Developments in the Theory of the Quantum Hall Effect, Proceedings of the 1994 Vancouver Semiconductor Conference

Abstract

The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting with a Chern-Simons gauge field, have been useful for explaining and predicting observations at even-denominator filling fractions where quantized Hall plateaus are not observed, as well as for giving new insight into the most prominent fractional quantized Hall states at odd-denominator fractions. Other theoretical approaches have led to important advances in our understanding of edge-excitations for systems in a fractional quantized Hall state, of phases and phase transitions in bilayer systems, of tunneling phenomena in the quantum Hall regimes, and of disorder-induced transitions between ``neighboring'' quantum Hall plateaus. Some highlights of these developments will be reviewed.