Observation of the logarithmic dispersion of high-frequency edge excitations

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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“…(11), just using |Y | in the RHS of Eq. (11). Notice that this expansion is valid only when the lowest LL is occupied.…”

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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“…1(c)]. We identify EMP modes in the data with frequencies set by the edge velocity and circumference of the disk, following the dependence f ∼ B −1 ½logðB 2 Þ þ const [20], and extract the effective dielectric constant ϵ Ã ≈ 8. medium [23,32] (see Ref. [28]).…”

Section: A Transmission-line Spectroscopy Of Emp Modesmentioning

confidence: 99%

On-Chip Microwave Quantum Hall Circulator

et al. 2017

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Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size 1=1000th the wavelength by exploiting the chiral, "slow-light" response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with 330 μm diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip.

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“…In this condition, scattering of EMPs by charges in the bulk graphene is suppressed and EMPs orbit along the graphene edge. Then the resonance occurs when the wavelength of the EMP mode corresponds to [25],…”

mentioning

confidence: 99%

Resonant Edge Magnetoplasmons and Their Decay in Graphene

et al. 2014

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We investigate resonant edge magnetoplasmons (EMPs) and their decay in graphene by high-frequency electronic measurements. From EMP resonances in disk shaped graphene, we show that the dispersion relation of EMPs is nonlinear due to interactions, giving rise to the intrinsic decay of EMP wave packets. We also identify extrinsic dissipation mechanisms due to interaction with localized states in bulk graphene from the decay time of EMP wave packets. We indicate that, owing to the linear band structure and the sharp edge potential, EMP dissipation in graphene can be lower than that in GaAs systems.

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Observation of the logarithmic dispersion of high-frequency edge excitations

Cited by 15 publications

References 12 publications

Temperature effects on edge magnetoplasmons in the quantum Hall regime

Temperature effects on edge magnetoplasmons in the quantum Hall regime

On-Chip Microwave Quantum Hall Circulator

Resonant Edge Magnetoplasmons and Their Decay in Graphene

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