Anomalous Disappearance of High-$T_c$ Superconductivity at High Hole Concentration in Metallic ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$

Samples of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_{4-\delta }$ have previously shown a maximum concentration of $p=0.15\mathrm{}$ holes per [Cu${\mathrm{O}}_2$] unit, because increasing $x>\mathrm{}0.15\mathrm{}$ normally induces compensating oxygen vacancies. Annealing samples in 100 bars of oxygen pressure fills the oxygen vacancies and greatly increases the range of accessible hole concentrations, up to $p=0.40\mathrm{}$ (or effectively ${\mathrm{Cu}}^{+2.40\mathrm{}}$). We find that $T_c$ is constant at ≃36 K from $p=0.15\mathrm{} \mathrm{to} 0.24$, where it begins to decrease. Beyond $p\simeq 0.32$, superconductivity disappears, even though the samples are more conducting.