Electronic structure of compressively strained thin film La$_2$PrNi$_2$O$_7$

The discovery of superconductivity in the bulk nickelates under high pressure is a major advance in physics. The recent observation of superconductivity at ambient pressure in compressively strained bilayer nickelate thin films has now enabled direct characterization of the superconducting phase through angle resolved photoemission spectroscopy (ARPES). Here we present an in-situ ARPES study of compressively strained La$_2$PrNi$_2$O$_7$ films grown by oxide molecular beam epitaxy, and the ozone treated counterparts with an onset T$_c$ of 40 K, supplemented with results from pulsed laser deposition films with similar T$_c$. We resolve a systematic strain-driven electronic band shift with respect to that of bulk crystals, in qualitative agreement with density functional theory (DFT) calculations. However, the strongly renormalized flat 3$d_{z2}$ band shifts a factor of 5-10 smaller than anticipated by DFT. Furthermore, it stays ~70 meV below the Fermi level, contradicting the expectation that superconductivity results from the high density of states of this band at the Fermi level. We also observed a non-trivial k$_z$ dispersion of the cuprate-like 3$d_{x2-y2}$ band. Combined with results from both X-ray diffraction and DFT, we suggest that the strained films are under ~5 GPa effective pressure, considerably larger than the na\"ive expectation from the DFT relaxed structure. Finally, the ~70 meV energy position is intriguingly close to the collective mode coupling more prominently seen in thin films, in the energy range of both oxygen related phonons and the maximum of the spin excitation spectrum.