Regulating oxygen content and superconductivity in La$_3$Ni$_2$O$_{7+δ}$
The synthesis of high-quality Ruddlesden-Popper (RP) nickelates remains challenging due to variations in oxygen content and the prevalence of intergrown RP phases. Precisely controlling the stoichiometry and characterizing the resulting physical properties are essential for understanding the mechanism of high-$T_c$ superconductivity in these materials. In this work, we synthesize a series of La$_3$Ni$_2$O$_{7+δ}$ samples with systematically controlled oxygen content and perform comprehensive structural and compositional analyses. Precise oxygen tuning enables us to tailor the microstructure, yielding a pure bilayer phase, a mixture of bilayer and hybrid single-layer-bilayer phases, and a predominantly bilayer phase containing trilayer intergrowths. High-pressure transport measurements reveal distinct superconducting transitions with contrasting $T_c$ values, corresponding to the bilayer phase, the hybrid phase, and trilayer inclusions. Notably, we find that oxygen content not only governs the phase purity$-$i.e., the presence of intergrowth phases$-$but also directly modulates the upper critical field ($H_{c2}$) of the bilayer superconductivity. By establishing a phase diagram of $T_c$ and $H_{c2}$ as functions of oxygen content in La$_3$Ni$_2$O$_{7+δ}$, this work advances synthetic control and provides new insights into the superconducting mechanism of RP nickelates.