  Based on the experimentally found existence of two gaps in MgB2 (one gap
associated to the boron sigma-states and the other to the boron pi-states), the
different contributions to the transport properties, electrical conductivity
and Hall coefficient, were studied using the full potential-linearized
augmented plane wave method and the generalized gradient approximation. MgB2
doping was analyzed in the rigid band approximation. This permitted the study
of the partial substitution of magnesium for aluminium (Mg1-xAlxB2) as well as
other substitutions such as AB2 (A=Be, Zr, Nb and Ta). The sigma-bands (boron
sigma-states), which are associated to the large superconducting gap, are very
anisotropic at EF, while the pi-bands have very little anisotropic character.
In (Mg1-xAlxB2) Tc diminishes with Al content, the other compounds are not
superconductors. In this work it was found that with electron doping, such as
Al substitution, the sigma-band conductivity decreases and the corresponding
bands become less anisotropic. sigma-band contribution for BeB2 and ScB2 at EF
is very small and the anisotropy is much lower. For Zr, Nb and Ta there are no
sigma-bands at EF. These results give a connection between superconductivity
and the character of the sigma-band; band conductivity and band anisotropy.
This gives a plausible explanation for the diminution of Tc with different
doping of MgB2.
