First principles study of Al and C-doped MgB2: evolution of two gaps and critical temperature

We have studied the electron-phonon and superconducting properties of the Mg1-xAlxB2 and MgB2(1-x)C2x alloys within the framework of density functional perturbation theory, using a mixed-basis pseudopotential method and the virtual crystal approximation (VCA) for modeling the alloys. For both systems, the Eliashberg spectral function (α2F(ω)) and the electron-phonon coupling parameter (λ) have been calculated in the two band model (σ,π) for several concentrations until x(Al)=0.55 and x(C)=0.175. Using the calculated α2ijF(ω) and a diagonal expression for the Coulomb pseudopotential matrix, μ*, we solved numerically the Eliashberg gap equations in the two band model without interband scattering. We reproduce the experimental decreasing behavior of Δσ(x), Δπ(x), and Tc(x) for both alloy systems. The role of the interband scattering in the observed behavior of the superconducting gaps and Tc in the Al- and C-MgB2 alloys is discussed.