Nonadiabatic high-$T_c$ superconductivity in hole-doped fullerenes

In this paper we address the possibility of high-$T_c$ superconductivity ${(T}_c\sim 100\mathrm{K})$ in hypothetical hole doped ${\mathrm{C}}_{60}$ within the context of the nonadiabatic theory of superconductivity. Our analysis shows that electron doped fullerenes, represented by the $A_3{\mathrm{C}}_{60}$ family, are characterized by relatively small values of the electron–phonon coupling constant λ, which can thus be further increased by hole doping before lattice instabilities occur. In particular we show that $T_c$ larger than 100 K are compatible in the nonadiabatic context with microscopic parameters ${\lambda }_h\simeq 0.5–1.0,$ ${\mu }^{*}\simeq 0.3–0.5$ and phonon frequencies ${\omega }_{\mathrm{ph}}\simeq 1500–2000\mathrm{K}.$ These results provide a stimulus for material engineering and optimization along the lines indicated.