Electronic Origin of Density Wave Orders in a Trilayer Nickelate

The discovery of superconductivity in Ruddlesden-Popper nickelates has established a new frontier in the study of high-temperature superconductors. However, the underlying pairing mechanism and its relationship to the material’s electronic and magnetic ground states remain elusive. Since unconventional superconductivity often emerges from a complex interplay of magnetic correlations, elucidating the magnetic ground state of the nickelates at ambient pressure is crucial for understanding the emergence of superconductivity under high pressure. Here, we combine high-resolution angle-resolved photoemission spectroscopy with tight-binding model simulation to investigate the electronic structure of the representative trilayer Ruddlesden-Popper nickelate La$4$Ni$3$O${10}$. We provide the first experimental evidence of band splitting induced by interlayer coupling and further resolve the momentum-dependent density wave gap structures along all the Fermi surfaces. Our findings identify the mirror-selective Fermi surface nesting as the origin of the interlayer antiferromagnetic spin density wave and demonstrate the dominant role of Ni-3d${z^2}$ orbitals in the low-energy physics of La$_4$Ni$3$O${10}$. These results provide a fundamental framework for understanding the magnetic interactions and high-temperature superconductivity mechanism in the Ruddlesden-Popper nickelate family.

💡 Research Summary

This paper presents a comprehensive investigation of the electronic structure and density‑wave phenomena in the trilayer Ruddlesden‑Patterson nickelate La₄Ni₃O₁₀, a material that becomes superconducting under high pressure. Using high‑resolution angle‑resolved photoemission spectroscopy (ARPES) with both laser (6.994 eV) and synchrotron (85 eV) photon sources, the authors map the full Fermi surface (FS) and resolve fine band features under different light polarizations. They identify four distinct FS sheets: an electron‑like α pocket centered at Γ and three hole‑like pockets (β, β′, γ) centered at M. The β′ sheet, observed for the first time, originates from a band splitting caused by strong interlayer coupling. Additional √2 × √2 folded bands (α_f, β_f, β′_f, γ_f) are also detected, with the β_f band clearly linked to spin‑density‑wave (SDW) induced folding.

To interpret these observations, the authors construct a trilayer tight‑binding (TB) model that includes the Ni 3d x²‑y² and 3d z² orbitals on each Ni site, intra‑ and inter‑layer hoppings, and the mirror symmetry of the inner Ni‑O plane. Optimized TB parameters reproduce the measured FS topology and band dispersions. The model classifies the bands into bonding (α, γ), antibonding (β), and non‑bonding (β′) groups. Importantly, the bonding and antibonding bands possess even (+) mirror parity, whereas the non‑bonding β′ band has odd (–) parity.

The calculated FS reveals that near the Γ‑M diagonal the α, β, and β′ sheets are primarily of d x²‑y² character, gradually mixing d z² away from this line, while the γ sheet is dominated by d z². This orbital composition leads to selective nesting vectors: Q₁ connects α with β′, Q₂ connects α with γ, and Q₃ connects α with β. Because Q₁ links bands of opposite mirror parity, it drives a phase‑locked interlayer antiferromagnetic SDW. The nesting is “mirror‑selective”: only bands with opposite parity efficiently scatter, producing a density‑wave instability without requiring strong local moments.

Temperature‑dependent ARPES shows that the α and γ pockets develop an energy gap (Δ) that reaches ~33 meV at low temperature, while β′ exhibits a smaller, anisotropic gap only near the Γ‑M diagonal, and β/β_f remain gapless. The gap closes around 140 K, coinciding with the resistivity and magnetic‑susceptibility signatures of the combined SDW/CDW transition previously reported. This establishes that the observed gaps are directly tied to the density‑wave order.

The authors argue that the interlayer coupling of the Ni 3d z² orbitals is the primary driver of the SDW, as the d z²‑derived bands dominate the nesting that produces the gap. Under high pressure, the monoclinic distortion is suppressed, the crystal symmetry becomes tetragonal (I4/mmm), and the SDW is quenched, releasing interlayer spin fluctuations that can mediate Cooper pairing. Thus, the suppression of the mirror‑selective SDW provides a natural pathway to the emergence of high‑temperature superconductivity in the RP nickelate family.

In summary, the paper delivers (i) the first complete experimental mapping of all FS sheets in La₄Ni₃O₁₀, (ii) direct evidence of interlayer‑induced band splitting, (iii) a clear identification of mirror‑selective FS nesting as the origin of an interlayer antiferromagnetic SDW, and (iv) a demonstration that Ni 3d z² orbitals dominate low‑energy physics and density‑wave formation. These insights create a solid framework for understanding how pressure‑induced suppression of the SDW can give rise to superconductivity, linking the electronic structure of trilayer nickelates to the broader phenomenology of unconventional high‑Tc superconductors.