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.