Superconductivity emerging from the N${é}$el state in ${\it infinite}$-${\it stage}$ single-layer cuprate La$_2$CuO$_{4+δ}$

In copper oxides (cuprates) with single CuO$_2$ layer such as La$_{2-x}$Ba(Sr)$_x$CuO$_4$, antiferromagnetism coexists with superconductivity at small doping levels $x$, where chemical disorders are significant. Here, we report that superconductivity occurs in a uniform and fully ordered N${é}$el state in a single-layer cuprate La$_2$CuO$_{4+δ}$ with a small amount of excess oxygen $(δ= 0.015)$ as demonstrated by the $^{139}$La nuclear quadrupole resonance measurement. A uniform oxygen distribution in the crystal is crucial for achieving microscopic phase coexistence and overcoming the miscibility gap associated with the staging instability; self-organized periodic oxygen arrangement driven by mobile oxygen atoms. This finding prompts the reconsideration of superconductivity in cuprates, highlighting that it can emerge in a robust N${é}$el state that retains sizable magnetic moments and hosts only a small carrier density.