Simultaneous quantization of edge and bulk Hall conductivity

Details Simultaneous quantization of edge and bulk Hall conductivity Simultaneous quantization of edge and bulk Hall conductivity

1999-12-10

arxiv.org/abs/cond-mat/9912186v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages Latex, 1 figure

Scientific paper

10.1088/0305-4470/33/2/102

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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