Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 412

Simultaneous quantization of edge and bulk Hall conductivity

H. Schulz-Baldes, J. Kellendonk and Th. Richter

The edge Hall conductivity is shown to be an integer multiple of $e^2/h$ which is almost surely independent of the choiceof the disordered configuration. Its equality to the bulk Hallconductivity given by the Kubo-Chern formula follows from K-theoreticarguments. This leads to quantization of the Hall conductance for anyredistribution of the current in the sample. It is argued that inexperiments at most a few percent of the total current can be carriedby edge states.

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