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Direct observation of nodeless superconductivity and phonon modes in electron-doped copper oxide Sr$_{1-x}$Nd$_x$CuO$_2$

The microscopic understanding of high-temperature superconductivity in cuprates has been hindered by the apparent complexity of crystal structures in these materials. We used scanning tunneling microscopy and spectroscopy to study an electron-doped copper oxide compound Sr$_{1-x}$Nd$_x$CuO$_2$ that has only bare cations separating the CuO$_2$ planes and thus the simplest infinite-layer structure among all cuprate superconductors. Tunneling conductance spectra of the major CuO$_2$ planes in the superconducting state revealed direct evidence for a nodeless pairing gap, regardless of variation of its magnitude with the local doping of trivalent neodymium. Furthermore, three distinct bosonic modes are observed as multiple peak-dip-hump features outside the superconducting gaps and their respective energies depend little on the spatially varying gaps. Along with the bosonic modes with energies identical to those of the external, bending and stretching phonons of copper oxides, our findings indicate their origin from lattice vibrations rather than spin excitations.