Edge Magnetoplasmons Modes Research Articles

Observation of Edge Magnetoplasmon Squeezing in a Quantum Hall Conductor.

Squeezing of the quadratures of the electromagnetic field has been extensively studied in optics and microwaves. However, previous works focused on the generation of squeezed states in a low impedance (Z_{0}≈50 Ω) environment. We report here on the demonstration of the squeezing of bosonic edge magnetoplasmon modes in a quantum Hall conductor whose characteristic impedance is set by the quantum of resistance (R_{K}≈25 kΩ), offering the possibility of an enhanced coupling to low-dimensional quantum conductors. By applying a combination of dc and ac drives to a quantum point contact, we demonstrate squeezing and observe a noise reduction 18% below the vacuum fluctuations. This level of squeezing can be improved by using more complex conductors, such as ac driven quantum dots or mesoscopic capacitors.

Non-reciprocal magnetoplasmon graphene coupler

The non-reciprocity of the edge magnetoplasmon modes of a graphene strip is leveraged to design a non-reciprocal magnetoplasmon graphene coupler, coupling only in one direction. The proposed coupler consists of two coplanar parallel magnetically biased graphene strips. In the forward direction, the modes along the adjacent strip edges of the strips have the same wavenumber and therefore couple to each other. In the backward direction, the modes along the adjacent strip edges have different wavenumbers and therefore no coupling occurs.

Manifestations of incompressible strips in the edge magnetoplasmon spectrum in the quantum Hall effect regime

The behavior of the main edge magnetoplasmon mode in the quantum Hall effect (QHE) regime has been analyzed by the method of optical detection of resonance microwave absorption. Near a filling factor of 2 at a temperature of about 0.3 K, the main edge mode splits into two modes seemingly due to broadening of the incompressible strip at the edge of the two-dimensional electron gas under such conditions.

Helical edge magnetoplasmon in the quantum Hall effect regime

We present the microscopic treatment of edge magnetoplasmons (EMPs) for the regime of not-too-low temperatures defined by the condition ℏωc⪢kBT⪢ℏvg/2ℓ0, where vg is the group velocity of the edge states, ℓ0=ℏ/m∗ωc is the magnetic length and ωc is the cyclotron frequency. We find a weakly damped symmetric mode, named helical EMP, which is localized at the edge states region for filling factors ν=1,2 and very strong dissipation ηT=ξ/kxℓT≳ln(1/kxℓT)⪢1, where the characteristic length ℓT=kBTℓ02/ℏvg⪢ℓ0/2 with ξ being the ratio of the local transverse conductivity to the local Hall conductivity at the edge states and kx is the wave vector along the edge; here other EMP modes are strongly damped. The spatial structure of the helical EMP, transverse to the edge, is strongly modified as the wave propagates along the edge. In the regime of weak dissipation, ηT⪡1, we obtain exactly the damping of the fundamental mode as a function of kx. For ν=4 and weak dissipation we find that the fundamental modes of n=0 and 1 Landau levels are strongly renormalized due to the Coulomb coupling. Renormalization of all these EMPs coming from a metal gate and air half-space is studied.

Far-infrared photoconductivity of electrons in an array of nanostructured antidots

We present far-infrared (FIR) photo-conductivity measurements for a two-dimensional electron gas in an array of nano-structured antidots. We detect, resistively and spectrally resolved, both the magnetoplasmon and the edge-magnetoplasmon modes. Temperature-dependent measurements demonstrates that both modes contribute to the photo resistance by heating the electron gas via resonant absorption of the FIR radiation. Influences of spin effect and phonon bands on the collective excitations in the antidot lattice are observed.

Edgemagnetoplasmons in a partially screened system

We present a study of partially screened edgemagnetoplasmon modes to test theoretical predictions. Fetter's theory fits the data for small magnetic fields. Deviations at larger fields occur when the penetration length becomes shorter than the width of the density profile at the sample perimeter. At large fields the resonant mode frequencies are in reasonable agreement with the theoretical predictions of Volkov and Mikhailov.

Edge magnetoplasmon excitations in a quantum dot in high magnetic fields

We investigate the collective magnetoplasmon excitations in a quantum dot containing finite number of electrons in the high magnetic field limit. We consider the electrons in the lowest Landau level and neglect mixing between the higher Landau levels. The dispersion relation of these edge modes are estimated following the energy weighted sum-rule approach. In this finite size system the edge magnetoplasmon modes have different multipolarities (or angular momemtum k). Their dependence on the magnetic field and on the system size is investigated. With increasing magnetic field, energy of these collective modes decreases and in the bulk limit they become gapless. We also consider the breathing mode of a dot in the presence of a strong magnetic field, and the energy of this mode approaches the cyclotron frequency ?\(\).

Temperature effects on edge magnetoplasmons in the quantum Hall regime

A microscopic treatment of edge magnetoplasmons (EMPs) is presented for the case of not-too-low temperatures in which the inequality $k_{B}T\gg \hbar v_{g}/\ell_{0}$, where $v_{g}$ is the group velocity of the edge states and $\ell_{0}$ is the magnetic length, is fulfilled, and for filling factors $\nu =1(2)$. 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 $\ell_{T}=\ell_{0}^{2}k_{B}T/\hbar v_{g}$. 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.

