Multiorbital character of the density wave in trilayer nickelate superconductors

Summary

Using polarization-resolved Raman scattering combined with a two-orbital model calculation, this study reveals the multi-orbital character of the density wave in the trilayer nickelate La₄Ni₃O₁₀. In the phonon sector, the oxygen bond-stretching mode exhibits a pronounced intensity anomaly near the density-wave transition temperature T_DW, while the phonon line shape remains essentially symmetric with negligible changes in frequency shift and linewidth, indicating a moderate electron-phonon coupling and suggesting that the density wave is primarily driven by electronic instability rather than by the lattice. In the electronic Raman scattering, as temperature decreases, the spectral weight of the continuum is significantly depleted below ∼114 meV (∼910 cm^-1), and a polarization-dependent sharp peak emerges at this energy; this peak is strongest in the B₂g channel and nearly absent in the B₁g channel. B_y constructing a two-orbital density-wave state model that simultaneously includes Ni-3dx²−y² and Ni-3dz² orbitals and retains the Raman vertices in the orbital space, calculations confirm that this peak corresponds to the density-wave energy gap 2Δ_DW, whose opening displays incoherent and non-mean-field behavior, and that the spectral response necessarily relies on the mixed contributions of both orbitals and cannot be reduced to any single-orbital projection. These results demonstrate that the density-wave instability in La₄Ni₃O₁₀ has an intrinsic multi-orbital origin, providing crucial experimental and theoretical insights for understanding its competition or coexistence with superconductivity.

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 density-wave energy gap in La₄Ni₃O₁₀ is 2ΔDW = 114 meV, identified by a Raman peak at 910 cm^-1.
  • Evidence: Observation of a pronounced peak at 910 cm^-1 in electronic Raman scattering, strongly temperature- and polarization-dependent.,Model calculations reproduce the peak energy and polarization dependence when a DW potential is introduced.
• The Raman-active DW excitation has multiorbital character, requiring contributions from both Ni-3d_x²_-y² and Ni-3d_z² orbitals and their mixing.
  • Evidence: Single-orbital projections of the Raman vertex cannot reproduce the experimentally observed intensity ratio between B₁g and B₂g channels nor the linewidths.,Full orbital-matrix treatment of the Raman vertex yields agreement with experiment.
• The DW gap opens incoherently and exhibits non-mean-field behavior, with spectral weight depleting gradually and the 2ΔDW peak persisting above the transition temperature.
  • Evidence: Temperature-dependent Raman intensity shows gradual depletion of continuum spectral weight below 114 meV upon cooling, rather than a sharp gap edge.,The 910 cm^-1 peak is observable above TDW, contrary to BCS mean-field expectations.
• Electron-phonon coupling is weak, and the DW is primarily driven by electronic instabilities rather than by lattice.
  • Evidence: Symmetric phonon lineshapes without Fano profiles indicate absence of strong electron-phonon coupling.,Phonon self-energy anomalies (frequency, linewidth) near TDW are subtle, consistent with weak coupling.

Workflow

• sample_preparation — High-qualityLa₄Ni₃O₁₀ single crystals with a density-wave transition at ≈140 K were synthesized.
  • Materials: La₄Ni₃O₁₀ single crystals
  • Methods: optical floating-zone method; post-annealing in oxygen; single-crystal X-ray diffraction; magnetic susceptibility measurements
  • Observations: high-quality single crystals; phase purity confirmed (XRD, STEM); magnetic transition at 140K
• measurement — Raman spectra reveal phonon anomalies and an electronic excitation at 114 meV associated with the density-wave transition.
  • Materials: La₄Ni₃O₁₀ single crystal
  • Methods: polarized Raman scattering; temperature-dependent spectroscopy
  • Observations: phonon modes at 355, 400, 515 cm^-1 show intensity anomalies across TDW; broad electronic continuum with spectral weight depletion up to 910 cm^-1; prominent peak at 910 cm^-1 (114 meV) strongest in B₂g channel, nearly absent in B₁g
• analysis — The 910 cm^-1 peak corresponds to the density-wave gap 2ΔDW = 114 meV, and its multiorbital character is essential to explain the experimental spectra.
  • Materials: DFT phonon calculations; minimal two-orbital model
  • Methods: density-functional perturbation theory (DFPT); two-orbital Hubbard model with d_x²_-y² and d_z² orbitals; DW potential with ordering vector Q=(0.5π,0.5π); Raman response calculation with orbital-resolved vertices
  • Observations: calculated phonon frequencies match experiment; model reproduces the 910 cm^-1 peak and its polarization-dependent intensity; single-orbital projections fail to match the experimentally observed intensity ratio and linewidth
• interpretation — The density wave in La₄Ni₃O₁₀ has a multiorbital origin involving both Ni-3d_x²_-y² and Ni-3d_z² states, with incoherent gap opening and dominant electronic-driving instability.
  • Methods: comparison of model and experimental temperature dependencies; analysis of DW gap opening behavior
  • Observations: spectral weight depletes gradually upon cooling, not a sharp onset; the DW peak persists above the transition temperature; symmetric phonon lineshapes indicate weak electron-phonon coupling