Two-band Eliashberg equations and the experimental Tc of the diboride Mg1-xAlxB2

The variation of the superconducting critical temperature Tc as a function of x in the diboride Mg1-xAlxB2 has been studied in the framework of the two-bands Eliashberg theory and traditional phonon coupling mechanism. We have solved the two-bands Eliashberg equations using first-principle calculations or simple assumptions for the variation of the relevant physical quantities. We have found that the experimental Tc curve can be explained only if the Coulomb pseudopotential changes with x by tuning the Fermi level toward the sigma band edge. In polycrystal samples the x dependence of the sigma and pi-band gap has been found and is in agreement with experiments.