Edge channels and Chern numbers in the integer quantum Hall effect
Kellendonk J, Richter T, Schulz-Baldes H (2002)
Publication Type: Journal article
Publication year: 2002
Journal
Publisher: World Scientific Publishing
Book Volume: 14
Pages Range: 87-119
URI: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=00-266
DOI: 10.1142/S0129055X02001107
Abstract
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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APA:
Kellendonk, J., Richter, T., & Schulz-Baldes, H. (2002). Edge channels and Chern numbers in the integer quantum Hall effect. Reviews in Mathematical Physics, 14, 87-119. https://dx.doi.org/10.1142/S0129055X02001107
MLA:
Kellendonk, Johannes, Thomas Richter, and Hermann Schulz-Baldes. "Edge channels and Chern numbers in the integer quantum Hall effect." Reviews in Mathematical Physics 14 (2002): 87-119.
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