The Quantum Hall Effect and Resistance Standards

Abstract

Following the discovery of the quantum Hall effect in 1980 metrologists were eager to develop the effect as a resistance standard in a similar manner to the development, a decade earlier, of the Josephson effects in superconductors as a voltage standard. This article reviews the progress made by many national laboratories to assess and compare the quality and limitations of semiconductor devices, mainly silicon MOSFETs and GaAs/AlGaAs heterostructures, as quantized Hall resistance standards with values RH (i) = RK/i = h/ie2, where RK = 25812,807 Ω is the von Klitzing constant and i is an integer. Potentiometric and cryogenic current comparator bridge techniques for the measurement of RK in terms of conventional resistance standards with 1 σ relative accuracies better than 1 part in 108 are compared, and determinations of RK in ohms with accuracies as high as 2,4 parts in 108 using calculable capacitors are described. The comparison of direct determinations of RK with alternative derivations of h/e2 leading to the CCE recommendations and subsequent international adoption, from 1 January 1990, of the value 25812,807 ± 0,005 Ω for RK are also described.

Imaging Transport Resonances in the Quantum Hall Effect

“…Since then, the accuracy has been improved to better than 1 part per billion. The quantum Hall effect is now used as the official international resistance standard [6], and plays a fundamental role in the quantum metrology triangle [7]. For this discovery, von Klitzing was awarded the Nobel prize Two years before von Klitzing's discovery, another significant change to the field of semiconductor physics had occurred.…”

Proposal of a new method of measurement of the quantized hall resistance with a Binary Josephson array in a bridge configuration

“…One of the main advantages of CCC systems in QHR measurements, by comparison with potentiometers, is the lower Johnson noise, due to compare QHR with a 100 Ω room temperature standard, instead of a several k Ω resistor , resulting in typically 2 nV/√Hz versus 10 nV/√Hz in potentiometric methods [1].…”

“…However, the "odd" value of the von Klitzing made difficult to relate QHR to conventional resistance standards, typically decimal multiples of the ohm. Two types of measurement system, based on potentiometric and cryogenic current comparator (CCC) bridges, are commonly used to make these measurements [1].…”

Integer quantum Hall effect in a lattice model revisited: Kubo formalism

“…Immediately after this discovery scientists from various disciplines were launched into a frenzy of activity to understand the underlying physics and also to explore its technological importance in designing different electronic devices. Such efforts have led to the endowment of a new metrological standard, the resistance quantum, h/e 2 , containing two fundamental constants, the electronic charge e and the Planck's constant h 3 . The scaling theory of localization 4 suggests that in absence of magnetic field all the states of a 2D disordered noninteracting electron system are localized due to quantum interference.…”