A microscopic treatment of edge magnetoplasmons (EMPs) is presented for the case of not-toolow temperatures in which the inequality kBT ≫hvg/ℓ0, where vg is the group velocity of the edge states and ℓ0 is the magnetic length, is fulfilled, and for filling factors ν = 1(2). We have obtained independent EMP modes spatially symmetric and antisymmetric with respect to the edge. We describe in detail the spatial structure and dispersion relations of the new edge waves (edge helicons, dipole, quadrupole and octupole EMPs), which have the characteristic length ℓT = ℓ 2 0 kBT /hvg. We have found that, in contrast to well-known results for a spatially homogeneous dissipation within the channel, the damping of the fundamental EMP at not-too-low temperatures is not quantized and has a T −1 dependence. PACS 73.20.Dx, 73.40.Hm
I. INTRODUCTION.Edge magnetoplasmons (EMPs) in the two-dimensional electron system (2DES) have received much attention in recent years. Experimental studies have been performed to determine the dispersion relation and the role of edge states in the transport properties of the 2DES both on liquid helium [1-3] as in high-mobility AlGaAs-GaAs heterostructures [4][5][6][7][8][9][10][11]. The interest have even increased with the advent of time-resolved transport experiments [7,9,10]. From a theoretical point of view, a lot of work have been also devoted to study the characteristics of these collective excitations propagating along the edge of the 2DES in the presence of a normal magnetic field B and different edge-wave mechanisms have been proposed [12][13][14][15][16][17][18][19][20][21][22][23]. First, the EMPs dispersion were determined theoretically within essentially classical models [13,16] in which the charge density varies at the edge, but the edge position of the 2DES is kept constant. Other, distinctly different, quantum-mechanical edge-wave mechanisms was proposed [14,15,17,18] in which only the edge change and the density profile is taken as the unperturbed 2DES with respect to the fluctuating edge.Recently a microscopic model was proposed in Refs. [21,22] that effectively incorporates the edge-wave mechanisms mentioned above in the quantum Hall effect (QHE) regime. Even though EMPs have been studied in the limit of low temperatures k B T ≪hv g /ℓ 0 , where v g is the group velocity of the edge states and the magnetic length ℓ 0 = h/m * ω c with ω c = |e|B/m * c, in the calculation of the current density J was assumed that the components of the electric field E of the wave are smooth on the ℓ 0 scale. However, this assumption can not be well justified for EMPs at very low temperatures. Here, we extend the approach of Refs. [21,22] for not-too-low temperatures, wherehω c ≫ k B T ≫hv g /ℓ 0 . In this regime the typical scales of in-plane components of E are of the order of ℓ T = ℓ 2 0 k B T /hv g , which is much larger than ℓ 0 . Our model to treat EMPs consists in considering a 2DES, of width W , length L x = L, and negligible thickness, in the presence of a strong B parallel to the z axis, such ...
