Equality of bulk and edge Hall conductance revisited

Details Equality of bulk and edge Hall conductance revisited Equality of bulk and edge Hall conductance revisited

2002-03-11

arxiv.org/abs/math-ph/0203019v1

Physics

Mathematical Physics

LaTeX with 1 .pstex/.pstex_t figure

Scientific paper

10.1007/s00220-002-0698-z

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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