Dynamics of fractional vortices in two-band superconductors

The entry of fractional vortices and their subsequent dynamics inside a two-band superconductor is explored based on the numerical solutions of time-dependent Ginzburg–Landau (TDGL) equations. We consider the case when superfluid electron condensates from two zones are characterized by quite different parameters, such as coherence lengths ξi, and London penetration depths λi, which in turn leads to the different critical magnetic fields Hc,iand fractional flux quanta ϕivalues for the superconducting state in these two zones. Numerical solutions of TDGL equations in increasing external magnetic field followed by mathematical modeling of magnetic flux penetration were performed for this case by finite element method. We have explored the time evolution for the fractional vortices penetration process and their subsequent dynamics inside the specimens for two geometries: the circular disk, and the circular disk with a triangular cutout. Obtained results indicate that magnetic flux penetrates inside the specimen in the form of fractional vortices when they can overcome the edge barrier, which may be different for these two vortex types. Therefore, in increasing external magnetic field first penetrate vortices with a lower barrier height (i.e., lower Hc,i) while the other type of fractional vortices start their penetration at higher external field value. Another mechanism for the formation of fractional vortices during their entrance in a two-band superconductor is related to the difference in their flux values and viscosity coefficients which determine the rate of vortex proliferation inside the sample. Within the specimen, fractional vortices move in order to arrange. Vortices of different types attract to each other and try to stick together thus forming composite vortices with the whole flux quantum value ϕ0 = h/2e.