Jm. Leinaas et S. Viefers, BULK AND EDGE PROPERTIES OF THE CHERN-SIMONS GINZBURG-LANDAU THEORY FOR THE FRACTIONAL QUANTUM HALL-EFFECT, Nuclear physics. B, 520(3), 1998, pp. 675-696
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.