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In this publication a microscopic theory for the coupling of intrinsicJosephson oscillations in layered superconductors with longitudinalc-axis-phonons is developed. It is shown that the influence of latticevibrations on the c-axis transport can be fully described by introducing aneffective longitudinal dielectric function. Resonances in theI-V-characteristic appear at van Hove singularities of both acoustical andoptical longitudinal phonon branches. This provides a natural explanation ofthe recently discovered subgap structures in the I-V-characteristic of highlyanisotropic cuprate superconductors. The effect of the phonon dispersion on thedamping of these resonances and the coupling of Josephson oscillations indifferent resistive junctions due to phonons are discussed in detail.Comment: submitted to Phys. Rev. B, corrections following referee repor

Theory for the coupling between longitudinal phonons and intrinsic Josephson oscillations in layered superconductors