Vortex Structure in a Superconductor under a Rotating Field: Entanglement and Recombination

In a type-II superconductor under a uniform magnetic field H(H_c1<H<H_c2), quantized magnetic fluxes or vortices enter the superconductor. They are parallel to the external field. Then, what happens if the magnetic field is slightly rotated? In order to answer this question, we have solved the Ginzburg-Landau equations for cuboids under rotated magnetic fields. We have found that for low field, a vortex appears at the center of the superconductor and it is parallel to the magnetic field at that point. For stronger field, when four vortices enter the superconductor, at both sides, two pairs of vortices interact and recombination occurs. As a result, two center vortices form a braid as if they are entangled.
We will discuss interaction between two tilted vortices under the rotated magnetic field.