Edge helicons and repulsion of fundamental edge magnetoplasmons in the quantum Hall regime

A quasi-microscopic treatment of edge magnetoplasmons (EMPs) is presented for very low temperatures and confining potentials smooth on the scale of the magnetic length 0 but sufficiently steep at the edges that Landau-level (LL) flattening can be discarded. The profile of the unperturbed electron density is sharp and the dissipation taken into account arises only from electron intra-edge and intra-LL transitions due to scattering by acoustic phonons. For wide channels and filling factors = 1 and 2, there exist independent EMP modes spatially symmetric and antisymmetric with respect to the edge. Some of these modes, named edge helicons, can propagate nearly undamped even when the dissipation is strong. Their density profile changes qualitatively during propagation and is given by a rotation of a complex vector function. For >2, the Coulomb coupling between the LLs leads to a repulsion of the uncoupled fundamental LL modes: the new modes have very different group velocities and are nearly undamped. The theory accounts well for the experimentally observed plateau structure of the delay times as well as for the spectral properties (phase and group velocities) of the EMPs and decay rates.

Soft Edge Magnetoplasmons in 2D Circular Pools of He 4 ions

The recent experimental discovery of anomalous soft edge magnetoplasmons (EMP) in 2D charged systems 1,2 and the problem of their identification requires an analysis of their physical nature. We consider three different scenarios for the appearance of soft EMP modes proposed by different authors. Our analysis indicates that the anomalous soft modes reported in Ref. 2 have the smooth variation of the charge density near the edge of the 2D system as their origin, although other satellite modes remain unexplained.

Edge magnetoplasmons 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 \ensuremath{\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 ${\mathcal{l}}_{0}$ 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 or 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 ${T}^{\ensuremath{-}3}$, 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 ${\mathcal{l}}_{0}$. The screening of the metallic gates, when present, is taken into account.

Evidence for the edge magnetoplasmon “Acoustic” mode in an electron layer over liquid helium

The spectrum of new modes of edge magnetoplasmons (EMP) in an electron layer over liquid helium was studied. The experiments were carried out in the temperature range 0.5–0.7 K at frequencies 0.87–1 MHz and electron density (1.5–3.5) ⋅ 1012 m−2 in a magnetic field up to 0.5 T. Besides conventional edge magnetoplasmons and the EMP mode connected with the displacement of the electron sheet boundary, a new “ acoustic” edge magnetoplasmon mode was observed in an electron layer over liquid helium for the first time. Spectrum of all three types of the magnetoplasmon modes are compared with the existing theories.

Pulse propagation in spin-polarized edge channels and at fractional filling factors

We have studied time-resolved transport in a two-dimensional electron gas in high magnetic fields. At filling factor v = 3, two edge magnetoplasmon modes appear which contribute to the transmission of negative pulses, whereas for positive pulses the signal is transmitted by only one collective mode. While the spreading of the potential just above v = 1 is not restricted to edge channels alone, a fast propagating signal in an edge mode was observed at filling factor v = 4/3.

Coupled modes and filling factor dependent edge potentials in double-layered antidot arrays

Double-layered antidot arrays have been prepared by deep mesa etching of modulation-doped Al x Ga 1− x As GaAs double-quantum-wells. In far infra-red transmission spectroscopy we observe a rich mode spectrum arising from collective optical (in phase) and acoustic (out of phase) oscillation in the two layers. In a magnetic field we find huge filling factor dependent oscillations of the frequency of the edge magnetoplasmon modes which are caused by self-consistent screening of the edge potential.

Soft edge magnetoplasmons in 2D systems with smooth density profile

Recent experimental discovery of novel soft edge magnetoplasmons (EMP) in a circular pool of He+ ions trapped below the surface of liquid helium [1] identified as the modes occurring due to smooth density profile [2] revived interest in the nature of low-frequency collective excitations in charged 2D systems placed in normal magnetic field. We consider various mechanisms which can be responsible for appearance of soft EMP modes.

Theory of electromagnetic response and collective excitations in antidots.

The theory of collective excitations in a single antidot and in a system of interacting antidots is presented. The problem is solved within the framework of classical electrodynamics neglecting the nonlocal and retardation effects. It is shown that the spectrum of collective excitations in a single antidot consists of two branches. The first mode coincides with the single-particle cyclotron resonance \ensuremath{\omega}=${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$; the second one is the edge magnetoplasmon (EMP) mode. The EMP mode has the vanishing damping (in the collisionless approximation) only at \ensuremath{\omega}${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$. At \ensuremath{\omega}>${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ it decays on account of emission of two-dimensional (2D) bulk magnetoplasmons to the surrounding 2D medium. The induced electric potential and charge density of the EMP mode have the form of outgoing cylindrical waves at \ensuremath{\omega}>${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$. As a consequence, the interantidot interaction cannot be neglected in an array of antidots at \ensuremath{\omega}>${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$. Collective excitations in an array of interacting antidots are considered in the modified-dipole and effective-medium approximations. The results obtained explain the main features of the antidot excitation spectrum observed in recent experiments.

Novel edge excitations of two-dimensional electron liquid in a magnetic field.

We investigate the low-energy spectrum of excitations of a compressible electron liquid in a strong magnetic field. These excitations are localized at the periphery of the system. The analysis of a realistic model of a smooth edge yields new branches of acoustic excitation spectrum in addition to the well known edge magnetoplasmon mode. The velocities are found and the observability conditions are established for the new modes.

Tunneling and anticrossing of edge magnetoplasmons in a quantum-dot superlattice.

We calculate edge magnetoplasmons for a superlattice of quantum dots where a uniform magnetic field is applied along the superlattice direction. The confinement is assumed parabolic. We find (a) anticrossing of the edge magnetoplasmon modes and (b) splitting of the tunneling magnetoplasmon branch. Similarities with experimental data for a quantum-dot array within a plane are discussed.