Percolative superconductivity in electron-doped Sr1−xEuxCuO2+y films

Electron-doped infinite-layer ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_x\mathrm{Cu}{\mathrm{O}}_2+y$ films over a wide doping range have been prepared epitaxially on $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}₃$(001) using reactive molecular beam epitaxy. In-plane transport measurements of the single-crystalline samples reveal a dome-shaped nodeless superconducting phase centered at $x\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}$ 0.15, a Fermi-liquid behavior and pronounced upturn in low-temperature resistivity. We show that the resistivity upturn follows square-root temperature dependence, suggesting the emergence of superconductivity via a three-dimensional percolation process. The percolative superconductivity is corroborated spectroscopically by imaging the electronic phase separation between superconducting and metallic phases with low-temperature scanning tunneling microscopy. Furthermore, we visualize interstitial and apical oxygen anions that rapidly increase in number as $x>$ 0.12 and elucidate their impacts on the superconductivity and normal-state resistivity.