Direct measurement of critical exponents in the quantum Hall regime

Stephan W Koch, R. J. Haug, K. von Klitzing, K. Ploog

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We have studied the magnetoresistance of AlGaAs/GaAs-heterojunctions at millikelvin temperatures in small Hall bar and Corbino geometries with different sizes. Below a characteristic temperature Tc which increases with decreasing sample width, the phase-breaking length Lin is larger than the sample size. Under these conditions the half width ΔB of the longitudinal magnetoresistance no longer depends upon temperature but only upon size. By varying the size it is thus possible to directly investigate the localization transition in the integer quantum Hall regime and to measure the critical exponent v of the localization length ξ α |B - Bc|-v. Our results show a universal behaviour in the three lowest Landau levels. This is in agreement w universality statement of the field-theoretic approach to the metal-insulator transition in the quantum Hall effect. By studying the characteristic temperature Tc for different widths, the temperature exponent p 2 of the inelastic scattering length can also be measured.

Original languageEnglish (US)
Pages (from-to)108-111
Number of pages4
JournalSurface Science
Volume263
Issue number1-3
DOIs
StatePublished - Feb 19 1992
Externally publishedYes

Fingerprint

exponents
Magnetoresistance
Temperature
temperature
Quantum Hall effect
Inelastic scattering
Metal insulator transition
quantum Hall effect
integers
aluminum gallium arsenides
Heterojunctions
heterojunctions
inelastic scattering
insulators
Geometry
geometry
metals

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Condensed Matter Physics
  • Surfaces and Interfaces

Cite this

Direct measurement of critical exponents in the quantum Hall regime. / Koch, Stephan W; Haug, R. J.; von Klitzing, K.; Ploog, K.

In: Surface Science, Vol. 263, No. 1-3, 19.02.1992, p. 108-111.

Research output: Contribution to journalArticle

Koch, Stephan W ; Haug, R. J. ; von Klitzing, K. ; Ploog, K. / Direct measurement of critical exponents in the quantum Hall regime. In: Surface Science. 1992 ; Vol. 263, No. 1-3. pp. 108-111.
@article{c108ba359a944c568846bb130226ac6e,
title = "Direct measurement of critical exponents in the quantum Hall regime",
abstract = "We have studied the magnetoresistance of AlGaAs/GaAs-heterojunctions at millikelvin temperatures in small Hall bar and Corbino geometries with different sizes. Below a characteristic temperature Tc which increases with decreasing sample width, the phase-breaking length Lin is larger than the sample size. Under these conditions the half width ΔB of the longitudinal magnetoresistance no longer depends upon temperature but only upon size. By varying the size it is thus possible to directly investigate the localization transition in the integer quantum Hall regime and to measure the critical exponent v of the localization length ξ α |B - Bc|-v. Our results show a universal behaviour in the three lowest Landau levels. This is in agreement w universality statement of the field-theoretic approach to the metal-insulator transition in the quantum Hall effect. By studying the characteristic temperature Tc for different widths, the temperature exponent p 2 of the inelastic scattering length can also be measured.",
author = "Koch, {Stephan W} and Haug, {R. J.} and {von Klitzing}, K. and K. Ploog",
year = "1992",
month = "2",
day = "19",
doi = "10.1016/0039-6028(92)90316-X",
language = "English (US)",
volume = "263",
pages = "108--111",
journal = "Surface Science",
issn = "0039-6028",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - Direct measurement of critical exponents in the quantum Hall regime

AU - Koch, Stephan W

AU - Haug, R. J.

AU - von Klitzing, K.

AU - Ploog, K.

PY - 1992/2/19

Y1 - 1992/2/19

N2 - We have studied the magnetoresistance of AlGaAs/GaAs-heterojunctions at millikelvin temperatures in small Hall bar and Corbino geometries with different sizes. Below a characteristic temperature Tc which increases with decreasing sample width, the phase-breaking length Lin is larger than the sample size. Under these conditions the half width ΔB of the longitudinal magnetoresistance no longer depends upon temperature but only upon size. By varying the size it is thus possible to directly investigate the localization transition in the integer quantum Hall regime and to measure the critical exponent v of the localization length ξ α |B - Bc|-v. Our results show a universal behaviour in the three lowest Landau levels. This is in agreement w universality statement of the field-theoretic approach to the metal-insulator transition in the quantum Hall effect. By studying the characteristic temperature Tc for different widths, the temperature exponent p 2 of the inelastic scattering length can also be measured.

AB - We have studied the magnetoresistance of AlGaAs/GaAs-heterojunctions at millikelvin temperatures in small Hall bar and Corbino geometries with different sizes. Below a characteristic temperature Tc which increases with decreasing sample width, the phase-breaking length Lin is larger than the sample size. Under these conditions the half width ΔB of the longitudinal magnetoresistance no longer depends upon temperature but only upon size. By varying the size it is thus possible to directly investigate the localization transition in the integer quantum Hall regime and to measure the critical exponent v of the localization length ξ α |B - Bc|-v. Our results show a universal behaviour in the three lowest Landau levels. This is in agreement w universality statement of the field-theoretic approach to the metal-insulator transition in the quantum Hall effect. By studying the characteristic temperature Tc for different widths, the temperature exponent p 2 of the inelastic scattering length can also be measured.

UR - http://www.scopus.com/inward/record.url?scp=0026819749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026819749&partnerID=8YFLogxK

U2 - 10.1016/0039-6028(92)90316-X

DO - 10.1016/0039-6028(92)90316-X

M3 - Article

AN - SCOPUS:0026819749

VL - 263

SP - 108

EP - 111

JO - Surface Science

JF - Surface Science

SN - 0039-6028

IS - 1-3

ER -