In this thesis the microscopic theory of the intrinsic Josephsoneffect in high-temperature superconductors and its interaction with lattice vibrations is investigated.
Special attention is paid to the role of nonequilibrium states, which are connected with an asymmetric occupation of particle- and holelike quasiparticles in the superconductor ("charge imbalance"). A consistent treatment of this degree of freedom is essential for a correct description of a novel capacitive coupling of the dynamics in different junctions due to charge fluctuations between the superconducting -layers. As a first result the collective modes of this electronic model are studied.
An outlook is given to the so-called ``Spin-Josephsoneffect'', where - in analogy to the usual Josephsoneffect - the spin current between the layers is determined by the difference of the phases of interlayer Cooperpairs.
In the second part the interation between Josephsonoscillations and phonons due to the Coulomb interaction is derived microscopically starting from the fundamental hamiltonian of solid state physics. The effect of phonons on the electronic transport perpendicular to the superconduncting layers can be fully taken into account by introducing an effective dielectric constant of the phonons.
The coupled system of nonlinear differential equations for the dynamics of the phases in different junctions is solved analytically with the help of a Greensfunction method. An important result is the fact that resonances in the current-voltage-characteristic appear exactly at the longitudinal optical eigenfrequencies of the lattice system.
This explains well all experimental features of recently discovered ``subgap structures'' in the -axis transport and thereby provides a new measurement technique for optical phonon frequencies in these materials. The detected microwave emission and absorption in the GHz region is reproduced in detail.
The renormalization of the phonon- and the plasmafrequencies by the electron-phonon-interaction is discussed and the enhancement of the nonlinear mixing amplitudes and microwave absorption and emission near the eigenfrequencies of the system (in the THz region) is shown.