Quantum Hall Edge Channels Research Articles

Electronic Wave-Packets in Integer Quantum Hall Edge Channels: Relaxation and Dissipative Effects.

We theoretically investigate the evolution of the peak height of energy-resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor equal to two. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energies. We investigate this quantity assuming a short-range capacitive coupling between the edges. Moreover, we also phenomenologically take into account the possibility of energy dissipation towards additional degrees of freedom—both linear and quadratic—in the injection energy. Through a comparison with recent experimental data, we rule out the non-dissipative case as well as a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate for describing the behavior of the quasi-particle peak at short enough propagation lengths.

Gate-controlled unitary operation on flying spin qubits in quantum Hall edge states

Spin and orbital freedoms of electrons traveling on spin-resolved quantum Hall edge states (quantum Hall ferromagnets) are maximally entangled. The unitary operations on these two freedoms are hence equivalent, which means one can manipulate the spins with non-magnetic methods through the orbitals. If one takes the quantization axis of spins along the magnetization axis, the zenith angle is determined by the partition rate of spin-separated edges while the azimuth angle is defined as the phase difference between the edges. Utilizing these properties, we have realized electrically controlled unitary operation on the electron spins on the quantum Hall ferromagnets. The zenith angle of the spin was controlled through the radius of gyration at a corner by means of applying voltage to a thin gate placed at one edge. The subsequent rotation in the azimuth angle was controlled via the distance between the edge channels also by a gate voltage. The combination of the two operations constitutes the first systematic electric operation on spins in the quantum Hall edge channels.

Collisional interferometry of levitons in quantum Hall edge channels at ν=2

We consider a Hong-Ou-Mandel interferometer for Lorentzian voltage pulses applied to Quantum Hall edge channels at filling factor $\nu=2$. Due to inter-edge interactions, the injected electronic wave-packets fractionalize before partitioning at a quantum point contact. Remarkably enough, differently from what theoretically predicted and experimentally observed by using other injection techniques, we demonstrate that, when the injection occurs through time-dependent voltage pulses (arbitrarily shaped), the Hong-Ou-Mandel noise signal always vanishes for a symmetric device, and that a mismatch in the distances between the injectors and the point of collision is needed in order to reduce the visibility of the dip. We also show that, by properly tuning these distances or by applying different voltages on the two edge channels in each arm of the interferometer, it is possible to estimate the intensity of the inter-edge interaction. The voltage pulses are chosen of the Lorentzian type because of their experimental relevance.

Suppression of gate screening on edge magnetoplasmons by highly resistive ZnO gate

We investigate a way to suppress high-frequency coupling between a gate and low-dimensional electron systems in the gigahertz range by measuring the velocity of edge magnetoplasmons (EMPs) in InAs quantum Hall systems.We compare the EMPvelocity in three samples with different electromagnetic environments-one has a highly resistive zinc oxide (ZnO) top gate, another has a normal metal (Ti/Au) top gate, and the other does not have a gate. The measured EMP velocity in the ZnO gate sample is one order of magnitude larger than that in the Ti/Au gate sample and almost the same as that in the ungated sample. As is well known, the smaller velocity in the Ti/Au gate sample is due to the screening of the electric field in EMPs. The suppression of the gate screening effect in the ZnO gate sample allows us to measure the velocity of unscreened EMPs while changing the electron density. It also offers a way to avoid unwanted high-frequency coupling between quantum Hall edge channels and gate electrodes.

Quantum teleportation of single-electron states

We consider a scheme for on-demand teleportation of a dual-rail electron qubit state, based on single-electron sources and detectors. The scheme has a maximal efficiency of 25%, which is limited both by the shared entangled state as well as the Bell-state measurement. We consider two experimental implementations, realizable with current technology. The first relies on surface acoustic waves, where all the ingredients are readily available. The second is based on Lorentzian voltage pulses in quantum Hall edge channels. As single-electron detection is not yet experimentally established in these systems, we consider a tomographic detection of teleportation using current correlators up to (and including) third order. For both implementations we take into account environmental effects.

