Fractional quantum Hall effects and composite fermions

When electrons are confined to two dimensions, cooled to near absolute zero temperature and subjected to a strong magnetic field, they produce a plethora of remarkable liquids with fractionally quantized Hall resistances, which have provided new paradigms for collective behavior of strongly interacting particles. The underlying physics of these liquids is characterized by the formation of a new kind of topological particles called composite fermions, which are bound states of electrons and quantized vortices. The fractional quantum Hall effects at most of the odd- and even-denominator fractions result, respectively, from the integer quantum Hall effect and from the Bardeen-Cooper-Schrieffer pairing of composite fermions. The excitations of the fractional Hall liquids have fractionally quantized charge and have been predicted to obey fractional Abelian or non-Abelian braid statistics. This article describes the essential phenomenology of the fractional quantum Hall effects, its explanation in terms of composite fermions, the origin of fractional charge and statistics, and lists many open questions.