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Topological Aspects of Superconductors at Dual Point

We study the properties of the Ginzburg–Landau model at the dual point for the superconductors. By making use of the U(1) gauge potential decomposition and the ϕ-mapping theory, we investigate the topological inner structure of the Bogomol'nyi equations and deduce a modified decoupled Bogomol'nyi equation with a nontrivial topological term, which is ignored in conventional model. We find that the nontrivial topological term is closely related to the N-vortex, which arises from the zero points of the complex scalar field. Furthermore, we establish a relationship between Ginzburg–Landau free energy and the winding number.