Self-dual Vortices in Schrdinger-Chern-Simons Model

By making use of the U(1) gauge potential decomposition theory and the φ-mapping topological currenttheory,we investigate the Schrdinger-Chern-Simons model in the thin-film superconductor system and obtain anexact Bogomolny self-dual equation with a topological term.It is revealed that there exist self-dual vortices in thesystem.We study the inner topological structure of the self-dual vortices and show that their topological charges aretopologically quantized and labeled by Hopf indices and Brouwer degrees.Furthermore,the vortices are found generatingor annihilating at the limit points and encountering,splitting or merging at the bifurcation points of the vector field φ.