Small Fermi energy effects in MgB2 and related compounds

Superconductivity at Tc ' 40 K in MgB2 is thought to origin from the strong electron-phonon (el-ph) coupling of the r-bands, whereas the residual interband scattering gives rise to the multigap phenomenology. The extremely low charge density of the r-bands is reflected in the small Fermi energy EFr , a fraction of eV, a common feature which is shared also by cuprates and fullerides. In our contribution we discuss the anomalous effects arising from the small Fermi energy phenomenology, when EFr becomes comparable with the other energy scales of the systems. In particular we analyze the nonadiabatic effects arising from the finite adiabatic ratio xph =EFr ; the anharmonic character of the E2g phonon mode, which is shown to be related to the smallness of the Fermi energy with respect to the electron-phonon coupling gE2 g : EFr ? gE2 g ; the anomalous effects of disorder when impurity scattering rate cimp is compared with EFr . We discuss also the possibility of an enhancement of the nonadiabatic character due to zero point quantum fluctuations.