Between the two big classes of superconductors, the “old” low-Tcs and the “recent” high-Tcs, lies the unexpected magnesium diboride with a transition temperature of 39 K. First sinthesized in 1953, already known as a light and hard compound, its supercoducting properties have not been detected until 2001 by Nagamatzu et al. [Nag01]. Despite its high transition temperature with respect to the BCS– type superconductors, studies on the isotope effect of B in MgB2 have shown that the pairing mechanism is a phonon mediated one [Bud01]...