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_N^σ(E_F) and N_N^π(E_F), recently calculated for Mg(B_1−xC_x)₂ at various x values from first-principles density functional methods. We then take the prefactor in the Coulomb pseudopotential matrix, μ, and the interband scattering parameter, Γ^σπ, as the only adjustable parameters. The dependence on the C content of T_c and of the gaps (Δ_σ and Δ_π) recently measured in Mg(B_1−xC_x)₂ single crystals indicate an almost linear decrease of μ 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.