Nonadiabatic superconductivity in K3C60 and Rb3C60

We discuss the validity of Migdal–Eliashberg theory applied to the superconductor fullerides K₃C₆₀ and Rb₃C₆₀. Recently, the relevant superconductor properties have been measured, like the isotope coefficient, the energy gap and critical temperatures for these compounds and compared with their optical properties. They all present a very disperse band of phonon frequencies, running from very small to very large energies, the latter being close to the Fermi edge. Therefore, these materials exceed the limit of validity of the adiabatic Migdal theorem, measured with a nonadiabatic parameter m=w₀/E_F, where w₀ is a characteristic phonon frequency and E_F=250 meV, the Fermi level. We examine previous theories incorporating vertex corrections into the Eliashberg equations to deal with such a situation. We compare these approaches by calculating the critical temperatures using a multimodal Eliashberg spectral function ²F(w) to study the contribution of the various phononic modes. We arrive at the conclusion that the optical modes, not the intramolecular ones, are among those which maximize T_c independently of including vertex corrections or not. This result goes in the direction to understand why doped fullerides A₃C₆₀ are superconductors.