In-plane Ni–O–Ni bond angles as structural fingerprints of superconductivity in layered nickelates: Effects of pressure, strain, layering, and correlations

We investigate the structural and electronic conditions conducive to superconductivity in layered nickelates using density-functional theory. For both the bilayer and 1--3 polymorphs of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, we find that the in-plane Ni--O--Ni bond angles under pressure strongly correlate with the experimentally observed superconducting transition temperature (${T}_{c}$) dome, and may serve as a reasonable proxy. Under compressive strain, the bond angles straighten, peaking near 2% strain, consistent with experimental reports of superconductivity in strained bilayer thin films. However, the bond angles at this strain are more bent than those achieved under hydrostatic pressure, correlating with a lower ${T}_{c}$. We show that increasing the number of ${\mathrm{NiO}}_{2}$ layers, as in ${\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}$, or substituting heavier rare-earth elements (e.g., Pr), raises the pressure required to reach the structural configuration associated with superconductivity. Our results indicate that these systems require higher external pressure to achieve in-plane bond straightening. Varying the on-site Coulomb interaction $U$ reveals that stronger electronic correlations delay the structural transition and favor high-spin states. This suggests that moderate correlation strength may be optimal for superconductivity, with stronger correlation preventing the formation of favorable bond geometries. Electronic structure analysis shows that the Ni ${e}_{g}$ orbitals dominate near the Fermi level and shift downward with pressure, enhancing Ni--O hybridization. These results highlight how pressure and strain tune structural features that may be essential for engineering high-${T}_{c}$ phases in nickelate superconductors.