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Electron-doped infinite-layer Sr$_{1-x}$Eu$_{x}$CuO$_{2+y}$ films over a widedoping range have been prepared epitaxially on SrTiO$_3$(001) using reactivemolecular beam epitaxy. In-plane transport measurements of the singlecrystalline samples reveal a dome-shaped nodeless superconducting phasecentered at $x$ $\sim$ 0.15, a Fermi-liquid behavior and pronounced upturn inlow temperature resistivity. We show that the resistivity upturn followssquare-root temperature dependence, suggesting the emergence ofsuperconductivity via a three-dimensional percolation process. The percolativesuperconductivity is corroborated spectroscopically by imaging the electronicphase separation between superconducting and metallic phases withlow-temperature scanning tunneling microscopy. Furthermore, we visualizeinterstitial and apical oxygen anions that rapidly increase in number as $x>$0.12, and elucidate their impacts on the superconductivity and normal-stateresistivity.

Percolative Superconductivity in Electron-Doped Sr$_{1-x}$Eu$_{x}$CuO$_{2+y}$ Films