Localization in the quantum Hall regime
Abstract
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 to 0 ( integer) is predicted if the localization length exceeds the distance between the edges.
Cite
@article{arxiv.cond-mat/0309115,
title = {Localization in the quantum Hall regime},
author = {Bernhard Kramer and Stefan Kettemann and Tomi Ohtsuki},
journal= {arXiv preprint arXiv:cond-mat/0309115},
year = {2015}
}
Comments
16 pages, to be published in Physica E, Proceedings of the Symposium "Quantum Hall Effect: Past, Present and Future"