Novel edge magnetoplasmons with dissipation localized near the edges for very low temperatures and sharp density profiles

A treatment of edge magnetoplasmons (EMP), based on a microscopic evaluation of the local contributions to the current density, is presented. It is valid in the quantum Hall regime for filling factor \nu=1 or 2 and low temperatures when the dissipation is localized near the edge. The confining potential, flat in the interior of the channel, is assumed smooth on the magnetic length scale but sufficiently steep at the edges that the density profile is sharp and the dissipation considered results only from electron intraedge-intralevel transitions due to scattering by piezoelectrical phonons. For wide channels there exist independent EMP modes spatially symmetric and antisymmetric with respect to the edge. Certain of these modes can propagate nearly undamped even when the dissipation is strong and are thus termed edge helicons. In contrast with well-known results for a spatially homogeneous dissipation within the channel, we obtain that the damping of the fundamental EMP is not quantized and varies as T**3 or $T**(-3), where T is the temperature, in the high- and low-frequency limits, respectively. The characteristic length of the resulting dispersion relation and of the charge density distortion is the magnetic length. The screening of the metallic gates, when present, is taken into account.