Resolving Structural Origins for Superconductivity in Strain-Engineered La$_3$Ni$_2$O$_7$ Thin Films

The discovery of high-temperature superconductivity in bulk La$_3$Ni$_2$O$_7$ under high hydrostatic pressure and, more recently, biaxial compression in epitaxial thin films has ignited significant interest in understanding the interplay between atomic and electronic structure in these compounds. Subtle changes in the nickel-oxygen bonding environment are thought to be key drivers for stabilizing superconductivity, but specific details of which bonds and which modifications are most relevant remains so far unresolved. While direct, atomic-scale structural characterization under hydrostatic pressure is beyond current experimental capabilities, static stabilization of strained La$_3$Ni$_2$O$_7$ films provides a platform well-suited to investigation with new picometer-resolution electron microscopy methods. Here, we use multislice electron ptychography to directly measure the atomic-scale structural evolution of La$_3$Ni$_2$O$_7$ thin films across a wide range of biaxial strains tuned via substrate. By resolving both the cation and oxygen sublattices, we study strain-dependent evolution of atomic bonds, providing the opportunity to isolate and disentangle the effects of specific structural motifs for stabilizing superconductivity. We identify the lifting of crystalline symmetry through modification of the nickel-oxygen octahedral distortions under compressive strain as a key structural ingredient for superconductivity. Rather than previously supposed $c$-axis compression, our results highlight the importance of in-plane biaxial compression in superconducting thin films, which suggests an alternative -- possibly cuprate-like -- understanding of the electronic structure. Identifying local regions of inhomogeneous oxygen stoichiometry and high internal strain near crystalline defects, we suggest potential pathways for improving the sharpness and temperature of the superconducting transition.