Carbon substitutions in MgB2 within the two-band Eliashberg theory

We study the effects of C substitutions in MgB2 within the two-band model in the Eliashberg formulation. We use as input the B-B stretching-mode frequency and the partial densities of states N^(sigma)(E_F) and N^(pi)(E_F), recently calculated for Mg(B_(1−x)C_x)_2 at various x values from first-principles density functional methods. We then take the prefactor in the Coulomb pseudopotential matrix, mu, and the interband scattering parameter, Gamma^(sigma,pi), as the only adjustable parameters. The dependence on the C content of Tc and of the gaps (Delta_sigma and Delta_pi) recently measured in Mg(B_(1−x)C_x)_2 single crystals indicate an almost linear decrease of mu on increasing x, with an increase in interband scattering that makes the gaps merge at x=0.132. In polycrystals, instead, where the gap merging is not observed, the fit of the experimental data is obtained without the presence of interband scattering.