also produce nodal or near-nodal behavior near the diagonal, in conflict with experiment. This work therefore clarifies the dominant role of the d_(x²−y²) orbital in pairing and establishes the Hund’s-rule-driven pairing mechanism as the most relevant superconducting picture for La₃Ni₂O₇.

Materials

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Methods

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Keywords

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Highlights

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Conclusions

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Main claims

• The pairing gap along the BZ diagonal serves as a decisive probe of the pairing mechanism in La₃Ni₂O₇.
  • Evidence: Symmetry analysis shows orbital hybridization vanishes along the BZ diagonal, causing the pairing gaps on the γ and α/β pockets to reflect the intrinsic pairing strengths of dz2 and dx2-y2 orbitals respectively.
• The Hund’s rule driven pairing mechanism with dominant dx2-y2 orbital pairing yields a full gap consistent with ARPES and STM experiments.
  • Evidence: Mean-field model of Hund’s rule mechanism produces a U-shaped STM spectrum and nodeless gap distribution, matching the experimental observations of a nearly isotropic full gap.
• Weak-coupling (RPA) and orbital-hybridization driven strong-coupling theories produce gap nodes or near-nodes conflicting with experiments because they overestimate the role of the dz2 orbital.
  • Evidence: RPA calculation shows gap nodes near the BZ diagonal on the α/β pockets due to dz2-dominated pairing from its large density of states.,Orbital-hybridization mechanism inevitably forces gap nodes on the α/β pockets along the diagonal (V-shaped STM).

Workflow

• symmetry_analysis — The pairing gap along the BZ diagonal directly reflects the intrinsic pairing strengths of dz2 and dx2-y2 orbitals.
  • Materials: two-orbital tight-binding model (from Ref. Hu et al.)
  • Methods: mirror reflection symmetry about the Brillouin zone diagonal to deduce vanishing orbital hybridization
  • Observations: The tight-binding Hamiltonian decouples into pure dz2 and dx2-y2 components along the BZ diagonal; the γ pocket is purely dz2, and α/β pockets are purely dx2-y2.
• model_comparison — Only the Hund’s rule driven mechanism with dominant dx2-y2 pairing can reproduce the ARPES/STM observations.
  • Materials: ARPES and STM data from literature (full gap, U-shaped dI/dV); tight-binding model; mean-field Hamiltonians for three pairing mechanisms
  • Methods: projecting mean-field pairing gaps onto the Fermi surface; simulating STM dI/dV curves using BCS density of states convolved with thermal kernel (T=4.2 K)
  • Observations: Orbital-hybridization mechanism: V-shaped STM, gap nodes on α/β pockets along diagonal (inconsistent with data).; Hund’s rule mechanism: U-shaped STM, full gap on all pockets (consistent).; Adding interlayer NN pairing allows perfect fit to ARPES and STM.
• weak_coupling_evaluation — Weak-coupling theories inherently overestimate dz2 pairing due to large DOS, leading to conflict with experimental full gap.
  • Materials: Hubbard-Kanamori model; RPA code; standard interaction parameters (U, J, U')
  • Methods: random-phase-approximation (RPA) to compute spin-fluctuation mediated pairing; Fourier transform to obtain real-space pairing components
  • Observations: RPA yields gap nodes/near-nodes on α/β pockets along BZ diagonal; dz2 orbital pairing dominates over dx2-y2
• interpretation — Hund’s rule driven pairing mechanism with dominant dx2-y2 orbital pairing is the most relevant pairing picture for La₃Ni₂O₇.
  • Materials: all above results
  • Methods: synthesis of symmetry analysis, model comparison, and RPA
  • Observations: Hund’s rule mechanism is the only one that satisfies the experimental constraint; dx2-y2 orbital is the dominant pairing channel; weak-coupling and hybridization-driven theories fail due to nodes