Vortex chain states and phase transitions

In the presence of the Josephson vortex lattice in layered superconductors, a small c-axis magnetic field penetrates in the form of vortex chains. The key parameter which determines the chain structure at fixed magnetic field is the ratio a of the two typical lengths: the London penetration depth and the Josephson length. As this ratio a increases with temperature, the chain structure also varies with temperature. Typically, in BSCCO varies from 0.3 to 0.7 depending on temperature and doping. With increasing the chain structure transforms between the two simple limiting configurations: crossing chain and tilted chain.

Computing the ground state configurations, we found that the chain phase diagram is very rich. In general, the chain structure depends on three parameters: pancake separation along the chain, number of layers between Josephson vortices, N, and ratio a. An important feature of the phase diagram is pancake-density jumps which appear due to the attractive interaction between the deformed pancake stacks located on the Josephson vortices. In the region of intermediate values of a we found two different nontrivial scenarios of chain structure evolutions with increasing c-axis field:

(1st scenario) In the range 0.4 < a < 0.5 and large N small c-axis field first penetrates in the form of pancake-stacks 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 first evolves into modulated tilted vortices, which then transform via a second order phase transition into the tilted straight vortices.

Figure shows the chain phase diagram for the ratio a=0.5. Chain configurations are shown for three values of pancake separation for N=20.

(2nd scenario) In the range 0.5 < a < 0.65 (smaller anisotropies) small c-axis field first penetrates in the form of kinks creating kinked tilted vortices. With increasing c-axis field this structure is replaced via a first-order phase transition by the pancake-stack chain, which are typically strongly deformed. This transition is accompanied by a large jump of pancake density. Further evolution of the chain structure is similar to the higher anisotropy scenario: the structure first transforms into modulated tilted vortices and then, via second order phase transition, into tilted straight vortices.

Figure shows evolution of the chain structure with increase of c-axis field and phase diagram for parameter a = 0.6. First penetration of c-axis field occurs in the form of kinks and kinked tilted chains are formed. With increasing field this state is replaced via a first-order phase transition with strongly-deformed crossing chains. This transition is accompanied by a very large density jump (from upper to lower green line ). At even higher field this structure continuously transforms back into the tilted-chain state at lower red line.

Evolution of chain structure for N=16 is illustrated by animation (avi file, 5.6 MB )