Tcvs Carrier Concentration in Cubic Fulleride Superconductors

The effect of carrier concentration on fulleride superconductivity is studied by x ray, Raman, magnetization, and ESR of two new cubic families: ${\mathrm{Na}}_2{\mathrm{Cs}}_x{\mathrm{C}}_{60}$ $(0<x<\mathrm{}1\mathrm{})$ and $M_{3-y}{\mathrm{Ba}}_y{\mathrm{C}}_{60}$ ( $0.2<y<\mathrm{}2\mathrm{}$, $M=\mathrm{K}$, Rb, or Cs). These are isostructural with known $\mathrm{Pa}\overline{3}$ and $\mathrm{Fm}\overline{3}m$ trivalent superconductors, respectively, but with variable valence $2<n<\mathrm{}5\mathrm{}$. $T_c$ is peaked at or very near $n=3\mathrm{}$, decreasing rapidly in either direction to $<0.5\mathrm{}\mathrm{K}$ for $n=2.5\mathrm{}$ and 5. These results underscore the failure of both one-electron and strong correlation models to explain the dependence of $T_c$ on band filling.