Band Filling and Interband Scattering Effects in MgB₂: 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 λ 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 π 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 π 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.