Crossing Lattices, Vortex Chains, and Angular Dependence of Melting Line in Layered Superconductors

We investigate vortex structure in very anisotropic layered superconductors at fields tilted with respect to the $c$ axis. We show that even a small in-plane field does not tilt the vortex lattice but, instead, penetrates inside the superconductor in the form of Josephson vortices (JVs). At high $c$-axis magnetic field the phase field of the JV is built up from the phase perturbations created by displacements of pancake vortices. The crossing-lattices ground state leads to linear dependence of the c-axis melting field on the in-plane field, in agreement with recent experimental observations. At small fields stacks of JVs accumulate additional pancake stacks creating vortex rows with enhanced density. This mechanism explains the mixed chains-lattice state observed by decorations.