$MgB_2$: doped or with pressure, four systems same behaviour

$MgB_2$, the intermediate $T_c$ superconductor, can be doped with carbon, aluminium and scandium and it has been also studied experimentally under pressure, in these four cases $T_c$ diminishes. In previous studies we have shown, with electronic structure calculations, that when $Mg$ is substituted with $Sc$ [$(Mg,Sc)B_2$] the drop of $T_c$ can be associated with the loss of electrical anisotropy of the $\sigma$-bands [1]. When $Mg$ is substituted with $Al$ $[(Mg,Al)B_2]$ or $B$ is substituted with $C$ [$Mg(B,C)_2$] then, with a change of doping scale, a common $T_c$ curve is obtained for both systems, comparison with the $\sigma$-$DOS$ shows that $T_c$ drop is due to $\sigma$-band-filling and to $\sigma$-band anisotropy loss [2]. In further studies we have found that both these features, $\sigma$-band anisotropy reduction and the loss of $\sigma$-band-carriers, can be associated to the drop of $T_c$ in these three doped systems [$Mg(B,C)_2$, $Mg,Al)B_2$ and $(Mg,Sc)B_2$] and in $MgB_2$ under pressure. All these studies show that: (a) with a change of doping scale then $T_c$ in both the C and Al doped systems follows the same curve which is very close to the $\sigma$-DOS; (b) for the four systems both the $\sigma$-band anisotropy and the number of $\sigma$-carriers are two fundamental physical properties of the relatively high $T_c$ in $MgB_2$. [1] J. Phys.: Condens. Matter 18 (2006) 1403-1412 [2] cond-mat/0606019