Influence of Coupling Strength Between a Magnetic Quantum Dot and Quantum Hall Edge Channels on Valley-isospin-dependent Dirac Fermion Transport

We investigate Dirac fermion transport through opposite quantum Hall edge channels in armchair graphene nanoribbons where a magnetic quantum dot (MQD) is placed between the edges. The resulting conductance shows distinguished resonant features according to the angle Φ between the valley isospins at the opposite edges. Particularly, for Φ = 0, the conductance exhibits a behavior characteristic of dissipative resonances when the edge—dot distance is sufficiently small even though the unitarity of the whole system is conserved. As the edge—dot distance increases, a crossover behavior emerges between two distinct regimes: largely perturbed and unperturbed MQD. Resonant energy converges to a specific energy corresponding to the eigenenergy of the localized states in the unperturbed MQD. For sufficiently weak couplings, a fine splitting of the conductance resonances is observed, of which splitting energy is several μeV. The finding of these finely split localized states in the MQD allows us to better elucidate related electronic and transport properties in graphene.

Ballistic hot-electron transport in a quantum Hall edge channel defined by a double gate

Ballistic transport of hot electrons in a quantum Hall edge channel is attractive for studying the electronic analog of quantum optics, where the edge potential profile is an important parameter that governs the charge velocity and scattering by longitudinal-optical (LO) phonons. Here, we use a parallel double gate to control the electric field of the edge potential and investigate the ballistic length of the channel by using hot-electron spectroscopy. The ballistic length is significantly enhanced by reducing the LO phonon scattering rate in the tailored potential.

Interaction-induced charge transfer in a mesoscopic electron spectrometer

A novel mesoscopic electron spectrometer allows for the probing of relaxation processes in quantum Hall edge channels. The device is composed of an emitter quantum dot that injects energy-resolved electrons into the channel closest to the sample edge, to be subsequently probed downstream by a detector quantum dot of the same type. In addition to inelastic processes in the sample that stem from interactions inside the region between the quantum dot energy filters (inner region), anomalous signals are measured when the detector energy exceeds the emitter energy. Considering finite range Coulomb interactions in the sample, we find that energy exchange between electrons in the current inducing source channel and the inner region, similar to Auger recombination processes, is responsible for such anomalous currents. In addition, our perturbative treatment of interactions shows that electrons emitted from the source, which dissipate energy to the inner region before entering the detector, contribute to the current most strongly when emitter-detector energies are comparable. Charge transfer in which the emitted electron is exchanged for a charge carrier from the Fermi sea, on the other hand, preferentially occurs close to the Fermi level.

Interaction-induced supercurrent in quantum Hall setups

Recently we have proposed an unusual mechanism of superconducting current that is specific for Quantum Hall Edge channels connected to superconducting electrodes. We have shown that the supercurrent can be mediated by a nonlocal electon-electon interaction that provide an opportunity for a long-distance information transfer in the direction opposite to the electron flow. A convenient model for such interaction is that of an external circuit. The consideration has been done for the case of a single channel. In this work, we extend these results to more sophisticated setups that include the scattering between Quantum Hall channels of opposite direction and multiple superconducting contacts. For a single Quantum Hall constriction, we derive a general and comprehensive relation for the interaction- induced supercurrent in terms of scattering amplitudes and demonstrate the non-local nature of the current by considering its sensitivity to scattering. We understand the phase dependences of the supercurrents in multi-terminal setups in terms of interference of Andreev reflection processes. For more complex setups encompassing at least two constrictions we find an interplay between non-interacting and interaction-induced currents and contibutions of complex interference processes.

Auger-spectroscopy in quantum Hall edge channels and the missing energy problem

Quantum Hall edge channels offer an efficient and controllable platform to study quantum transport in one dimension. Such channels are a prospective tool for the efficient transfer of quantum information at the nanoscale, and play a vital role in exposing intriguing physics. Electric current along the edge carries energy and heat leading to inelastic scattering, which may impede coherent transport. Several experiments attempting to probe the concomitant energy redistribution along the edge reported energy loss via unknown mechanisms of inelastic scattering. Here we employ quantum dots to inject and extract electrons at specific energies, to spectrally analyse inelastic scattering inside quantum Hall edge channels. We show that the missing energy puzzle could be untangled by incorporating non-local Auger-like processes, in which energy is redistributed between spatially separate parts of the sample. Our theoretical analysis, accounting for the experimental results, challenges common-wisdom analyses which ignore such non-local decay channels.

