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We argue, based on band structure calculations and Eliashberg theory, thatthe observed decrease of $T_c$ of Al and C doped MgB$_2$ samples can beunderstood mainly in terms of a band filling effect due to the electron dopingby Al and C. A simple scaling of the electron-phonon coupling constant$\lambda$ by the variation of the density of states as function of electrondoping is sufficient to capture the experimentally observed behavior. Further,we also explain the long standing open question of the experimental observationof a nearly constant $\pi$ gap as function of doping by a compensation of theeffect of band filling and interband scattering. Both effects together generatea nearly constant $\pi$ gap and shift the merging point of both gaps to higherdoping concentrations, resolving the discrepancy between experiment andtheoretical predictions based on interband scattering only.Comment: accepted by PR

physical review letters

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

Band Filling and Interband Scattering Effects inMgB2: Carbon versus Aluminum Doping