A model Hamiltonian for MgB2 which takes into account its unusual phononic features

Taking as a starting point the results of LDA calculations, which show that in MgB2 the phonons have a strong quartic anharmonicity and that the bond-stretching electron-phonon interaction (EPI) has both a linear and a large quadratic component, we propose a model Hamiltonian which succesfully matches a number of experimental evidences. We relate the single critical temperature for both superconducting gaps to a phonon-induced inter-band coupling whose amplitude increases with temperature. We also obtain phonon frequencies and linewidths depending on the band filling, as well as band energies and hybridization amplitudes depending on the phonon number.