Quantitative theory of superconductivity in doped ${\mathrm{C}}_{60}$

The electronic part η (the Hopfield factor) of the electron-phonon coupling constant λ for alkali-metal-doped fullerenes ${\mathit{A}}_3$${\mathrm{C}}_{60}$ is calculated within the rigid muffin-tin-potential approximation. It is found that η is large for tangential atomic motions, while for the radial vibrations η is 20 times smaller. We have calculated η for three lattice constants (a=14.1, 14.4, and 14.6 Å) corresponding approximately to those of ${\mathrm{C}}_{60}$, ${\mathrm{Rb}}_3$${\mathrm{C}}_{60}$, and (hypothetical) ${\mathrm{Cs}}_3$${\mathrm{C}}_{60}$, and found η=21, 32, and 36 eV/A${\mathrm{̊}}^2$. Using semiempirical nearest-neighbor force constants we estimated λ=0.49, 0.77, and 0.83, and 〈${\mathrm{\omega }}_{\log }$〉=870 ${\mathrm{cm}}^{\mathrm{-}1}$ for the average phonon frequency. The McMillan formula yields ${\mathit{T}}_{\mathit{c}}$=5, 36, and 44 K for these lattice constants, in reasonable agreement with the available experimental data. The relatively high-temperature superconductivity in ${\mathit{A}}_3$${\mathrm{C}}_{60}$, as well as the strong dependence of ${\mathit{T}}_{\mathit{c}}$ on the dopant, is fully explained within the framework of the conventional superconductivity theory.