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Quantum Hall Effect

 

In 1980 the German physicist Klaus von Klitzing discovered a new quantum effect when he studied the Hall voltage of MOS field effect transistors at low temperatures in high magnetic fields. To reach these low temperatures liquified Helium is needed. In order to utilize high magnetic flux densities of about 10 to 20 Tesla von Klitzing had to travel the European High Magnetic Field Laboratrory in Grenoble, France, at that time. Meanwhile such high fields can be generated with superconducting solenoids and are routinely available in many laboratories worldwide.

 

The picture shows one of von Klitzing's original samples which he used in his discovery. This sample is now part of an exhibition at the Deutsches Museum in Bonn.

 

Von Klitzing observed deviations from a "smooth" relation when he measured the Hall voltage in dependence of a gate voltage applied to the sample. (Original paper)

 

 

He explained them as a quantization of the Hall resistance. The Hall resistance, which is the quotient of Hall voltage and sample current, amounted to fractions of h/e² (h Planck's constant, e elementary charge). The values were particularly pronounced when the constant h/e² was divided by an integer number, e.g. by 2 or by 4, i.e. at about 12906 Ω and at about 6453 Ω.

One of the prerequisites for the effect is the existence of a two dimensional electron gas (2DEG) inside the sample. On the basis of gallium arsenide one can nowadays produce, e.g. in PTB's clean room facility, crystalline heterostructures. They exhibit a much cleaner and easier to observe effect than the originally used transistors, especially when the Hall voltage is measured in dependence on magnetic field.

The crystals are grown with a molecular beam epitaxy system. In technical applications they represent the "heart" of modern satellite receivers or of mobile phones. In some sense the quantum Hall effect and its use in precision metrology is a spin-off product of the rapid development of modern semiconductor industry.

 

A picture of a sample for quantum Hall effect measurements made at PTB. The following link displays the result of a measurement made with a sample of this type (GIF, 140 kByte).

 

After the discoverer of the effect the quantity h/e² has been named "von-Klitzing constant" and it is abbreviated as RK:

 

RK = h/e2

 

To honour his discovery, von Klitzing was awarded the Nobel prize for physics in 1985.
Resistance values realized with the quantum Hall effect can be reproduced with relative uncertainties of one part in a billion. For this reason the effect is used as the basis for constant reference resistors for calibrations in national metrology institutes all over the world since 1990. Since the von-Klitzing constant RK = h/e² was not known with the necessary precision by that time, everywhere the same stipulated value was used for the purpose of calibrations from 1. January 1990 until 19. May 2019: RK-90 = 25812,807 Ω

 

Since May 20, 2019, the day the revision of the International System of Units (SI) came into force, a new reference value is valid. It is determined by the defined values for the Planck constant h and for the elementary charge e:

 

RK = h/e2 = 25 812.807 459 304 5… Ω

 

The discovery of the quantum Hall effect opened up a completely new field of work in physics. With the increasingly rapid improvement of artificially made semiconductor crystals new and theoretically unpredicted effects were discovered. Already in 1983, only three years after von Klitzings work, the physicist Horst L. Störmer and his team found that deviations from the "smooth" relation also occurred when h/e² was not divided by an integer, but by a fractional number. To observe this effect one needed, in addition to extremely clean semiconductor crystals, even higher magnetic fields and lower temperatures than von Klitzing had used.

Though the new effect is seemingly very similar to the one discovered by von Klitzing, its theoretical explanation is different and much more involved. The basis of the nowadays accepted model was laid by the US-american Physicist Robert BettsLaughlin, who was, together with the discoverers Horst Störmer und Daniel Tsui, awarded the 1998 Nobel prize for physics.

This new effect is called "Fractional Quantum Hall Effect" (abbr. FQHE), in distinction to the "Integer Quantum Hall Effect" (IQHE) discovered by von Klitzing.