Influence of quantum confinement and strain on orbital polarization of strained four-layer LaNiO$_3$ superlattices: a DFT+DMFT study

Here we use the combination of density functional theory and dynamical mean field theory to study Ni d orbital polarization in strained LaNiO$_3$/LaAlO$_3$ superlattices consisting of four layers of nominally metallic NiO$_2$ and four layers of insulating AlO$_2$ separated by LaO layers. The layer-resolved orbital polarization is calculated as a function of strain and analysed in terms of structural, quantum confinement, and correlation effects. The overall dependence of orbital polarization on strain in superlattices is qualitatively consistent with recent X-ray absorption spectroscopy and resonant reflectometry data. However, interesting differences of detail are found depending on the sign of strain. Under tensile strain, the two inequivalent Ni ions display orbital polarization similar to that calculated for strained bulk LaNiO$_3$ and observed in experiment. Compressive strain produces a larger dependence of orbital polarization on Ni position and even the inner Ni layer exhibits orbital polarization different from that calculated for strained bulk LaNiO$_3$. The quantum confinement effect is as important as the strain effect and more stronger for tensile strain.