A numerical study of steady-state vortex configurations and vortex pinning in type-II superconductors



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Texas A&M University


In part I, a numerical study of the mixed states in a mesoscopic type-II superconducting cylinder is described. Steady-state configurations and transient behavior of the magnetic vortices for various values of the applied magnetic field H are presented. Transitions between different multi-vortex states as H is changed is demonstrated by abrupt changes in vortex configurations and jumps in the B vs H plot. An efficient scheme to determine the equilibrium vortex configuration in a mesoscopic system at any given applied field, not limited to the symmetry of the system, is devised and demonstrated. In part II, a superconducting thin film is subject to a non-uniform magnetic field from a vertical magnetic dipole, consisting of two magnetic monopoles of opposite charges. For a film with constant thickness and with no pins, it has been found that the film carries two pairs of vortex-antivortex in the steady state in the imposed flux range of 2.15 < (Phi)+ < 2.90 (in units of flux quantum) and no vortex at all for (Phi)+ <= 2.15. Transitions from a superconducting state with 3 pairs of vortex-antivortex to one with 2 pairs, where a pair of vortex-antivortex annihilates, have been observed in the pseudo-time sequence. With a perturbation with antidots (holes), vortexantivortex pair has been created for lower magnetic fluxes down to (Phi)+ = 1.3. In the sample of size 16(Xi) x 16(Xi), the attraction force between the vortex and antivortex always dominates over the pinning force, so that they eventually come out of pins, move toward each other, and annihilate each other. The annihilation rate, measured with time taken for the annihilation, is reduced noticeably by the increase of the distance between pins, or the increase in the pin size. A simulation of the magnetic vortex pinning in the sample of size 32(Xi) x 32(Xi) suggests we are likely to achieve pinning of the vortex-antivortex pair with the sample size around this and vortex-antivortex separation of 22(Xi). Using this sample as a template, the maximum density of pinned vortices achievable is calculates to be about 7.6 x 10^14 vortices/m2 for (Xi) =~ 1.6A?.