A quantum mechanical version of the Hall effect found at very low temperatures, in which the Hall coefficient RH is proportional to h/e2, where h is the Planck constant and e is the charge of the electron. Thus, the Hall coefficient is quantized. There are two types of quantum Hall effect. The integer quantum Hall effect has RH given as an integer with great precision. It can be used for precision measurements of constants such as e and h. In the fractional quantum Hall effect, RH has fractional values.
The integer quantum Hall effect can be understood in terms of noninteracting electrons, whereas the fractional effect is thought to result from many-electron interactions in two-dimensional systems, and be an example of anyons (see quantum statistics).
Analogues of the quantum Hall effect exist for spin; see spin Hall effect.