Similarities and differences between nickelate and cuprate films grown on a SrTiO$_3$ substrate

The recent discovery of superconductivity in Sr-doped NdNiO$_2$ films grown on SrTiO$_3$ started a novel field within unconventional superconductivity. To understand the similarities and differences between nickelate and cuprate layers on the same SrTiO$_3$ substrate, here based on the density functional theory we have systematically investigated the structural, electronic, and magnetic properties of NdNiO$_2$/SrTiO$_3$ and CaCuO$_2$/SrTiO$_3$ systems. Our results revealed a strong lattice reconstruction in the case of NdNiO$_2$/SrTiO$_3$, resulting in a polar film, with the surface and interfacial NiO$_2$ layers presenting opposite displacements. However, for CaCuO$_2$/SrTiO$_3$, the distortions of those same two CuO$_2$ layers were in the same direction. In addition, we found this distortion to be approximately independent of the studied range of film thickness for both the nickelate and cuprates films. Furthermore, we also observed a two-dimensional electron gas at the interface between NdNiO$_2$ and SrTiO$_3$, caused by the polar discontinuity, in agreement with recent literature. For NdNiO$_2$/SrTiO$_3$ the two-dimensional electron gas extends over several layers, while for CaCuO$_2$/SrTiO$_3$ this electronic rearrangement is very localized at the interface between CaCuO$_2$ and SrTiO$_3$. The electronic reconstruction found at the interface involves a strong occupation of the Ti $3d_{xy}$ state. In both cases, there is a significant electronic charge transfer from the surface Ni or Cu layers to the Ti interface layer. The interfacial Ni and Cu layer is hole and electron doped, respectively. By introducing magnetism and electronic correlation, we observed that the $d_{3z^2-r^2}$ orbital of Ni becomes itinerant while the same orbital for Cu remains doubly occupied, establishing a clear two- vs one-orbital active framework for the description of these systems.