Collective Josephson Vortex Dynamics in Long Josephson Junction Stacks

We investigate the collective phase dynamics in conventional long Josephson junction (LJJ) stacks and in layered superconductors, exhibiting intrinsic LJJ behaviors. Using a theoretical model which accounts for both the magnetic induction effect and the breakdown of local charge neutrality (i.e., charging effect), we show that the collective motion of Josephson vortices, including the dispersion of Josephson plasma mode and the Swihart-type velocity, in an intrinsic LJJ stack such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$ (BSCCO) is significantly modified from those in a conventional LJJ stack. In BSCCO, the strength of the charging effect $\alpha$ is small (i.e., $\alpha \sim 0.1-0.4$), but it leads to notable changes in collective phase dynamics, including changes to the stability condition. Also, we show that splitting of the supercurrent branch in the resistive state is due to collective motion of Josephson vortices. The width of spread of these sub-branches in the linear current-voltage regime depends on $\alpha$, suggesting another way to measure the charging effect in BSCCO.