The Peculiar Properties od Quantum Hall Systems

For more than two and a half decades, experiments on two dimensional electron systems in strong magnetic fields, at low temperatures have given rise to a series of surprising phenomena, known collectively as the quantum Hall effects. I shall give here a brief overview of the field, beginning with a description of the integer and quantized Hall effects, and the basic conditions associated with their occurrence: an absence of mobile carriers in the bulk of the 2D system, combined with unidirectional electrical conduction along the sample boundary. The way in which these conditions are satisfied, in the case of the integer quantized Hall effect can be understood in terms of non-interacting electrons, using a semiclassical argument. The quantized Hall effect depends fundamentally on electron-electron interactions, which lead to a peculiar highly correlated ground state, with elementary quasiparticle excitations that carry charge and fractional statistics. I shall discuss briefly a number of other phenomena that occur in quantum Hall systems, and indicate some areas where open questions exist.