Band filling and disorder effects on the normal state thermoelectric behavior in MgB₂

The goal of this work is providing a comprehensive interpretation framework for the wide and varied experimental phenomenology of the Seebeck effect in MgB₂ samples with different levels of doping in either π or σ bands and different levels of disorder, using a combined experimental and theoretical approach. We calculate the temperature dependent diffusive Seebeck coefficient S _diff(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 S _diff magnitude, as it tunes the relative contributions of σ and π bands. Disorder also affects the S _diff temperature dependences, eventually yielding a linear S _diff(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 the Seebeck effect measurements on neutron-irradiated Mg¹¹B₂, and on two series of doped samples Mg_1-x Al _x B₂ and Mg(B_1-x C _x )₂. From comparison of calculated S _diff(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 σ or π bands, respectively. With the help of our theoretical approach, we are able to disentangle the various effects and prove that the Seebeck coefficient is a very sensitive probe of this kind of disorder.