Quantum Hall Effect

by David Bradley

The quantum Hall effect (QHE) has connections to nearly all fields in physics, from black hole physics to quarks, said Professor Klaus von Klitzing, a foreign member of the Royal Society based at the Max Planck Institute for Solid State Research in Germany, who first discovered the QHE. His talk focused on how the QHE relates to fundamental constants, precision measurements, and the SI base units.

The Hall effect, named after American physicist Edwin Hall who discovered it in 1879, occurs when an electric current flows through a conductor in a magnetic field, creating a measurable transverse voltage. The effect is widely exploited in sensor technology, electronics, and in materials characterisation. However, this is a classical effect where the Hall resistance (transverse voltage divided by the electric current) increases monotonically with increasing magnetic field. The quantum Hall effect with a step-like variation of the Hall resistance is observed in strong magnetic fields and low temperatures for measurements on semiconductor materials. The steps occur at very precise resistance levels irrespective the material being investigated - they are quantised, in other words.

Von Klitzing explained that the QHE can be exploited to make high-precision measurements of two fundamental constants, mentioned earlier. Firstly, the fine structure constant, ? (see Inconstant constants) can be obtained by comparing the quantized Hall resistance with a resistance standard calibrated in the SI unit of resistance the ohm and secondly the Planck constant, via the Watt balance.

The quantized Hall resistance is stable and experimentally reproducible at the level of two parts in a billion (experimental uncertainty). Today, all high precision measurements on electrical resistors are based on the QHE.

The QHE could also play a role in defining the SI base units. The base unit “kilogram”, for instance, is an artefact of nineteenth century science based on an ingot of metal alloy housed in a Parisian basement. One possible way to replace this artefact with a "modern" definition would be to compare electrical power, measured on the basis of the QHE and the so-called Josephson effect, a phenomenon of quantum mechanics associated with the tunnelling of electron pairs through superconducting materials, with mechanical power, which is dependent on the unit of mass. A more detailed discussion of putative new definitions of the kilogram are described below by Professor Davis in "Weighing up the new kilo". There is a good chance, that fundamental constants will play an increasing role for the SI base units, explained von Klitzing, with defined values for the velocity of light (already used for the realization of the unit of length), the Planck constant and the elementary charge, he added. For such a system the base units kilogram and Ampere will be replaced by other definitions and the quantized Hall resistance will be a fixed fundamental constant without any uncertainty.

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