| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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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 |
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ZHANG Xiu-Ming, DUAN Yi-Shi 2010 Chin. Phys. Lett. 27 077301 |
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Abstract 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.
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| Keywords:
73.43.-f
11.15.-q
02.40.Pc
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Received: 21 December 2009
Published: 28 June 2010
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