Band Filling and Interband Scattering Effects in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow><mml:mi mathvariant="normal">M</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">B</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math>: Carbon versus Aluminum Doping

We argue, based on band structure calculations and the Eliashberg theory, that the observed decrease of T(c) of Al and C doped MgB2 samples can be understood mainly in terms of a band filling effect due to the electron doping by Al and C. A simple scaling of the electron-phonon coupling constant lambda by the variation of the density of states as a function of electron doping is sufficient to capture the experimentally observed behavior. Further, we also explain the long standing open question of the experimental observation of a nearly constant pi gap as a function of doping by a compensation of the effect of band filling and interband scattering. Both effects together generate a nearly constant pi gap and shift the merging point of both gaps to higher doping concentrations, resolving the discrepancy between experiment and theoretical predictions based on interband scattering only.