The quantized Hall effect

The Hall effect is widely used in laboratories to determine the carrier concentration in a given semiconductor specimen. Recently, a startling observation created a new interest in the physical principles underlying the Hall effect. Von Klitzing et al. (1980) discovered that under certain conditions the Hall resistance of their specimen was surprisingly constant, and its magnitude coincided with the ratio of two fundamental physical constants to any accuracy to which they were able to measure the effect. The Hall resistance was found to be quantized. The present investigation is concerned with the current understanding of the origin of the quantized Hall effect. Attention is also given to aspects of fractional quantization observed in connection with investigations of GaAs-(AlGa)As heterostructures in magnetic fields as high as 200 kG and temperatures as low as 0.5 K.