Abstract:
The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of K-theory. We propose an alternative proof based on a generalization of the index of a pair of projections to more general operators. The equality of conductances is an expression of the stability of that index as a flux tube is moved from within the bulk across the boundary of a sample.
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Received: 11 March 2002 / Accepted: 1 April 2002 Published online: 12 August 2002
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Elbau, P., Graf, G. Equality of Bulk and Edge Hall Conductance Revisited. Commun. Math. Phys. 229, 415–432 (2002). https://doi.org/10.1007/s00220-002-0698-z
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DOI: https://doi.org/10.1007/s00220-002-0698-z