Scattering in MgB$_{2}$ produced by substitutions and damage

The two-gap nature of superconductivity is a unique feature of MgB$_{2 }$that stimulates many theoretical and experimental investigations. From the beginning it was pointed out that the peculiar role of disorder in a two-gap superconductor In fact, inter-band scattering by non-magnetic impurities is expected to suppresses the critical temperature T$_{c}$ down to 20 K, where an equivalent one-gap BCS system stabilizes. The verification of these predictions has motivated several efforts to introduce defects in MgB$_{2}$ by substitutions (Al in sites of Mg and C in sites of B) and by irradiation. Substitutions modify electronic structure so that superconductivity can be influenced. To overcome this problem we studied two different kind of samples: co-doped Mg$_{1-x}$(AlLi)$_{x}$B$_{2}$ in which the disorder induced by the Mg substitution is accompanied by a rather complete charge compensation, and neutron irradiated Mg$^{11}$B$_{2}$. In both the sample series remarkable changes in the band structure are not expected. The superconducting properties of Mg$_{1-x}$(AlLi)$_{x}$B$_{2 }$are compared with those of Mg$_{1-x}$Al$_{x}$B$_{2}$. All the properties scale systematically as a function of the Al content rather than electron doping. This suggests that the lattice deformations induced by Al, namely point-like defects and lattice compression, are very effective in tuning the superconducting properties. Similar conclusion can be drawn by the study of neutron irradiated samples. By increasing the neutron fluence, T$_{c}$ monotonously decreases down to 9 K, the resistivity raises by two order of magnitude and the cell volume increases (1.7{\%}). Our results demonstrate that the critical temperature is suppressed by the disorder well down the value of 20 K. On the other hand, the two-gap feature evident in the temperature range above 21 K, disappears when T$_{c}$ is lowered down to 11 and 8.7 K a single-gap superconductivity is established.