BULK AND EDGE PROPERTIES OF THE CHERN-SIMONS GINZBURG-LANDAU THEORY FOR THE FRACTIONAL QUANTUM HALL-EFFECT

The Chern-Simons Ginzburg-Landau theory for the fractional quantum Hal l effect is studied in the presence of a confining potential. We revie w the bulk properties of the model and discuss how the plateau formati on emerges without any impurity potential. The effect is related to ch anges, by accumulation of charge, at the edge when the chemical potent ial is changed. Fluctuations about the ground state are examined and a n expression is found for the velocity of the massless edge mode in te rms of the confining potential. The effect of including spin is examin ed for the case when the system is fully polarized in the bulk. In gen eral a spin texture may appear at the edge, and we examine this effect in the case of a small spin-down component. The low-frequency edge mo des are examined and a third-order equation is found for velocities wh ich indicates the presence of three different modes. The discussions a re illustrated by numerical studies of the ground states, both for the one- and two-component cases. (C) 1998 Elsevier Science B.V.