Mixed state in a superlattice

Presented in this paper is a theoretical calculation of the vortex solution in a chosen superlattice (Nb/NbZr) using the Gibbs free energy of an inhomogeneous superconductor. The eigenvalue obtained in this geometry from de Gennes-Werthamer proximity coupling theory is first examined according to a set of experimental data, while the correspondent eigenfunctions are then used to construct vortex solutions with either square lattice or triangle lattice symmetry. The Gibbs free energy is calculated in terms of the vortex solutions of both symmetries. The effective Ginzburg-Landau parameter,K_NS, for this superlattice is determined asK_NS=0.218 by requiring a consistency between the microscopic and macroscopic theoretical calculations. Of particular importance is a new mechanism revealed by this calculation that a highly localized state of superconducting condensate in its hosting layer, despite the spatially rapid varying characteristic of its correspondent nucleating order parameter, provides a lower eigenvalue state, which results in a dimensional crossover. A further examination of this mechanism is carried out in the mixed state calculation. Finally, a generalization of the present theoretical results to a large class of superlatices is discussed.