Nonlocal dispersion of edge magnetoplasma excitations in a two-dimensional electron system

Abstract

Edge magnetoplasma excitations in a two-dimensional electron system have been studied in radiofrequency experiments which exhibit a strong nonlocal behavior of the plasmon dispersion. The nonlocality is shown to be caused by the diagonal conductivity GXX, which, via a length IOZCTXX, governs the spatial distribution of the plasma charge oscillations in the direction perpendicular to the plasmon wave vector, i.e., to the edge of the two-dimensional layer.PACS numbers: 7I.45.Gm, 73.20.Dx, 73.20.Mf The collective excitation spectrum of an electronic system at large wave vectors q is governed by well-known nonlocal effects [1]. Nonlocal effects are of the order (qvf/cop)^, where Vf is the Fermi velocity and cOp is the "local" plasmon frequency, and are usually rather small. Here we report on a very different, large nonlocal effect on the plasmon dispersion which is a unique property of a finite-size two-dimensional electron system (2DES) when the edges become important. We have observed this nonlocal effect in magnetic-field experiments on two-dimensional electron systems of macroscopic size (1x1 cm^) for the low-frequency {l7if<^cOc) branch of the plasma excitations, i.e., the edge magnetoplasmons (EMP). The nonlocal effect arises from a significant influence of the diagonal conductivity Oxx on the EMP excitation which has not previously been observed. It can be characterized by a length l^^Oxxy which is related to the spatial extent of the plasma charge oscillations in the direction perpendicular to the plasmon wave vector, i.e., to the edge of a 2DES. It represents a kind of "transverse" nonlocality in contrast to the "longitudinal" nonlocality discussed above and also occurs for very small values of q.EMP excitations have recently attracted much attention due to their unique properties, in particular, a surprisingly small damping which also occurs for the condition 2;r/T <^ 1, where r is the B =0 momentum relaxation time [2][3][4][5][6][7][8][9][10]. The EMP frequency/EMP has been calculated by different authors [10][11][12][13] and is shown to be essentially proportional to the Hall conductivity Oxy and the wave vector q=^l7tn/P, where AZ = 1,2, ..., is the mode index and P is the perimeter of the finite-size 2DES. The theories in Refs. [10,11] include nonlocal efitects and, in spite of their different underlying physical models, give practically the same form for /EMP which is, if we neglect single-particle effects, density oscillations are concentrated in a very small region close to the edge. The interesting point for a 2DES is that the oscillating charge cannot be concentrated in a local ^-function "line" (which would lead to logarithmic divergences in the potential and electrostatic energy) [11]. This is a unique property of a 2DES and in contrast to surface plasmons at the surface of a 3DES (neglecting the spatial dispersion). Thus the oscillating charges of edge plasmons are inherently distributed over a certain region perpendicular to the edge and respond in a nonlocal manner. The calculation of this ...

Edge-magnetoplasmon wave-packet revivals in the quantum-Hall effect

“…For a millimeter-size sample at typical magnetic fields (2RϷ1 mm, Bϭ10 T͒, the ratio ⌫ M Ϫ1 /t rev ϳ1 (25) for M ϭ50 (20). The revival structure of EMP WP disussed in Sec.…”

“…Experimental studies [17][18][19][20][21][22][23][24]10,14 of EMP's have employed different excitation processes, including capacitive coupling 21 or Ohmic contacts 22 between the QH edge and an exciting voltage pulse. This paper is motivated most strongly by the capacitive coupling 21 approach and we comment later on the interpretation of these experiments.…”

Observation of the logarithmic dispersion of high-frequency edge excitations

“…In 6.9. Its value is found to be ~11, most probably enhanced by the presence of the metal surfaces along the sample [13], which distort the electric field lines.…”

“…However, very few experiments have actually traced a logarithmic dependence, as this would require a variation of the parameter ql over a wide range. At relatively low frequency, Grodnenski et al [13] have found evidence for a logarithmic dependence by varying σ xx , hence l, with temperature. At high frequency, Dahl et al [14] have reported a fixed value for l independent of B, in contrast with Eq.…”

Microwave absorption by a mesoscopic quantum Hall droplet

“…Therefore, for v = 10 4 − 10 5 m/s, the edge modes of such a drum can be 'heard' in the frequency range ≈ 1 − 100 GHz or, in other words, with microwaves. Such modes have already been observed using spectroscopy [3][4][5][6][7][8][9][10][11] in samples on the millimeter scale and analyzed using semiclassical models, 12,13 and have also been observed through time resolved measurements. [14][15][16][17][18] Here, we focus exclusively on the absorption spectrum of micron-scale samples tuned to quantum Hall plateaus.…”