Equality of the bulk and edge Hall conductances in a mobility gap

Details Equality of the bulk and edge Hall conductances in a mobility gap Equality of the bulk and edge Hall conductances in a mobility gap

2004-09-08

arxiv.org/abs/math-ph/0409017v3

Commun. Math. Phys. 259 (2005), p. 185-221

Physics

Mathematical Physics

38 pages, LaTeX, uses svjour class. Corrected a number of typos and an error in proof of Lemma four. The latter correction app

Scientific paper

10.1007/s00220-005-1369-7

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including a contribution from states in the localized band. In a further result on the Harper Hamiltonian, we show that this contribution is essential. In an appendix we establish quantized plateaus for the conductance of systems which need not be translation ergodic.

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