The von Klitzing resistance standard

Bachmair, Hans; Göbel, E. O.; Hein, G.; Melcher, J.; Schumacher, B.; Schurr, J.; Schweitzer, L.; Warnecke, P.

doi:10.1016/j.physe.2003.09.017

Cited by 19 publications

(10 citation statements)

References 24 publications

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“…However, this picture discounts the Coulomb interaction between electrons and, as a result, is unable to account for several important features of the IQHE. These features include the enormous accuracy with which the quantized resistance values can be reproduced experimentally [6] and the local potential and current distributions in narrow Hall bars as recently detected in "local probe" experiments [7,8].…”

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confidence: 96%

Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

Horas

Siddiki

Moser

et al. 2008

Physica E: Low-dimensional Systems and Nanostructures

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We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates on the surfaces of GaAs/AlGaAs heterostructures. In the low mobility regime the classical Hall resistance line is proportional to the magnetic field as measured in the high temperature limit and cuts through the center of each Hall plateau. For high mobility samples we observe in linear response measurements, that this symmetry is broken and the classical Hall line cuts the plateaus not at the center but at higher magnetic fields near the edges of the plateaus. These experimental results confirm the unconventional predictions of a model for the quantum Hall effect taking into account mutual screening of charge carriers within the Hall bar. The theory is based on solving the Poisson and Schrödinger equations in a self-consistent manner.At low temperatures, transport in low-dimensional electron systems is dominated by quantum mechanical properties. In particular, a two dimensional electron system (2DES) subjected to a strong magnetic field perpendicular to the 2DES exhibits the integer quantized Hall effect (IQHE) [1]. In a classical Email address: Jose.Horas@Physik.Uni-Muenchen.de (J. Horas).

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mentioning

confidence: 96%

Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

Horas

Siddiki

Moser

et al. 2008

Physica E: Low-dimensional Systems and Nanostructures

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“…A precise determination allows for a new normal for the unit Ohm [422], being two orders of magnitude more precise than the realization in the SI system, and an independent value for the fine-structure constant α = e 2 c 1 4π 0 . At the same time, the longitudinal resistivity, starting from the classical value for small magnetic fields, exhibits oscillations and eventually it is zero for the plateaus in ρ xy .…”

Section: Integral Qhementioning

confidence: 99%

The Physics of Semiconductors

Grundmann¹

2006

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“…The "Quantum Hall Effect" (QHE), discovered 1980 by K. von Klitzing [1], who was honored by the Nobel Price in 1985, presents a unique possibility to reproduce, in different materials, the electrical resistance (von-Klitzing constant) with extremely high accuracy, and is nowadays used as one basic constant for the definition of the international system of physical units [2,3]. The QHE was detected on a quasi-two-dimensional electron system (2DES) in a Si-MOSFET (silicon-based metal-oxide-semiconductor field-effect-transistor) in a strong perpendicular magnetic field at low temperatures.…”

Section: Introductionmentioning

confidence: 99%

Self-Consistent Theory of Screening and Transport in Narrow, Translation-Invariant Hall Bars under the Conditions of the Integer Quantum-Hall-Effect

Gerhardts¹

2020

Recent Progress in Materials

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We summarize and discuss a self-consistent screening and magneto-transport theory, developed to understand the results of scanning-force-microscope experiments on the current distribution in a two-dimensional electron system (2DES), located in a narrow Hall bar under the conditions of the integer quantum Hall effect (IQHE) and its breakdown. The theory explains why, at low temperatures, at certain intervals of the applied perpendicular magnetic field, the current density is confined to "incompressible stripes" (ISs), in which a fixed number of Landau levels is occupied, and the longitudinal and Hall resistivity assume quantized values. The theory also explains, how the position and shape of these ISs depend on magnetic field and temperature, and why the confinement of the current density on these ISs leads to precisely quantized values of the macroscopic longitudinal and Hall resistance. The theory, which leads, at high temperatures, to the well known Drude results for current density and resistance, shows that the IQHE is a consequence of the peculiar screening properties of a 2DES in a strong magnetic field at low temperatures, and that it can be understood without assumptions about special localization effects.

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The von Klitzing resistance standard

Cited by 19 publications

References 24 publications

Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

The Physics of Semiconductors

Self-Consistent Theory of Screening and Transport in Narrow, Translation-Invariant Hall Bars under the Conditions of the Integer Quantum-Hall-Effect

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