Superconducting phase diagram of finite-layer nickelates Nd _n+1Ni _n O_2n+2

Following the successful prediction of the superconducting phase diagram for infinite-layer nickelates, here we calculate the superconducting T _c vs. the number of layers n for finite-layer nickelates using the dynamical vertex approximation. To this end, we start with density functional theory, and include local correlations non-perturbatively by dynamical mean-field theory for n = 2-7. For all n, the Ni $d_{x^2-y^2}$ orbital crosses the Fermi level, but for n > 4 there are additional (π, π) pockets or tubes that slightly enhance the layer-averaged hole doping of the $d_{x^2-y^2}$ orbitals beyond the leading 1/n contribution stemming from the valence electron count. We finally calculate T _c for the single-orbital $d_{x^2-y^2}$ Hubbard model by dynamical vertex approximation.