Evolution of Electronic Correlations in the Ruddlesden-Popper Nickelates

We report on optical studies of the Ruddlesden-Popper nickelates La${}_{n+1}$Ni${}_n$O${}_{3n+1}$ with $n=2$ (La${}_3$Ni${}_2$O${}_7$), $n=3$ (La${}_4$Ni${}_3$O${}_{10}$) and $n=\mathrm{\infty }$ (LaNiO${}_3$). As the number of the NiO${}_6$ octahedra layers $n$ grows, the ratio of the kinetic energy determined from the experimental optical conductivity and that from band theory $K_{\text{exp}}\mathrm{/}{K}_{\text{band}}$ increases, suggesting a reduction of electronic correlations. While the strong electronic correlations in the bilayer La${}_3$Ni${}_2$O${}_7$ place it on the verge of the Mott insulating phase, the trilayer La${}_4$Ni${}_3$O${}_{10}$ and infinite-layer LaNiO${}_3$ exhibit moderate electronic correlations, falling into the regime of correlated metals. The evolution of the electronic correlations in La${}_{n+1}$Ni${}_n$O${}_{3n+1}$ is likely to be dominated by the Ni-$d_{z^2}$ orbital. Our results provide important information for understanding the superconductivity in Ruddlesden-Popper nickelates.