Theoretical aspects of the quantum Hall effect

Abstract

This talk will focus on the fractional quantum Hall effect, which is a remarkable many-body phenomenon occurring in the two-dimensional electron gas at high magnetic fields and low temperatures. The Hall conductance of a real, macroscopic device is quantized in the form: oxy = ve2/h, where v is a rational fractional quantum number. Associated with this are vortex-like excitations that have fractional charge and other bizarre features. There are deep connections between this phenomenon and superfluidity and analogies with models of current interest in high-energy physics. The essence of the effect is that electrons in a magnetic field can turn into bosons by attaching themselves to flux tubes. The discovery of the quantum Hall effect (for a recent review, see ref. 1) has revolutionized our understanding of transport in disordered systems in high magnetic fields in two dimensions and has important implications for other areas of physics as well as metrology. The integer quantum Hall effect is a one-body phenomenon associated with the gap between states of different kinetic energy (Landau levels) in a magnetic field. The basic experimental observation is that under special conditions the excitation gap causes the system to become dissipationless, and the Hall conductance takes on a universal value: