Collective oscillations in doped two–band superconductors

A study is made of the effect of a nonmagnetic impurity on the collective oscillations in two-band superconductors due to fluctuations in the phases of the order parameters of the different bands. A system of equations for the vertex functions that is valid for any carrier concentration is obtained. On the basis of this system, an equation is obtained for the frequency of collective excotations of a two-band supercodductor for phonon and nonphonon mechanisms of superconductivity. It is shown that at a low impurity concentration in two–band system two frequencies of exciton type determined by the presence of interband interaction and the impurity arise.