Microscopic theory of the coupling of intrinsic Josephson oscillations andphonons

A microscopic theory for the coupling: of intrinsic Josephson oscillations and dispersive phonon branches in layered superconductors is developed. The reby the effect of phonons on the electronic c-axis transport enters throug h an effective longitudinal dielectric function. This coupling: provides an explanation of recently observed subgap resonances in the I-dc-V-dc-curve of anisotropic cuprate superconductors forming a stack of short Josephson j unctions. Due to the finite dispersion these resonances can appear at van-H ove-singularities of both optical and acoustical phonon branches, explainin g low-voltage structures in the I-V-characteristic, which are not understoo d in phonon models without dispersion. In long junctions the dispersion of collective eletron-phonon modes parallel to the layers is investigated.