Splitting of conductance resonance through a magnetic quantum dot in graphene

We report a dual resonance feature in ballistic conductance through a quantum Hall graphene nanoribbon with a magnetic quantum dot. Such a magnetic quantum dot localizes Dirac fermions exhibiting anisotropic eigenenergy spectra with broken time-reversal symmetry. Interplay between the localized states and quantum Hall edge states is found to be two-fold, showing Breit-Wigner and Fano resonances, which is reminiscent of a double quantum dot system. By fitting the numerical results with the Fano-Breit-Wigner lineshape from the double quantum dot model, we demonstrate that the two-fold resonance is due to the valley mixing that comes from the coupling of the magnetic quantum dot with quantum Hall edge channels; an effective double quantum dot system emerges from a single magnetic quantum dot in virtue of the valley degree of freedom. It is further confirmed that the coupling is weaker for the Fano resonance and stronger for the Breit-Wigner resonace.

Nonlinear chiral refrigerators

We investigate a mesoscopic refrigerator based on chiral quantum Hall edge channels. We discuss a three-terminal cooling device in which charge transport occurs between a pair of voltage-biased terminals only. The third terminal, which is to be cooled, is set as a voltage probe with vanishing particle flux. This largely prevents the generation of direct Joule heating which ensures a high coefficient of performance. Cooling operation is based on energy-dependent quantum transmissions. The latter are implemented with the aid of two tunable scattering resonances (quantum dots). To find the optimal performance point and the largest temperature difference created with our refrigerator, it is crucial to address the nonlinear regime of transport, accounting for electron-electron interaction effects. Our numerical simulations show that the maximal cooling power can be tuned with the quantum dot couplings and energy levels. Further, we provide analytical expressions within a weakly nonlinear scattering-matrix formalism which allow us to discuss the conditions for optimal cooling in terms of generalized thermopowers. Our results are important for the assessment of chiral conductors as promising candidates for efficient quantum refrigerators with low dissipation.

Charge equilibration in integer and fractional quantum Hall edge channels in a generalized Hall-bar device

Charge equilibration between quantum-Hall edge states can be studied to reveal geometric structure of edge channels not only in the integer quantum Hall (IQH) regime but also in the fractional quantum Hall (FQH) regime particularly for hole-conjugate states. Here we report on a systematic study of charge equilibration in both IQH and FQH regimes by using a generalized Hall bar, in which a quantum Hall state is nested in another quantum Hall state with different Landau filling factors. This provides a feasible way to evaluate equilibration in various conditions even in the presence of scattering in the bulk region. The validity of the analysis is tested in the IQH regime by confirming consistency with previous works. In the FQH regime, we find that the equilibration length for counter-propagating $\delta \nu $ = 1 and $\delta \nu $ = -1/3 channels along a hole-conjugate state at Landau filling factor $\nu $ = 2/3 is much shorter than that for co-propagating $\delta \nu $ = 1 and $\delta \nu $ = 1/3 channels along a particle state at $\nu $ = 4/3. The difference can be associated to the distinct geometric structures of the edge channels. Our analysis with generalized Hall bar devices would be useful in studying edge equilibration and edge structures.

Spectroscopic study on hot-electron transport in a quantum Hall edge channel

Hot electron transport in a quantum Hall edge channel of an AlGaAs/GaAs heterostructure is studied by investigating the energy distribution function in the channel. Ballistic hot-electron transport, its optical-phonon replicas, weak electron-electron scattering, and electron-hole excitation in the Fermi sea are clearly identified in the energy spectra. The optical-phonon scattering is analyzed to evaluate the edge potential profile. We find that the electron-electron scattering is significantly suppressed with increasing the hot-electron's energy well above the Fermi energy. This can be understood with suppressed Coulomb potential with longer distance for higher energy. The results suggest that the relaxation can be suppressed further by softening the edge potential. This is essential for studying non-interacting chiral transport over a long distance.

Hong-Ou-Mandel characterization of multiply charged Levitons

We review and develop recent results regarding Leviton excitations generated in topological states of matter - such as integer and fractional quantum Hall edge channels - and carrying a charge multiple of the electronic one. The peculiar features associated to these clean and robust emerging excitations can be detected through current correlation measurements. In particular, relevant information can be extracted from the noise signal in generalized Hong-Ou-Mandel experiments, where Levitons with different charges collide against each other at a quantum point contact. We describe this quantity both in the framework of the photo-assisted noise formalism and in terms of a very interesting and transparent picture based on wave-packet overlap.

