Real-space imaging of Bose-Einstein condensation behavior in infinite-layer cuprates

We employ spectroscopic-imaging scanning tunneling microscopy to investigate the electronic properties of copper-oxide (${\mathrm{CuO}}_{2}$) planes in an electron-doped infinite-layer cuprate superconductor ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Nd}}_{x}{\mathrm{CuO}}_{2}$. Tunneling conductance spectra reveal distinct Bose-Einstein condensation (BEC)-like features in underdoped regions, characterized by a small Fermi energy, broad coherence peaks, and pronounced particle-hole asymmetry. As the local electron doping level increases, these features evolve into well-defined superconducting gaps, unveiling the long-sought crossover between the BEC and Bardeen-Cooper-Schrieffer (BCS) regions in cuprate superconductors. Additionally, we observe three distinct phonon excitations within the BEC regions, which underscores the potential role of lattice vibrations in electron pairing. Our results provide direct real-space experimental evidence for the BEC-BCS crossover on ${\mathrm{CuO}}_{2}$ planes, offering insights into the emergent superconductivity in doped Mott cuprates.