Nonadiabatic effects and the role of small Fermi energy in MgB2

There is nowadays a general agreement on a key role of the ? bands in the superconducting properties of MgB2. We show that peculiar characteristics of the ? bands give rise to nonadiabatic and anharmonic effects which break the conventional Migdal-Eliashberg framework. Both these features are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the ? bands. In this context we discuss how the nonadiabatic theory leads to a coherent interpretation of the superconducting properties of MgB2 without invoking very large couplings and it naturally explains the role of the disorder on Tc. It also leads to various specific predictions for the properties of MgB2 and for the material optimization of these type of compounds. Anharmonicity is also investigated by means of LDA calculations. We find that the anharmonic character of the E2g phonon is essentially driven by the small Fermi energy of the ? holes. We present a simple analytic model which allows us to understand in microscopic terms the role of the small Fermi energy and of the electronic structure. The relation between anharmonicity and nonadiabaticity is pointed out and discussed in relation to various materials.