Localization in the quantum Hall regime

Details Localization in the quantum Hall regime Localization in the quantum Hall regime

2003-09-04

arxiv.org/abs/cond-mat/0309115v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

16 pages, to be published in Physica E, Proceedings of the Symposium "Quantum Hall Effect: Past, Present and Future"

Scientific paper

The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced. Descriptions in terms of equivalent tight-binding Hamiltonians, and the 2D Dirac model, are outlined. Evidences for the universal critical behavior of the localization length are summarized. A short review of the supersymmetric critical field theory is provided. The interplay between edge states and bulk localization properties is investigated. For a system with finite width and with short-range randomness, a sudden breakdown of the two-point conductance from $ne^{2}/h$ to 0 ($n$ integer) is predicted if the localization length exceeds the distance between the edges.

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