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A new two-band polaronic Hamiltonian is derived from a generalized periodic Anderson model. The generalization consists in the completion of the periodic Anderson model with intra- and inter-band local phonon-electron interactions. The derivation is achieved by making use of two canonical transformations which enable us to remove these phonon-electron potentials from the initial Hamiltonian. This decoupling procedure leads to the appearance of new terms such as a pair-exchange potential, anisotropic Kondo-lattice terms, and a density-dependent hybridization. The final Hamiltonian describes a complicated interplay between different tendencies in the investigated system. Superconductivity can compete with the Kondo effect or magnetism as well. A simplified scenario in which the effect of the single-particle hybridization on superconductivity is investigated. It is shown that this factor is very efficient as a pair-breaker.

The Intra- and Interband Phonon-Electron Potentials in a Two-Band Model of Interacting Lattice Fermions