Influence of nonmagnetic impurities on superconductivity in two-band systems with variable charge carrier densities

Two-band superconductors with a nonmagnetic impurity are considered in the framework of perturbation theory. Analytical expressions are obtained for the temperature of the superconductivity transition T and the order parameters Δ (n = 1,2) at different values of the charge carrier density (chemical potential μ). An impurity introduced into the system can influence T and Δ in two ways: it can lead to a change in μ and can cause inter-band scattering by the impurity potential. These mechanisms can either cancel each other or destroy the superconductivity. Here a significant role is played by the occupation of the energy bands, by which superconductivity can be completely suppressed by the nonmagnetic impurity.