Quantised Hall effect

A review of the quantised Hall effect is given. The author surveys experiments and theories on the normal and fractional quantum Hall effect including recent developments. As a background to the effect, which is a most remarkable manifestation of the Landau quantisation, the author starts with the description of the two-dimensional electron system in magnetic fields. As a closely related topic, the author also discusses the singular localisation of states specific to systems under the Landau quantisation in two dimensions. The determination of the fine-structure constant including the quantum Hall method is also briefly reviewed. In giving a self-contained account of the effect we emphasise the special features of the quantised Hall effect, which has an aspect of macroscopic quantum phenomenon on the one hand, and invokes, in the presence of electron-electron interactions, a new quantum liquid state on the other.