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arXiv · cond-mat/9912186

Simultaneous quantization of edge and bulk Hall conductivity

H. Schulz-Baldes·J. Kellendonk·Th. Richter
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Abstract

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

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H. Schulz-Baldes, J. Kellendonk, Th. Richter. 1999-12-10. Simultaneous quantization of edge and bulk Hall conductivity. https://doi.org/10.1088/0305-4470%2F33%2F2%2F102

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