First-Principles Evidence for Strongly Correlated Superconductivity Driven by Structural Variations in La$_3$Ni$_2$O$_7$

We conduct first-principles simulations of La$_3$Ni$_2$O$_7$, a nickelate in which recent experiments have shown signs of high-temperature superconductivity. Within the hydrostatic pressure range where superconductivity is observed, we find a significant increase in effective on-site repulsion in the maximally localised Wannier functions comprising the Ni $e_g$ bands crossing the Fermi energy. We attribute this increase to an interplay between orbital localisation and competing screening channels arising from structural variations. Our results indicate that the superconducting region in the La$_3$Ni$_2$O$_7$ phase diagram coincides with a region of enhanced electronic correlations, which show a close correspondence with the critical temperature. Including finite temperatures up to 100 K, $ab$ $initio$ molecular dynamics simulations then provide new insights into the debated structural phase diagram and further clarify the origin of the right-triangular superconducting dome. Finally, we study Ac$_3$Ni$_2$O$_7$ to confirm the crucial role of the $A$-site cation in shaping the pressure-driven evolution of electronic correlations.