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

By means of magnetization, specific heat and muon-spin relaxation measurements, we investigate high-pressure oxidized \mohpo, in which overdoping is achieved up to $p \sim 0.45$ hole/Cu, well beyond the $T_c - p$ superconducting dome of cuprates, where Fermi liquid behavior is expected. Surprisingly, we find bulk superconductivity with $T_c$=84 K and superfluid density similar to those of optimally doped Y123. On the other hand, specific heat data display a large electronic contribution at low temperature, comparable to that of nonsuperconducting overdoped La214. These results point at an unusual high-$T_c$ phase with a large fraction of unpaired holes. Further experiments may assess the Fermi liquid properties of the present phase, which would put into question the paradigm that the high $T_c$ of cuprates originates from a non-Fermi liquid ground state.