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

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 ...

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“…In our solution of Eqs. (12)- (20), we are taking the long-wavelength limit |k x |ℓ T ≪ 1, so we can use the approxi-…”

Section: At Temperatures Such That the Inequality Kmentioning

confidence: 99%

Temperature effects on edge magnetoplasmons in the quantum Hall regime

Balev

Studart

2000

Phys. Rev. B

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“…This can be achieved, e.g., by applying a voltage pulse to a metallic gate close to the edge. 14,17 In general, the coupling of the inner and outer edges to the external perturbation will differ:…”

Section: Edge Wave Packets At Two-branch Edgesmentioning

confidence: 99%

“…For practical purposes, it is usually adequate to assume a local-capacitor model where the metallic gate and the part of the edge located in its immediate vicinity form the two 'plates' of a capacitor. 17 In such a model, a capacitor which covers the outer edge but not the inner edge would have V ext,i (x) = 0. We will see that excitation of the counterpropagating phonon mode requires differentiated coupling to the inner and outer edges; the local-capacitor model suggests that this could be achieved by arranging for an excitation gate which covers only the outer part of the edge region.…”

Section: Edge Wave Packets At Two-branch Edgesmentioning

confidence: 99%

“…Given the quadratic edge Hamiltonian, it is possible to solve the time-dependent Schrödinger equation explicitly for H = H 0 + V ext (t) with general pulse shape u(t) as detailed in Ref. 17. Wave packets of edge modes can be engineered by appropriately adjusting the characteristics of the voltage pulse.…”

Section: Edge Wave Packets At Two-branch Edgesmentioning

confidence: 99%

“…Wave packets of edge modes can be engineered by appropriately adjusting the characteristics of the voltage pulse. 17 Wave packets with narrow wave-vector distributions can be generated by repeating a length-T exc pulse N > 1 times.…”

Section: Edge Wave Packets At Two-branch Edgesmentioning

confidence: 99%

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Observability of counterpropagating modes at fractional quantum Hall edges

1998

Self Cite

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When the bulk filling factor is ν = 1 − 1/m with m odd, at least one counterpropagating chiral collective mode occurs simultaneously with magnetoplasmons at the edge of fractional-quantumHall samples. Initial experimental searches for an additional mode were unsuccessful. In this paper, we address conditions under which its observation should be expected in experiments where the electronic system is excited and probed by capacitive coupling. We derive realistic expressions for the velocity of the slow counterpropagating mode, starting from a microscopic calculation which is simplified by a Landau-Silin-like separation between long-range Hartree and residual interactions. The microscopic calculation determines the stiffness of the edge to long-wavelength neutral excitations, which fixes the slow-mode velocity, and the effective width of the edge region, which influences the magnetoplasmon dispersion.

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Quantum wave packet revivals

2004

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The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially localized quantum states which have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival in which the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet ('minipackets' or 'clones') is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental realization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide interest in the physics and chemistry communities.We review the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as discussing how information on the classical period and revival time is encoded in the energy eigenvalue spectrum. We discuss a number of one-dimensional model systems which exhibit revival behavior, including the infinite well, the quantum bouncer, and others, as well as several two-dimensional integrable quantum billiard systems. Finally, we briefly review the experimental evidence for wave packet revivals in atomic, molecular, and other systems, and related revival phenomena in condensed matter and optical systems.

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

Cited by 10 publications

References 60 publications

Temperature effects on edge magnetoplasmons in the quantum Hall regime

Temperature effects on edge magnetoplasmons in the quantum Hall regime

Observability of counterpropagating modes at fractional quantum Hall edges

Quantum wave packet revivals

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