The recent discovery of a superconducting transition at 39 K in MgB_2 has  arisen great interest, for both its technological and theoretical implications. Theoretical studies have thus been focused on the search for eventual anomalies in the e-ph coupling: one of the first results was the discovery that the E_2g phonon, which is mainly responsible for superconductivity,  is
highly anharmonic [1], but the connection between anharmonicity and T_c in this material is
still a controversial point. Furthermore, two fundamental questions are still open: is MgB_2 unique?  Why wasn't it discovered earlier? In this work we wish to address both questions, showing that MgB_2 presents strong similarities with other exotic superconductors, appearing in the Uemura plot.
We first present a detailed first-principles study of the E_2g phonon anharmonicity in MgB_2 and analogous compouds which are not superconducting, AlB_2 and graphite, and in a hypotetical hole-doped graphite  (C_2^{++}); we then introduce an analytical model which allows us to relate the onset of anharmonicity with the small Fermi energy of the carriers in  sigma bands [2]. We also show that other exotic superconductors show similar behaviour.
Our study suggests a possible relation between anharmonicity and non adiabaticity: non adiabatic effects, which can lead to a sensible increase of T_c with respect to values predicted by conventional theory become in fact relevant when phonon frequencies are comparable to electronic energy scales [2]. In this framework we suggest that in the search for higher critical
temperatures in e-ph systems simply increasing the DOS at the Fermi level would not be enough: details of the e-ph interaction are crucial.

References
[1.] T. Yildirim et al., Phys. Rev. Lett.  87, 037001 (2001)
[2.] L. Boeri, G.B.Bachelet, E.Cappelluti, L.Pietronero Phys. Rev. B 65, 214501 (2002)
[3.] L. Pietronero  et al.  Phys. Rev. B 52, 10516 (1995)