Granular Superconductivity in La$_{2}$PrNi$_{2}$O$_{7-\delta}$ Thin Films
Superconductivity realized in bilayer nickelate thin films enables direct spectroscopic and transport studies at ambient pressure. However, a persistent two-step resistive transition remains a major barrier to achieving optimal superconducting properties. Here, we show that the two-step transition in La$_2$PrNi$_2$O$_{7-\delta}$ thin films originates from the granular nature of superconductivity, specifically, the coexistence of two distinct superconducting grain phases coupled by a Josephson junction network. A secondary, lower-temperature transition appears in the $R(T)$ curve, even when residual resistance becomes vanishingly small near 30 K. This two-step behavior significantly lowers the zero-resistance transition temperature, $T_{c, zero}$$\approx$ 10 K, and limits advanced spectroscopic studies. Our findings reveal the microscopic mechanism underlying the two-step transition in thin films and underscore the need for improved oxygen homogeneity to achieve bulk superconductivity in this system.