Dual visão da energia cinética e as equações de Ginzburg Landau

Abstract

In this dissertation we propose a general method to calculate the Gibbs free energy diference between the left vortex and the normal states valid near the superconducting to normal transition, where the order parameter is small. This method is general since it applies to any vortex con guration in any geometry of the cross section area. The method applies to very long superconducting cylinders such that the vortex lines are parallel to each other and oriented along its major axis. As shown here, the order parameter that describes the left vortex state can be obtained from the well-known mathematical problem of conformal mapping. Remarkably the order parameter is just an analytical function with constant modulus at the boundary of a given cross section geometry. In power of the order parameter we obtain the Gibbs energy diference, the local magnetic fi eld and currents inside the superconductor. Besides we also obtain other interesting features, such as the magnetic field at the center of the vortex core, and also the paramagnetic magnetization. It is well-known that at low vortex density the magnetic fi eld inside the vortex core is twice the value of the lowest critical fi eld. For higher densities a vortex lattice sets in and the magnetic fi eld inside the vortex core varies according to the parameter k (the ratio between the penetration and the coherence lenghts) and the vortex density. Here we report the surprising result that as vortices move towards the boundary the magnetic fi eld at their cores, and also the paramagnetic magnetization, change according to their positions. The magnetization vanishes when vortices reach the boundary.