Vortex-chain phases in layered superconductors
  Layered superconductors in tilted magnetic field have a very rich spectrum of vortex lattice configurations. In the presence of in-plane magnetic field, a small c-axis field penetrates in the form of isolated vortex chains. The structure of a single chain is mainly determined by the ratio of the London [$\lambda$] and Josephson [$\lambda_{J}$] lengths, $\alpha= \lambda/\lambda_{J}$. At large $\alpha$ the chain is composed of tilted vortices [tilted chains] and at small $\alpha$ it consists of a crossing array of Josephson vortices and pancake stacks [crossing chains]. We studied the chain structures at intermediate $\alpha$'s and found two types of behavior. (I) In the range $0.4 < \alpha < 0.5$ a c-axis field first penetrates in the form of pancake-stack chains located on Josephson vortices. Due to attractive coupling between deformed stacks, their density jumps from zero to a finite value. With further increase of the c-axis field the chain structure smoothly evolves into modulated tilted vortices and then transforms via a second-order phase transition, into the tilted straight vortices. (II) In the range $0.5 < \alpha < 0.65$ a c-axis field first penetrates in the form of kinks creating kinked tilted vortices. With increasing the c-axis field this structure is replaced via a first-order phase transition by the strongly deformed crossing chain. This transition is accompanied by a large jump of pancake density. Further evolution of the chain structure is similar to the higher anisotropy scenario: it smoothly transforms back into the tilted straight vortices. 
A. E. Koshelev