  In present study, we report an inter-comparison of various physical and
electronic properties of MgB2 and AlB2. Interestingly, the sign of S(T) is +ve
for MgB2 the same is -ve for AlB2. This is consistent our band structure plots.
We fitted the experimental specific heat of MgB2 to Debye Einstein model and
estimated the value of Debye temperature (theta) and Sommerfeld constant
(gamma) for electronic specific heat. Further, from gamma the electronic
density of states (DOS) at Fermi level N(EF) is calculated. From the ratio of
experimental N (EF) and the one being calculated from DFT, we obtained value of
Lembda to be 1.84, thus placing MgB2 in the strong coupling BCS category. The
electronic specific heat of MgB2 is also fitted below Tc using pi-model and
found that it is a two gap superconductor. The calculated values of two gaps
are in good agreement with earlier reports. Our results clearly demonstrate
that the superconductivity of MgB2 is due to very large phonon contribution
from its stretched lattice. The same two effects are obviously missing in AlB2
and hence it is not superconducting. DFT calculations demonstrated that for
MgB2 the majority of states come from Sigma and Pi 2p states of boron on the
other hand Sigma band at Fermi level for AlB2 is absent. This leads to a weak
electron phonon coupling and also to hole deficiency as Pi bands are known to
be of electron type and hence obviously the AlB2 is not superconducting. The
DFT calculations are consistent with the measured physical properties of the
studied borides, i.e., MgB2 and AlB2
