Annular Vortex Solutions to the Landau-Ginzburg Equations in Mesoscopic Superconductors

The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of a step-like external magnetic field with zero average which could model the field resulting from a ferromagnetic disk or a current carrying loop. The regions of existence of the multi-vortex state and the giant vortex state are found. We analyzed the phase transitions between them and found regions in which ring-shaped vortices contribute. Further...

In this work we solved the time-dependent Ginzburg-Landau equations, TDGL, to simulate two superconducting systems with different lateral sizes and with an antidot inserted in the center. Then, by cycling the external magnetic field, the creation and annihilation dynamics of a vortex-antivortex pair was studied as well as the range of temperatures for which such processes could occur. We verified that in the annihilation process both vortex and antivortex acquire an elongated...

The nonlinear Ginzburg-Landau equations are solved numerically in order to investigate the vortex structure in thin superconducting disks of arbitrary shape. Depending on the size of the system and the strength of the applied magnetic field giant vortex, multi-vortex and a combination of both of them are found. The saddle points in the energy landscape are identified from which we obtain the energy barriers for flux penetration and expulsion.

The transitions between the different vortex states of thin mesoscopic superconducting disks and rings are studied using the non-linear Ginzburg-Landau functional. They are saddle points of the free energy representing the energy barrier which has to be overcome for transition between the different vortex states. In small superconducting disks and rings the saddle point state between two giant vortex states, and in larger systems the saddle point state between a multivortex s...

The quantization of magnetic flux in superconductors is usually seen as vortices penetrating the sample. While vortices are unstable in bulk type I superconductors, restricting the superconductor causes a variety of vortex structures to appear. We present a systematic study of giant vortex states in type I superconductors obtained by numerically solving the Ginzburg-Landau equations. The size of the vortices is seen to increase with decreasing film thickness. In type I superc...

Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as funct...

In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau (TDGL) equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the magnetization, and the number of vortices. This algorithm is applied to a circular sector. We evaluate the superconduting-normal magnetic field transition, the magnetization, and the superconducting density. Furthermore, we study the nucleatio...

Self-consistent solutions of the Ginzburg-Landau system of equations, which describe the order parameter and the magnetic field distribution in a long superconducting cylinder of finite radius R, in external magnetic field H, when vortex line, carrying m flux quanta, is situated on the cylinder axis (a giant m-vortex state), are studied numerically. If the field H exceeds some critical value H_s, the giant m-vortex solution becomes unstable and passes to a new stable edge-sup...

Inspired by the seminal, ground-breaking work of Abrikosov in 1957, we developed a new approximation to the interaction between two widely separated superconducting vortices. In contrast with Abrikosov's, we take into account the finite size of the vortices and their internal magnetic profile. We consider the vortices to be embedded within a superconducting, infinitely long hollow cylinder, in order to simplify the symmetry and boundary conditions for the mathematical analysi...

In 1988, Nelson proposed that neighboring vortex lines in high-temperature superconductors may become entangled with each other. In this article we construct solutions to the Ginzburg--Landau equations which indeed have this property, as they exhibit entangled vortex lines of arbitrary topological complexity.