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

A. Elgart, G. M. Graf, J. H. Schenker

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


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.

Original languageEnglish
Pages (from-to)185-221
Number of pages37
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - 1 Oct 2005
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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