Self-Dual Vortices in the Fractional Quantum Hall System

Abstract

Based on the $\varphi$-mapping theory, we obtain an exact Bogomol'nyi self-dual equation with a topological term, which is ignored in traditional self-dual equation, in the fractional quantum Hall system. It is revealed that there exist self-dual vortices in the system. We investigate the inner topological structure of the self-dual vortices and show that the topological charges of the vortices are quantized by Hopf indices and Brouwer degrees. Furthermore, we study the branch processes in detail. The vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the vector field $\vec{\varphi }$.

13 pages 10 figures. accepted by IJMPB

References in corpus (7)

• Quantum Spin Hall Effect
• Universal Intrinsic Spin-Hall Effect
• Dissipationless Quantum Spin Current at Room Temperature
• Fractional Quantum Hall Effect of Composite Fermions
• Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
• Magnetic monopoles in a charged two-condensate Bose-Einstein system
• Vortices in the Landau--Ginzburg Model of the Quantized Hall Effect