Heavily Sr-Doped La$_{2}$SrNi$_{2}$O$_{7-δ}$ as a Tetragonal Ruddlesden-Popper Phase at Ambient Pressure
High-temperature superconductivity has been found in bilayer Ruddlesden-Popper (RP) nickelates in bulk samples under high pressure, or in thin films via compressive strain. In the superconducting state, a tetragonal structure with a straight Ni-O-Ni bond along c-axis has been commonly observed, together with the suppression or diminishing of the density-wave orders. Therefore, it remains an open question whether these factors are sufficient for achieving superconductivity at ambient pressure. Here we report the first successful synthesis of heavily Sr-doped La$_{2}$SrNi$_{2}$O$_{7-δ}$ under high-pressure and high-temperature (HPHT) conditions with a flux method. X-ray diffraction and scanning transmission electron microscopy (STEM) confirm that the material adopts a tetragonal (I4/mmm) structure with an 180$^{\circ}$ Ni-O-Ni bond angle along c-axis. Resistance measurements reveal metallic behavior with a low-temperature upturn and no density-wave features are observed. However, neither pressure nor oxygen variation induces superconductivity. Density functional theory calculations indicate that the holes introduced by Sr doping are predominantly doped into the Ni-3d$_{z^2}$ orbital, leading to the appearance of a very large $γ$ pocket on the Fermi surface at ambient pressure and significantly reducing the occupation of the Ni-3d$_{z^2 }$ orbital. Combining the experimental observations with theoretical calculations, we attribute the absence of superconductivity to the serious deviation from the half-filling state of the Ni-3d$_{z^2 }$ band, which is crucial for the interlayer antiferromagnetic interaction and thus for pairing. Our work unravels important issues for achieving superconductivity in bilayer nickelate system.