## Ginzburg-Landau simulations of narrow superconducting strips

##### Abstract

In this thesis I will present the results of a detailed study of vortex configurations in narrow superconducting strips. The underlying model we used to analyze these configurations is the Ginzburg-Landau theory for superconductivity. Advanced numerical schemes on massively parallel systems allowed us to solve the time-dependent Ginzburg-Landau equations in a reasonable amount of time, thus making this study possible. The research presented here was performed on the high performance GPU cluster Gaea at NIU's Computer Science Department.;Our motivation for studying vortex configurations in narrow superconducting strips comes from recent experimental work, where interesting phenomenon, like the re-entrance of the superconducting state in increasing magnetic fields, were observed. In order to understand the experimental results it is fundamentally important to study the equilibrium vortex configurations in long, narrow, two-dimensional superconducting strips, whose widths are close to the zero-temperature superconducting coherence length of the system. During our examination of these systems we found that the vortex patterns which form depend on temperature, external magnetic field, and strip width. Strips ranging from two zero-temperature coherence lengths to twenty zero-temperature coherence lengths in width were the main focus of our analysis.;The computational resources required to study these systems are significant because the system has to equilibrate for each value of the external parameters and also for each strip width in order to reach an equilibrium steady state. Each system is discretized with over half a million grid points on which the time-dempendent Ginzburg-Landau equation is solved.;The main results of our work are the state diagrams for the vortex configurations of a given strip, which are affected by the surface barriers which form on either side of the strip. Two examples of the effect that the surface barrier can have on the system are the steps which can form in the magnetization curve when the vortices are prevented from entering or leaving the system by the surface barrier, and the superconducting edge states which exist up to the third critical field. Furthermore, we found that the minimal width at which vortices can enter the system depends inversely on the square root of 1- T/Tc where Tc is the critical temperature of the system. For the lowest temperature studied here, T = Tc/2, the minimal width is about 2.5 zero-temperature coherence lengths which increases up to 6.5 zero-temperature coherence lengths for T = 0.9Tc. Both values are still larger than the temperature dependent coherence lengths. For narrow strip widths we also found that vortices still exist in the central region of the strip even above the bulk critical magnetic field as surface states which are close enough to each other to allow a finite order parameter and vortices in the center of the strip.;As an addendum, I present our experimental results on resistivity measurements in (quasi) one-dimensional superconducting networks. In (quasi) one-dimensional superconducting nanowires vortices do not exist anymore, as their cross-section dimensions are below the coherence length. The dissipation mechanism is replaced by so-called phase-slip processes, which occur when flux quanta cross the wires. We show that the resulting resistivity measurements are in agreement with theoretical predictions.