Conductivity of infinite-layer NdNiO$_{2}$ as a probe of spectator bands

Using a density-functional theory plus dynamical mean-field theory methodology, we compute the many-body electronic structure and optical conductivity of NdNiO$_{2}$ under the influence of large scattering rates on the Nd($5d$) bands and including dynamical interactions on the Nd($5d$) orbitals with shifts of the Nd-Ni $d$-level energy difference. We find a robust conducting pathway in the out-of-plane direction arising from strong hybridization between the Ni-$d_{z^2}$ and Nd($5d$) orbitals. This pathway can be ``short-circuited'' if this hybridization is suppressed through large electronic scattering rates but is not reduced to zero even by very large beyond-DFT shifts of the Nd-Ni $d$-level energy splitting. The computed in-plane conductivity for NdNiO$_{2}$ predicts the material to be a ``good metal'' in contrast to experiments indicating the material is a ``bad metal'' or ``weak insulator''. Our results motivate future experiments measuring the $c$-axis resistivity as a proxy for the spectator bands and suggests the essential difference between the infinite-layer nickelates and the cuprates is dimensionality of their electronic structures.