High frequency conductivity of few unit cell thick LaNiO$_{3}$ layers*

We have measured the dc and optical conductivity of ultra-thin films of the correlated metal LaNiO$_{3}$ and of superlattices with alternating LaNiO$_{3}$ and insulating SrTiO$_{3}$ layers, all grown epitaxially on LSAT substrates with modest tensile strain in the LaNiO$_{3}$. In the superlattices, the LaNiO$_{3}$ layers are 4 unit cells (1.6 nm) thick and the SrTiO$_{3}$ is either 4 or 10 unit cells thick. Isolated films thinner than 4 nm are insulating; however, both the superlattices and thicker films consistently show a coherent peak in the optical conductivity. Furthermore, the optical conductivity at several hundred GHz is in excellent agreement with the dc electrical conductivity. We consider the possibility of a percolation threshold in ultra-thin LaNiO3 layers and discuss implications for the nature of the LaNiO$_{3}$/SrTiO$_{3}$ interface.