On nonlocal Ginzburg-Landau superconductivity and Abrikosov vortex

Abstract

In this study, the basic concepts of superconductivity based on nonlocal momentum operator have been addressed. The theory is characterized by the presence of higher-order moments and a symmetric kernel which give rise to a higher-derivative superconductivity theory. We have derived the Ginzburg-Landau equations and we have analyzed their properties. The solution has been found to be periodic comparable to the one obtained in chaotic regimes. The magnitude of the coherence length was found to depend on the first moment of order zero. Both decrease of increase in magnitude occurs in semiconductors engineering including hybrid superconductors. It was observed the emergence of bound states in the continuum holding two-degree degenerate energy and the presence of non-periodic vortex arrangement occurring in nano-superconductors. Furthermore, type-III superconductor arises which is characterized by a negative flux, although a weird property, it has been detected thin films superconductor and in type-II superconductors characterize by flux-antiflux interface.