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 j'(0) across the defect as compared to j(0) 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 H-cl, vortex mass M, viscous drag coefficient mu, and the nonlinear current-voltage characteristic V(j) for a vortex moving along planar defects. It is shown that for identical junctions (j'(0)=j(0)) our approach reproduces results of Clem, Coffey, and Hao [Phys. Rev. B 42, 6209 (1990); 44, 2732 (1991); 44, 6903 (1991)] for mu, M, and H-cl. In the opposite limit j'(0) much less than j(0), 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 much less than T-c) and overdamped T similar or equal to T-c dynamics of interlayer junctions as the temperature T is increased. Implications of the results on the c-axis current transport in high-T-c superconductors are discussed.