Universal electronic structure of multi-layered nickelates via oxygen-centered planar orbitals

Superconductivity has been demonstrated in the family of multi-layered nickelates La$_3$Ni$_2$O$_7$ and La$_4$Ni$_3$O$_{10}$. Key questions remain open regarding the low-energy electronic states that support superconductivity in these compounds. Here we take advantage of the natural polymorphism between bilayer (2222) and alternating monolayer-trilayer (1313) stacking sequences that arises in bulk La$_3$Ni$_2$O$_7$ crystals, and by employing angle-resolved photoemission spectroscopy (ARPES) we identify a universal low-energy electronic structure in this family of materials. We observe the fingerprint of a doping-dependent spin-density wave (SDW) instability -- strong and coherent enough to reconstruct the Fermi surface, both by gapping out regions of the low-energy electronic structure as well as translating the $β$ pocket by a vector $Q_{tβ}$ consistent with the results of previous neutron and x-ray scattering experiments. Using an effective tight-binding model, we simulate the spectral weight distribution observed in our ARPES dichroism experiments and establish that the low-energy electronic phenomenology is dominated by oxygen-centered planar orbitals, which evolve from the $d_{3x^2-r^2}$ and $d_{3y^2-r^2}$ symmetry characteristic of 3-spin polarons (3SP) to the familiar $d_{x^2-y^2}$ Zhang-Rice singlets (ZRS) that support high-temperature superconductivity in cuprates. By inclusion of magnetic moments on plaquettes of oxygen orbitals in our model, we show that ZRS-like states mediate the SDW. Combined with the observation that oxygen annealing is required to induce superconductivity in both thin films and bulk La$_3$Ni$_2$O$_7$, this demonstrates that the ZRS population dictates whether the ground state favors density-wave order or superconductivity -- with hole doping suppressing the former and stabilizing the latter, as in the cuprates.