Fractional Quantum Hall Effect and Composite Fermions

When a two-dimensional electron system is exposed to a strong transverse magnetic field, it forms a new quantum liquid whose phenomenology rivals superconductivity and superfluidity in its richness and elegance. The investigation of this wonderful mystery has led to the discovery of some of the most profound and unprecedented emergent structures in modern physics. A large body of phenomena associated with this effect are explained by the formation of topological electron vortex-bound states, known as composite fermions, which have also been observed directly. This chapter describes the essential phenomenology of the fractional quantum Hall effect and numerous manifestations of composite fermions. It also mentions some unresolved challenges.