Small Fermi energy, strong electron-phonon effects and anharmonicity in MgB2

The investigation of the electron-phonon properties in MgB2 has attracted a huge interest after the discovery of superconductivity with Tc = 39 K in this compound. Although superconductivity is often described in terms of the conventional Eliashberg theory, properly generalized in the multiband/multigap scenario, important features distinguish MgB2 from other conventional strong-coupling superconductors. Most important it is the fact that a large part of the total electron-phonon strength seems to be concentrated here in only one phonon mode, the boron-boron E2g stretching mode. Another interesting property is the small Fermi energy of the σ bands, which are strongly coupled with the E2g mode. In this contribution, we discuss how the coexistence of both these features give rise to an unconventional phenomenology of the electron-phonon properties.