EDGE MAGNETOPLASMONS FOR VERY-LOW TEMPERATURES AND SHARP DENSITY PROFILES

A treatment of edge magnetoplasmons (EMP), based on a microscopic eval uation of the local contributions to the current density, is presented . It is valid in the quantum Hall regime for filling factor v=1 or 2 a nd low temperatures when the dissipation is localized near the edge. T he confining potential, flat in the interior of the channel, is assume d smooth on the magnetic length to scale, but sufficiently steep at th e edges that the density profile is sharp and the dissipation consider ed results only from electron intraedge-intralevel transitions due to scattering by piezoelectrical phonons. For wide channels there exist i ndependent EMP modes spatially symmetric or antisymmetric with respect to the edge. Certain of these modes can propagate nearly undamped, ev en when the dissipation is strong, and are thus termed edge helicons. In contrast with well-known results for a spatially homogeneous dissip ation within the channel, we obtain that the damping of the fundamenta l EMP is not quantized and varies as T-3 or T-3, where T is the temper ature, in the high-and low-frequency limits, respectively. The charact eristic length of the resulting dispersion relation and of the charge density distortion is l(0). The screening of the metallic gates, when present, is taken into account.