Phonons, Rotons and Fractionally Charged Vortices in the Quantum Hall Effect

The fractional quantum Hall effect (FQHE) is a remarkable many-body phenomenon occurring in the two-dimensional electron gas (2DEG) at low temperatures in a high magnetic field. As we learned in the lecture by Robert Laughlin at this conference, the experimental manifestations of the effect follow from the existence of an excitation gap and are quite similar to those of the integer case, but the gap arises for rather different reasons: The FQHE is intrinsically a many-body phenomenon associated with Coulomb correlations, while the integer effect is primarily a one-body effect associated with localization. The goal of this lecture is to explore further the FQHE with emphasis on the nature of the collective excitation modes and the origin of the gap. It turns out that a remarkable amount of progress can be made on this problem by drawing on analogies with superfluidity in ⁴He films.