The Topological Structure of the SU(2) Chern-Simons Topological Current in the Four-Dimensional Quantum Hall Effect
ZHANG Xiu-Ming1, DUAN Yi-Shi2
1Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054 2Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000
The Topological Structure of the SU(2) Chern-Simons Topological Current in the Four-Dimensional Quantum Hall Effect
ZHANG Xiu-Ming1, DUAN Yi-Shi2
1Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054 2Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000
In the light of the decomposition of the SU(2) gauge potential for I=1/2, we obtain the SU(2) Chern-Simons current over S4, i.e. the vortex current in the effective field for the four-dimensional quantum Hall effect. Similar to the vortex excitations in the two-dimensional quantum Hall effect (2D FQH) which are generated from the zero points of the complex scalar field, in the 4D FQH, we show that the SU(2) Chern-Simons vortices are generated from the zero points of the two-component wave functions Ψ, and their topological charges are quantized in terms of the Hopf indices and Brouwer degrees of Φ-mapping under the condition that the zero points of field Ψ are regular points.
In the light of the decomposition of the SU(2) gauge potential for I=1/2, we obtain the SU(2) Chern-Simons current over S4, i.e. the vortex current in the effective field for the four-dimensional quantum Hall effect. Similar to the vortex excitations in the two-dimensional quantum Hall effect (2D FQH) which are generated from the zero points of the complex scalar field, in the 4D FQH, we show that the SU(2) Chern-Simons vortices are generated from the zero points of the two-component wave functions Ψ, and their topological charges are quantized in terms of the Hopf indices and Brouwer degrees of Φ-mapping under the condition that the zero points of field Ψ are regular points.
ZHANG Xiu-Ming;DUAN Yi-Shi. The Topological Structure of the SU(2) Chern-Simons Topological Current in the Four-Dimensional Quantum Hall Effect[J]. 中国物理快报, 2010, 27(7): 77301-077301.
ZHANG Xiu-Ming, DUAN Yi-Shi. The Topological Structure of the SU(2) Chern-Simons Topological Current in the Four-Dimensional Quantum Hall Effect. Chin. Phys. Lett., 2010, 27(7): 77301-077301.
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2010, Vol. 27 
