Quantitative theory of superconductivity in doped C60.

Abstract

The electronic part \ensuremath{\eta} (the Hopfield factor) of the electron-phonon coupling constant \ensuremath{\lambda} for alkali-metal-doped fullerenes ${\mathit{A}}_{3}$${\mathrm{C}}_{60}$ is calculated within the rigid muffin-tin-potential approximation. It is found that \ensuremath{\eta} is large for tangential atomic motions, while for the radial vibrations \ensuremath{\eta} is 20 times smaller. We have calculated \ensuremath{\eta} for three lattice constants (a=14.1, 14.4, and 14.6 \AA{}) corresponding approximately to those of ${\mathrm{C}}_{60}$, ${\mathrm{Rb}}_{3}$${\mathrm{C}}_{60}$, and (hypothetical) ${\mathrm{Cs}}_{3}$${\mathrm{C}}_{60}$, and found \ensuremath{\eta}=21, 32, and 36 eV/A${\mathrm{\r{}}}^{2}$. Using semiempirical nearest-neighbor force constants we estimated \ensuremath{\lambda}=0.49, 0.77, and 0.83, and 〈${\mathrm{\ensuremath{\omega}}}_{\mathrm{log}}$〉=870 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for the average phonon frequency. The McMillan formula yields ${\mathit{T}}_{\mathit{c}}$=5, 36, and 44 K for these lattice constants, in reasonable agreement with the available experimental data. The relatively high-temperature superconductivity in ${\mathit{A}}_{3}$${\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.