Localization length at the conductivity minima of the quantum Hall effect

M. M. Fogler; A. Yu Dobin; B. I. Shklovskii

doi:10.1016/s1386-9477(97)00030-1

Localization length at the conductivity minima of the quantum Hall effect

M. M. Fogler
, A. Yu Dobin
, B. I. Shklovskii

Research output: Contribution to journal › Article › peer-review

Abstract

The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length ξ as a function of magnetic field B at such minima for several models of disorder ("white-noise", short-range, and long-range random potentials). We find that ξ ∝ B-α with the exponent α between one and 10/3, depending on the model. In particular, for the "white-noise" random potential ξ roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.

Original language	English (US)
Pages (from-to)	132-134
Number of pages	3
Journal	Physica E: Low-Dimensional Systems and Nanostructures
Volume	1
Issue number	1-4
DOIs	https://doi.org/10.1016/s1386-9477(97)00030-1
State	Published - Jan 19 1997

Bibliographical note

Funding Information:
We are grateful to V.I. Perel for valuable contributions to this work. A. Yu. D. was supported by the Russian Foundation for Basic Research. M. M. F. is a recipient of University of Minnesota’s Doctoral Dissertation Fellowship. M. M. F. and B. I. S. acknowledge support from NSF under Grant DMR-9616880.

Keywords

Localization
Quantum Hall effect
Weak magnetic field

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10.1016/s1386-9477(97)00030-1

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title = "Localization length at the conductivity minima of the quantum Hall effect",

abstract = "The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length ξ as a function of magnetic field B at such minima for several models of disorder ({"}white-noise{"}, short-range, and long-range random potentials). We find that ξ ∝ B-α with the exponent α between one and 10/3, depending on the model. In particular, for the {"}white-noise{"} random potential ξ roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.",

keywords = "Localization, Quantum Hall effect, Weak magnetic field",

author = "Fogler, \{M. M.\} and Dobin, \{A. Yu\} and Shklovskii, \{B. I.\}",

note = "Funding Information: We are grateful to V.I. Perel for valuable contributions to this work. A. Yu. D. was supported by the Russian Foundation for Basic Research. M. M. F. is a recipient of University of Minnesota{\textquoteright}s Doctoral Dissertation Fellowship. M. M. F. and B. I. S. acknowledge support from NSF under Grant DMR-9616880. ",

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doi = "10.1016/s1386-9477(97)00030-1",

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T1 - Localization length at the conductivity minima of the quantum Hall effect

AU - Fogler, M. M.

AU - Dobin, A. Yu

AU - Shklovskii, B. I.

N1 - Funding Information: We are grateful to V.I. Perel for valuable contributions to this work. A. Yu. D. was supported by the Russian Foundation for Basic Research. M. M. F. is a recipient of University of Minnesota’s Doctoral Dissertation Fellowship. M. M. F. and B. I. S. acknowledge support from NSF under Grant DMR-9616880.

PY - 1997/1/19

Y1 - 1997/1/19

N2 - The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length ξ as a function of magnetic field B at such minima for several models of disorder ("white-noise", short-range, and long-range random potentials). We find that ξ ∝ B-α with the exponent α between one and 10/3, depending on the model. In particular, for the "white-noise" random potential ξ roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.

AB - The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length ξ as a function of magnetic field B at such minima for several models of disorder ("white-noise", short-range, and long-range random potentials). We find that ξ ∝ B-α with the exponent α between one and 10/3, depending on the model. In particular, for the "white-noise" random potential ξ roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.

KW - Localization

KW - Quantum Hall effect

KW - Weak magnetic field

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UR - https://www.scopus.com/pages/publications/0031361605#tab=citedBy

U2 - 10.1016/s1386-9477(97)00030-1

DO - 10.1016/s1386-9477(97)00030-1

M3 - Article

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EP - 134

JO - Physica E: Low-Dimensional Systems and Nanostructures

JF - Physica E: Low-Dimensional Systems and Nanostructures

IS - 1-4

ER -

Localization length at the conductivity minima of the quantum Hall effect

Abstract

Bibliographical note

Keywords

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