  By a combined experimental and theoretical approach, we investigate normal
state thermoelectric transport in MgB2, as a probe of selective disorder and
doping in the sigma and pi bands. We calculate the temperature dependent
diffusive Seebeck coefficient Sdiff(T) with the Boltzmann equation resolved in
relaxation time approximation, taking into account the scattering with phonons
and impurities, the effect of renormalization and the effect doping in a rigid
band approximation. We show that selective disorder has a sizeable effect on
the Sdiff magnitude, as it tunes the relative contributions of sigma and pi
bands. Disorder also affects the Sdiff temperature dependences, eventually
yielding a linear Sdiff(T) behavior in the dirty limit. We also show that band
filling has opposite effects on S, depending on which band dominates transport.
In parallel, we carry out Seebeck effect measurements on neutron-irradiated
Mg11B2, and on two series of doped samples Mg1-xAlxB2 and Mg(B1-xCx)2. From
comparison of calculated Sdiff(T) and experimental S(T) curves, we demonstrate
that diffusive and phonon drag terms give comparable contributions in clean
samples, but the phonon drag term is progressively suppressed with increasing
disorder. In C and Al doped samples we observe very different experimental
behaviors in terms of sign, magnitude and temperature dependence. Indeed,
notwithstanding the similar electron doping introduced by both substitutions, C
or Al doping yields disorder which mainly affects either sigma or pi bands,
respectively. With the help of our ab-initio approach, we are able to
disentangle the several effects and prove that Seebeck coefficient is a very
sensitive probe of the kind of disorder.
