Vortices at planar defects in layered superconductors

We propose a self-consistent nonlocal approach for the description of vortices in layered supeconductors that contain planar defects parallel to the layers. The model takes account of interlayer Josephson coupling and of a reduced maximum Josephson current density (Formula presented)′ across the defect as compared to (Formula presented) for other interlayer junctions. Analytical formulas that describe the structure of both static and moving vortices, including the nonlinear Josephson core region, are obtained. Within the framework of the model, we have calculated the lower critical field (Formula presented), vortex mass M, viscous drag coefficient μ, and the nonlinear current-voltage characteristic V(j) for a vortex moving along planar defects. It is shown that for identical junctions ((Formula presented)′=(Formula presented)) our approach reproduces results of Clem, Coffey, and Hao [Phys. Rev. B 42, 6209 (1990); 44, 2732 (1991); 44, 6903 (1991)] for μ, M, and (Formula presented). In the opposite limit (Formula presented)′≪(Formula presented), our model gives an Abrikosov vortex with anisotropic Josephson core described by a nonlocal Josephson electrodynamics. A sign change in the curvature of V(j) is shown to occur due to a crossover between underdamped (T≪(Formula presented)) and overdamped T≃(Formula presented) dynamics of interlayer junctions as the temperature T is increased. Implications of the results on the c-axis current transport in high-(Formula presented) superconductors are discussed.