On the rate of Tc suppression by interband impurity scattering in MgB2

We calculate the change in the superconducting transition temperature T-c of MgB2 caused by interband nonmagnetic impurity scattering using the Eliashberg theory for the two-band model of this compound. A much slower rate of T-c suppression is obtained compared to the prediction based on the BCS treatment of the two-band model which ignores renormalization and damping associated with the electron-phonon interaction. Hence, the interband impurity scattering rates deduced from experiments on MgB2 using the formula which results from the BCS approach to the two-band model are underestimated. We generalize the BCS treatment of the two-band model to include renormalization effects of the electron-phonon interaction and find an excellent agreement with the full strong coupling calculation.