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Atomically precise superlattices involving transition metal oxides provide aunique opportunity to engineer correlated electron physics using strain(modulated by choice of substate) and quantum confinement (controlled by layerthickness). Here we use the combination of density functional theory anddynamical mean field theory (DFT+DMFT) to study Ni E$_g$ $d$-orbitalpolarization in strained LaNiO$_3$/LaAlO$_3$ superlattices consisting of fourlayers of nominally metallic NiO$_2$ and four layers of insulating AlO$_2$separated by LaO layers. The layer-resolved orbital polarization is calculatedas a function of strain and analyzed in terms of structural, quantumconfinement, and correlation effects. The effect of strain is determined fromthe dependence of the results on the Ni-O bond-length ratio and the octahedralrotation angles; quantum confinement is studied by comparison to bulkcalculations with similar degrees of strain; correlation effects are inferredby varying interaction parameters within our DFT+DMFT calculations. Thecalculated dependence of orbital polarization on strain in superlattices isqualitatively consistent with recent X-ray absorption spectroscopy and resonantreflectometry data. However, interesting differences of detail are foundbetween theory and experiment. Under tensile strain, the two inequivalent Niions display orbital polarization similar to that calculated for strained bulkLaNiO$_3$ and observed in experiment. Compressive strain produces a largerdependence of orbital polarization on Ni position and even the inner Ni layerexhibits orbital polarization different from that calculated for strained bulkLaNiO$_3$.

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