Isotopic disorder in superconducting fullerenes

The superconducting transition temperature of doped fullerenes appears to be unusually sensitive to partial substitution of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ for the naturally abundant isotope ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. We show that the electron-phonon coupling constant λ is generically independent of isotopic disorder. By studying the effects of isotopic substitution on phonon-mediated superconductivity in ${\mathrm{C}}_{60}$ within the Migdal-Eliashberg theory we conclude that the theoretical superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ does not show any anomalous dependence on isotopic substitution in weak or strong coupling. We comment on the possible causes of the experimentally observed effect.