A Fraction of the Fractional Quantum Hall Effect

There has been a series of remarkable experimental and theoretical developments during the six years since the discovery of the fractional quantum Hall effect. This introductory talk takes the form of a roughly chronological wander past some of these milestones. The fractional quantum Hall effect is observed at low temperatures in two-dimensional systems of highly mobile electrons when the high magnetic field intensity corresponds to fractional occupation of the spin-split Landau levels. Experimental milestones along the route include the observation of a series of odd-denominator fractions, determination of the precision of the quantization of the Hall resistivity, measurement of activation energies for various fractions, spectroscopic evidence of the energy gap, and the recent discovery of even-denominator fractions. Theoretical milestones, which may be visited in the course of experimental wanderings, include the many-body ground state wavefunction with fractionally charged excitations, the excitation spectrum containing both quasiparticles and magneto-rotons, the development of the hierarchical model for understanding the myriad of observed odd-denominator fractions, and a recent competing theory based on correlated ring exchanges in an electron lattice.