TY - JOUR
T1 - Localization length at the resistivity minima of the quantum Hall effect
AU - Fogler, M. M.
AU - Dobin, A. Yu
AU - Shklovskii, B. I.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1998
Y1 - 1998
N2 - The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length (Formula presented) of such states at even filling factors (Formula presented). The calculation is done for several models of disorder (“white-noise,” short-range, and long-range random potentials). We find that the localization length has a power-law dependence on the Landau level index, (Formula presented) with the exponent (Formula presented) between one and (Formula presented), depending on the model. In particular, for a “white-noise” random potential (Formula presented) roughly coincides with the classical cyclotron radius. Our results are in reasonable agreement with experimental data on low and moderate mobility samples.
AB - The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length (Formula presented) of such states at even filling factors (Formula presented). The calculation is done for several models of disorder (“white-noise,” short-range, and long-range random potentials). We find that the localization length has a power-law dependence on the Landau level index, (Formula presented) with the exponent (Formula presented) between one and (Formula presented), depending on the model. In particular, for a “white-noise” random potential (Formula presented) roughly coincides with the classical cyclotron radius. Our results are in reasonable agreement with experimental data on low and moderate mobility samples.
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U2 - 10.1103/PhysRevB.57.4614
DO - 10.1103/PhysRevB.57.4614
M3 - Article
AN - SCOPUS:0542371843
VL - 57
SP - 4614
EP - 4627
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
SN - 1098-0121
IS - 8
ER -