Optical properties of the infinite-layer La$_{1-x}$Sr$_{x}$NiO$_{2}$ and hidden Hunds physics

We investigate the optical properties of the normal state of the infinite-layer La$_{1-x}$Sr$_x$NiO$_2$ using DFT+DMFT. We find a correlated metal which exhibits substantial transfer of spectral weight to high energies relative to the density functional theory. The correlations are not due to Mott physics, which would suppress the charge fluctuations and integrated optical spectral weight as we approach a putative insulating state. Instead we find the unusual situation, that the integrated optical spectral weight {it decreases} with doping and {it increases } with increasing temperature. We contrast this with the coherent component of the optical conductivity, which {it decreases} with increasing temperature as a result of a coherence$-$incoherence crossover. Our optical studies support a picture of a Hunds metallic state, where dynamical orbital fluctuations are visible at intermediate energies, even if at low energies the Fermi surface has primarily $d_{x^2 - y^2}$ character and we propose a low-energy two-band model with atom centered $e_g$ states.