1.4.5 Pairing Mechanism in the Fulleride Superconductors

The narrowness of the conduction bands in the A₃ materials and the large predicted values of the electron-electron Coulomb repulsion prompted exotic ``all electronic'' theoretical pairing models, e.g. [55]. In this model the electron screening is found under some conditions to reduce the electron-electron Coulomb repulsion to such a degree that it becomes effectively attractive in some energy range. However, nearly all the observations can be understood by a conventional electron-phonon pairing mechanism in which:

• The order parameter is s-wave.
• The attractive interaction leading to pairing is of the standard electron-phonon variety.
• The important phonons mediating the electron pairing are the high frequency intramolecular phonons. The dimensionless coupling to these phonons is $\lambda_m \approx 0.7$.
• The Coulomb Pseudopotential is reasonably small $\mu^* \approx 0.15$. This has been explained in various ways, for example as a result of compensation by a Jahn-Teller energy (particular to the trianionic C₆₀[56]). Another explanation for the small $\mu^*$ uses the renormalization discussed previously, but with a much higher characteristic electron energy (replacing E_F in Eq.1.14). This is rationalized by appealing to the contribution of Coulomb scattering into higher bands[37].

The success of this conventional pairing scheme challenges our understanding of superconductivity more generally, because

• The conduction bandwidth is small and the phonon frequencies are high, so the applicability of Migdal's theorem, on which the Eliashberg theory (section 1.4.3) rests, is questionable, e.g. see [51]. In particular, the Eliashberg theory is only correct in the limit of small E_D / E_F.
• The electron-electron Coulomb interaction is expected to be large: U for two electrons on a sphere of radius 3.5Å is estimated to be 3 eV. Screening by molecular polarization may reduce this to about 1 eV, yielding an estimate of the Coulomb parameter $\mu \approx 10$. Because E_F is not much greater than the phonon energies, though, the screening renormalization of $\mu$ (Eq. 1.14), should be ineffective in reducing $\mu^*$ relative to $\mu$.
• The molecular wavefunctions that make up the conduction band have spatial extent which is roughly an order of magnitude larger than that of typical (``atomic'' rather than molecular) metals.
• These systems, at least for the Fm$\bar{3}$m case, are intrinsically disordered (in the molecular orientation).

In light of these considerations, perhaps the important question is why superconductivity in the fullerides can apparently be explained in the conventional picture of electron-phonon mediated pairing.