Quantum Hall effect

Summary

The quantum Hall effect is the quantisation of the Hall conductance of a two-dimensional electron system in a strong perpendicular magnetic field at low temperature. On plateaus of the field or density, the Hall conductance equals $\nu e^2/h$ and the longitudinal resistance vanishes. Here $\nu$ is an integer, or in the fractional effect a simple fraction. Klaus von Klitzing discovered the integer effect in 1980; Daniel Tsui, Horst Störmer and Arthur Gossard found the fractional effect in 1982. The integer effect has a topological explanation: the conductance is a Chern number, the TKNN invariant.