Teoria de Ginzburg-Landau com parâmetro de ordem escondido aplicada ao estudo da supercondutividade de interface

Abstract

In recent years, several experiments have been reported in which interface superconductivity was observed in heterostructures of different materials, inclunding non-superconductors. The origin of this superconductivity has not yet been elucidated and there is no well-established theory to explain this phenomenon. In 2015 a model based on the Ginzburg-Landau theory was proposed that would explain the interface superconductivity phenomenon assuming a system with two order parameters. It has been proposed that the order parameter characterizing the bulk material with a defective or doped layer permits the formation of a second parameter which competes with the former and prevails over it in the vicinity of the interface. The superconductivity at the interface is then explained by the growth of this second order parameter only in this region, remaining still ``hidden" inside the bulk. The model was applied to a one-dimensional system with an interface, which presented a surprising result: the ``hidden" superconductivity appers in quantized critical temperatures, this allowing the existence of several eigenstates of the system, with different critical temperatures. In this dissertation, we use this model and investigate the unfolding of hidden superconductivity and its quantized temperatures. We observe that the interfaces resemble one-dimensional quantum wells, with the critical temperature playing the role of the energy in the quantum case. Following this idea we use numerical methods to solve the Ginzburg-Landau equations for a system with an arbitrary number of parallel interfaces. Our results show that in this case, the critical temperatures are quantized and degenerate when the interfaces are very separated, but it has its degeneracy broken when we approach the interfaces, as it happens in a lattice of square wells. We then proposed a tight-binding model to estimate critical temperatures on parallel interfaces and verified the validity of this approximation through the numerical solution of the complete problem. We also analyze the vortex states for a square two-dimensional defect, verifying the possibility of creating or destroying vortices in the region of `` hidden" superconductivity through an external magnetic field.