Physics and Applications of the Quantum Hall Effect

Abstract

The most fascinating property of the Quantum Hall Effect (QHE) is the phenomenon that from a relatively simple experiment on a semiconductor a new type of electrical resistor R₀ can be deduced which is independent of microscopic properties of the semiconductor and reproducable at a level of better than 10^-6. In the recent publication of “The 1986 Adjustment of the Fundamental Physical Constants”¹ one finds a new general constant, the quantized Hall resistance with a recommended value R₀=(25812.8056±0.00012) Ohm. This value is identical with the ratio h/e², the ratio between the Planck constant h and the square of the electron charge e. The surprising result is, that this universal constant R₀ can be measured directly on a macroscopic system. In principle all Hall effect measurements in strong magnetic fields and low temperatures on a two- dimensional electron gas show the QHE. However, for the experimental realization of this quantum phenomenon one has to specify the condition “low temperature”, “high magnetic field” and “two-dimensional system”. The inversion layer at the Si-Si0₂ interface of a silicon MOS fieldeffect transistor is the classical example for a two-dimensional system² but in a more general way all structures with a vanishing conductivity in one direction may be called two-dimensional electron gas. Even a superlattice with a macroscopic thickness of some micrometers can show two-dimensional properties if the periodicity of the superlattice leads to well separated minihands³. In this respect most of the structures discussed at this school are related to the physics of two-dimensional systems and can be used for a discussion of the quantum Hall effect. The reduced dimensionality is necessary in order to obtain gaps in the electronic spectrum.