Bulk superconductivity at 84 K in the strongly overdoped regime of cuprates

By means of magnetic susceptibility, specific heat and muon-spin relaxation ($\mu$SR) measurements, we report on bulk superconductivity at 84 K in high-pressure oxidized Cu$_{0.75}$Mo$_{0.25}$Sr$_2$YCu$_2$O$_{7.54}$. A record short apical Cu-O distance and a large excess of electronic specific heat at low temperature give evidence of hole overdoping, $p \approx 0.43$ hole/Cu, well beyond the superconducting dome relating $T_c$ and $p$, considered universally valid for cuprates, where a normal Fermi liquid behavior is expected. On the other hand, the superfluid density measured by means of $\mu$SR is similar to that of optimally doped YBa$_2$Cu$_3$O$_{7-\delta}$, which indicates that the extra-holes do not contribute to superconductivity, thus leading to a phase separation between superconducting and normal carriers, or that Cooper pairs are strongly localized. In both cases, the unexpected observation of high $T_c$ in the strongly overdoped regime constitutes a further open issue for the theoretical explanation of superconductivity in cuprates.