Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 475

The Edge current channels and Chern numbers in the integer quantum Hall effect

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

To be published in Comm. Math. Phys. (to appear)

A quantization theorem for the edge currents is proven for discrete magnetic half-plane 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 Kubo-Chern formula. For the proof of this equality, we consider an exact sequence of C^* algebras (the Toeplitz extension) linking the half-plane and the planar problem, and use a duality theorem for the pairings of K-groups with cyclic cohomology.

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