As with the Josephson effect before it (see the 1975 Helmholtz Prize), the quantum Hall effect also links, on the one hand, macroscopic electric quantities and, on the other hand, two fundamental constants: e (elementary charge) and h (Planck’s constant). In the quantum Hall effect, which he discovered in 1980, Klaus von Klitzing found a new method of realizing electric resistance values with very high accuracy. If a thin, current-carrying layer (“two-dimensional electron gas”) is exposed at very low temperatures to a strong magnetic field that is perpendicular to the layer, the Hall resistance RH (i.e. the ratio of the Hall voltage to the current) shows a stair-shaped characteristic curve when the magnetic field is changed.
On these “stairs”, the Hall resistance is constant and has the following discrete values, which can be reproduced with high accuracy: RH = RK/i (i = 1,2,...), die man mit hoher Genauigkeit reproduzieren kann. Die Größe RK, die „von Klitzing-Konstante“, ist durch RK = h/e2.
The quantity RK (the “von Klitzing constant”) is given by RK = h/e2. Its value is approximately 25,8 kΩ.
The potential of the quantum Hall effect for realizing resistance values was harnessed by PTB and other metrology institutes as early as 1980. The question of which physical systems are best suited for precision measurements of the von Klitzing constant RK was investigated by four physicists – Günther Ebert, Thomas Herzog, Harald Obloh and Bert Tausendfreund when they were doctoral candidates under von Klitzing. They received the 1983 Helmholtz Prize (at the time endowed with 5,000 German marks) for their work, which was titled “On the application of the quantized Hall effect in metrology”.
Within the scope of their work, these four physicists measured the Hall resistance of silicon MOS transitions, indium antimonide field effect transistors and a range of semiconductor heterostructures as precisely as possible. As the measurements performed on GaAs-AlGaAs heterostructures at a temperature of 1.5 K and in a magnetic field of around 8 T showed, the Hall resistance remained almost constant within a magnetic field range of around 1 T. Its relative change was only a few 10–8. Today, it is possible to reproduce resistance values with a relative uncertainty of a few 10–9 with GaAs-AlGaAs heterostructures manufactured by means of (for example) molecular beam epitaxy. These heterostructures show especially pronounced resistance steps over a relatively large magnetic field range at i = 2 and i = 4. The von Klitzing constant is known, and can be reproduced, just as precisely.
By means of the quantum Hall effect and the Josephson effect, the two electrical units – the ohm and the volt – can be defined and disseminated in a uniform way.
