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

A microscopic theory for the coupling of intrinsic Josephson oscillations in layered superconductors with longitudinal c-axis phonons is developed, it is shown that the influence of lattice vibrations on the c-axis transport can be fully described by introducing an effective longitudinal dielectric function epsilon(ph)(L)(w). Resonances in the I-V characteristic appear at van Hove singularities of both acoustical and optical longitudinal phonon branches. This provides a natural explanation of the recently discovered subgap structures in the I-V characteristic of highly anisotropic cuprate superconductors. The effect of the phonon dispersion on the damping of these resonances and the coupling of Josephson oscillations in different resistive junctions due to phonons are discussed in detail.