Many-body electronic structure of $d^{9-\delta}$ layered nickelates

The recent observation of superconductivity in an infinite-layer and quintuple-layer nickelate within the same $R_{n+1}$Ni$_{n}$O$_{2n+2}$ series ($R$ = rare-earth, $n=2-\infty$, with $n$ indicating the number of NiO$_{2}$ layers along the $c$-axis), unlocks their potential to embody a whole family of unconventional superconductors. Here, we systematically investigate the many-body electronic structure of the layered nickelates (with $n=2-6,\infty$) within a density-functional theory plus dynamical mean-field theory framework and contrast it with that of the known superconducting members of the series and with the cuprates. We find that many features of the electronic structure are common to the entire nickelate series, namely, strongly correlated Ni-$d_{x^{2}-y^{2}}$ orbitals that dominate the low-energy physics, mixed Mott-Hubbard/charge-transfer characteristics, and $R$($5d$) orbitals acting as charge reservoirs. Interestingly, we uncover that the electronic structure of the layered nickelates is highly tunable as the dimensionality changes from quasi-two-dimensional to three-dimensional as $n \rightarrow \infty$. Specifically, we identify the tunable electronic features to be: the charge-transfer energy, presence of $R(5d)$ states around the Fermi level, and the strength of electronic correlations.