 00266 J. Kellendonk, T. Richter, H. SchulzBaldes
 Edge current channels and Chern numbers in the integer quantum Hall effect
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Jun 16, 00

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Abstract. A quantization theorem for the edge currents is proven for discrete magnetic halfplane operators. Hence the edge channel number is a valid concept also in presence of a disordered potential. Under a gap condition on the corresponding planar model, this quantum number is shown to be equal to the quantized Hall conductivity as given by the KuboChern formula.For the proof of this equality, we consider an exact sequence of
C$^*$algebras (the Toeplitz extension) linking the halfplane and the planar problem, and use a duality theorem for the pairings of $K$groups with cyclic cohomology.
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