Tilted and crossing vortex chains in layered superconductors

Abstract

In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [λ] and Josephson [λ J ] lengths, α=λ/λ J . The chain is composed of tilted vortices at large α's (tilted chain) and at small α's it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate α's and found two types of phase transitions. For α≲0.6 the groud state is given by the crossing chain in a wide range of pancake separationsa≳[2−3]λ J . However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and α. The first phase transition takes place with decreasing pancake-stack separation a ata≳[1−2]λ J , and rather wide range of the ratio α, 0.4≲α≲0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices,a ~ [20−30]λ J , and only when α exceeds a certain critical value ∼0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.