High-temperature superconductivity in two-band materials with interband pairing

Eliashberg theory is generalized with account of the specific properties of two-band electron-phonon (EP) systems. The superconducting transition temperature T _c is examined in two-band materials, one of the representatives of which are pnictides. The strong EP coupling and the pairing within the full width of the electron band and not only in a narrow region near the Fermi surface are taken into account. It is found that the effect of the pairing of electrons belonging to different bands is crucial to the appearance of high T _c in these materials. It is shown that the high T _c value in the materials, such as pnictides, is displayed with the use of a two-band spectral function of the EP interaction derived from calculations and from tunnel experiments. The existence of specific conditions for the high T _c appearance in the two-band materials is established.