Linewidth of c-axis plasma resonance in Josephson-coupled superconductors

We derive equations which describe the interaction of the phase collective mode with vortex oscillations in multilayer superconductors with Josephson interlayer coupling. Using these dynamic equations for the phase difference between neighboring layers and pancake coordinates we calculate the linewidth of the c-axis plasma resonance in the vortex glass phase when a magnetic field is applied along the c axis. Three mechanisms contribute to the linewidth: interlayer tunneling of quasiparticles, inhomogeneous Josephson interaction in the presence of randomly positioned vortices (inhomogeneous broadening), and dissipation of the plasma mode into vortex oscillations. The phase collective mode is mixed with vortex oscillations in the linear approximation via the Josephson interaction when pancakes are positioned randomly along the c axis due to pinning and thermal fluctuations. Analyzing experimental data for the plasma resonance linewidth in a Bi-2:2:1:2 superconductor we conclude that in magnetic fields below 7 T the linewidth is determined mainly by inhomogeneous broadening. This leads to a nearly temperature-independent linewidth which is inversly proportional to the magnetic field. At higher fields or lower pinning the dissipation of the plasmon into vortex oscillations may become the dominant mechanism of line broadening. In this case the linewidth weakly depends on the magnetic field.