A quantum-mechanical version of the Hall effect found at very low temperatures, in which the Hall coefficient R_H 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 R_H 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, R_H 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.