LaNiO$_3$ (LNO) is an intriguing member of the rare-earth nickelates in exhibiting a metal-insulator transition for a critical film thickness of about 4 unit cells [Son et al., Appl. Phys. Lett. 96, 062114 (2010)]; however, such thin films also show a transition to a metallic state in superlattices with SrTiO$_3$ (STO) [Son et al., Appl. Phys. Lett. 97, 202109 (2010)]. In order to better understand this transition, we have studied a strained LNO/STO superlattice with 10 repeats of [4 unit-cell LNO/3 unit-cell STO] grown on an (LaAlO$_3$)$_{0.3}$(Sr$_2$AlTaO$_6$)$_{0.7}$ substrate using soft x-ray standing-wave-excited angle-resolved photoemission (SWARPES), together with soft- and hard- x-ray photoemission measurements of core levels and densities-of-states valence spectra. The experimental results are compared with state-of-the-art density functional theory (DFT) calculations of band structures and densities of states. Using core-level rocking curves and x-ray optical modeling to assess the position of the standing wave, SWARPES measurements are carried out for various incidence angles and used to determine interface-specific changes in momentum-resolved electronic structure. We further show that the momentum-resolved behavior of the Ni 3d eg and t2g states near the Fermi level, as well as those at the bottom of the valence bands, is very similar to recently published SWARPES results for a related La$_{0.7}$Sr$_{0.3}$MnO$_3$/SrTiO$_3$ superlattice that was studied using the same technique (Gray et al., Europhysics Letters 104, 17004 (2013)), which further validates this experimental approach and our conclusions. Our conclusions are also supported in several ways by comparison to DFT calculations for the parent materials and the superlattice, including layer-resolved density-of-states results.
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