Microscopic theory of the coupling of intrinsic Josephson oscillations and phonons

A microscopic theory for the coupling of intrinsic Josephson oscillations and dispersive phonon branches in layered superconductors is developed. Thereby the effect of phonons on the electronic c-axis transport enters through 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 junctions. Due to the finite dispersion these resonances can appear at van-Hove-singularities of both optical and acoustical phonon branches, explaining low-voltage structures in the I-V-characteristic, which are not understood in phonon models without dispersion. In long junctions the dispersion of collective electron-phonon modes parallel to the layers is investigated.