Model of a polaron superconductor

This paper studies the mechanism of superconductivity in the case where the electrons are strongly coupled to lattice vibrations and, therefore, are in the state of small polarons. The consideration is based on the Holstein model with zero lattice-vibration dispersion and represents a consistent realization of the BCS approach (with no need arising for boson introduction). The ground state and the excitation spectrum are found. The current states are studied and the criterion of their stability is formulated. The superconducting transition temperature is shown to increase without limit with increasing electron-phonon coupling constant. This is accompanied by an exponential decrease in the critical current. Some fundamental properties of high-temperature superconductors are shown to follow directly from this model.