It had been clear from the very beginning that the properties of this material were related to an anomalous coupling between the charge carriers in the σ bands—due to in-plane bonds between B atoms — and the phonon mode (E2g) which involved in-plane vibrations of the B ions. Theoretical studies had therefore focused upon a search for possible anomalies in the e–ph coupling: One of the first results was the discovery that the E2g phonon was highly anharmonic, but the connection between anharmonicity and TC in this material was then still a controversial point. Here, a detailed first-principles study was made of the E2g phonon anharmonicity in MgB2 and of analogous compounds which were not superconducting: AlB2, graphite and a hypothetical hole-doped graphite (C22+). An analytical model was then introduced which permitted the onset of anharmonicity to be related to the small Fermi energy of the carriers in σ bands. The study suggested a possible relationship between anharmonicity and non-adiabaticity. Non-adiabatic effects, which could lead to a sensible increase of TC with respect to values predicted by conventional theory, become relevant when phonon frequencies were comparable to electronic energy scales.

The Origin of Phonon Anharmonicity in MgB2 and Related Compounds. L.Boeri, G.B.Bachelet, E.Cappelluti, L.Pietronero: Superconductor Science and Technology, 2003, 16, 143-6