The noncommutative geometry of the quantum Hall effect
- 1 October 1994
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 35 (10) , 5373-5451
- https://doi.org/10.1063/1.530758
Abstract
An overview of the integer quantum Hall effect is given. A mathematical framework using nonommutative geometry as defined by Connes is prepared. Within this framework, it is proved that the Hall conductivity is quantized and that plateaux occur when the Fermi energy varies in a region of localized states.Keywords
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