### 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 T_{c} which increases with decreasing sample width, the phase-breaking length L_{in} 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 - B_{c}|^{-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 T_{c} for different widths, the temperature exponent p 2 of the inelastic scattering length can also be measured.

Original language | English (US) |
---|---|

Pages (from-to) | 108-111 |

Number of pages | 4 |

Journal | Surface Science |

Volume | 263 |

Issue number | 1-3 |

DOIs | |

State | Published - Feb 19 1992 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Surface Science*,

*263*(1-3), 108-111. https://doi.org/10.1016/0039-6028(92)90316-X

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

Research output: Contribution to journal › Article

*Surface Science*, vol. 263, no. 1-3, pp. 108-111. https://doi.org/10.1016/0039-6028(92)90316-X

}

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 -