Taming electronic decoherence in one-dimensional chiral ballistic quantum conductors

Although interesting per se, decoherence and relaxation of single-electron excitations induced by strong effective screened Coulomb interactions in Quantum Hall edge channels are an important challenge for the applications of electron quantum optics in quantum information and quantum sensing. In this paper, we study intrinsic single-electron decoherence within an ideal single-electron channel with long-range effective Coulomb interactions to determine the influence of the material and sample properties. We find that weak-coupling materials characterized by a high velocity of hot-electron excitations may offer interesting perspectives for limiting intrinsic decoherence due to electron/electron interactions. We discuss quantitively how extrinsic decoherence due to the coupling with the channel's electromagnetic environment can be efficiently inhibited in specially designed samples at $\nu=2$ with one closed edge channel and we propose a realistic geometry for testing decoherence control in an Hong Ou Mandel experiment.

Coupling between quantum Hall edge channels on opposite sides of a Hall bar

We investigate the coupling between quantum Hall (QH) edge channels (ECs) located at opposite sides of a 50-μm-wide Hall bar by exciting a charged wavepacket in one EC and detecting time-dependent current in the other EC. In a QH state, the current shows a peak followed by a dip, demonstrating the existence of capacitive coupling across the incompressible two-dimensional electron system (2DES). The observed magnetic field dependence of the amplitude and time delay of the current suggests that the capacitance is affected by the presence of localized states. We also show that the dominant manner of the coupling changes gradually as the system changes between the QH and non-QH states.

Electronic energy spectroscopy of monochromatic edge magnetoplasmons in the quantum Hall regime

We investigate electronic excitation in a quantum Hall edge channel when a monochromatic plasmon wave is excited by applying a radio-frequency voltage to a long surface gate on an AlGaAs/GaAs heterostructure. A quantum-dot energy spectrometer is employed to evaluate the amplitude of the potential wave and possible electronic heating. The potential wave is analyzed with a capacitance model. Non-monotonic frequency dependence observed under specific conditions can be explained by destructive plasmon interference in the gated region. The observed small heating effect suggests that the single plasmon mode is dominantly excited with this scheme.

Tomonaga–Luttinger-liquid nature of edge excitations in integer quantum Hall edge channels

Abstract In interacting one-dimensional (1D) systems, the quasi-particle picture in Fermi-liquid theory cannot successfully describe low-energy physics. Instead, electron dynamics in one dimension can be described as collective excitations, i.e., charge- and/or spin-density waves, which are elementary excitations in a Tomonaga-Luttinger (TL) liquid. Integer quantum Hall (QH) edge channels, which are chiral 1D electron states formed along the periphery of integer QH systems, provide a unique opportunity for studying TL-liquid physics. When edge channels lie parallel to each other, inter-channel interactions induce significant TL-liquid behaviors in coupled plasmons. One can prepare an arbitrary number of co- and/or counter-propagating channels of spin-up or -down electrons to form such a multiple edge-channel system. The plasmon dynamics can be experimentally investigated by using various functional devices such as charge injectors, detectors, and spin filters to select spin and bidirectional-momentum degrees of freedom. This article reviews electron dynamics in such QH TL liquids. We first introduce the chiral distributed-element circuit model for describing interactions in single and multiple integer-edge-channel systems. This simple model captures the TL-liquid nature of the 1D plasmon transport. We then review experimental studies on TL-liquid behaviors. These experiments show that plasmon velocity is significantly enhanced by the intra-channel interaction. In addition, they show that co-propagating channels with spin degrees of freedom exhibit TL-liquid behavior known as spin-charge separation, in which spin and charge excitations behave differently. This is demonstrated with a novel time- and spin-resolved charge detection technique. They also reveal that charge fractionalization occurs at the boundaries of counter-propagating channels with bidirectional-momentum degrees of freedom. A charge excitation even as small as an electron charge is fractionalized into smaller charges to form coupled plasmons in the interacting region. These experiments highlight the intriguing quantum many-body nature of QH TL liquids.

On-demand electron source with tunable energy distribution

We propose a scheme to manipulate the electron–hole excitation in the voltage pulse electron source, which can be realized by a voltage-driven Ohmic contact connecting to a quantum hall edge channel. It has been known that the electron–hole excitation can be suppressed via Lorentzian pulses, leading to noiseless electron current. We show that, instead of the Lorentzian pulses, driven via the voltage pulse with duration t0, the electron–hole excitation can be tuned so that the corresponding energy distribution of the emitted electrons follows the Fermi distribution with temperature , with TS being the electron temperature in the Ohmic contact. Such Fermi distribution can be established without introducing additional energy relaxation mechanism and can be detected via shot noise thermometry technique, making it helpful in the study of thermal transport and decoherence in mesoscopic system.