Quantum Hall Edge Channels Research Articles

Impact of potential and temperature fluctuations on charge and heat transport in quantum Hall edges in the heat Coulomb blockade regime

We present a broad study of charge and heat transport in a mesoscopic system where one or several quantum Hall edge channels are strongly coupled to a floating Ohmic contact (OC). It is well-known that charge-current fluctuations emanating from the OC along the edge channels are highly susceptible to the OC charge capacitance in the heat Coulomb blockade regime (an impeded ability of the OC to equilibrate edge channels). Here, we demonstrate how potential and temperature fluctuations due to finite OC charge and heat capacities impact the heat-current fluctuations emitted from the OC. First, by assuming an infinite OC heat capacity, we show that the output heat-current noise is strongly dependent on the OC charge capacitance, following from a close relation between one-dimensional charge and heat currents. When also the OC heat capacity is finite, an interplay of potential and temperature fluctuations influences the heat transport. Concretely, we find that the effect of the charge capacitance on heat transport manifests in terms of a strongly increased energy relaxation time in the heat Coulomb blockade regime. Furthermore, we find expressions for a broad set of output observables, such as charge and heat auto- and cross correlations, as functions of input and OC fluctuations, depending on the relation between charge and energy relaxation times compared to the frequency of fluctuations and inverse (local) temperatures as well as on the number of edge channels attached to the OC. Finally, we show that a finite OC heat capacity transforms the full counting statistics of the output charge from Gaussian to non-Gaussian. Our findings provide opportunities to experimentally probe and harness the quantum nature of heat transport in strongly coupled electron circuits. Published by the American Physical Society 2024

Emission and coherent control of Levitons in graphene

Flying qubits encode quantum information in propagating modes instead of stationary discrete states. Although photonic flying qubits are available, the weak interaction between photons limits the efficiency of conditional quantum gates. Conversely, electronic flying qubits can use Coulomb interactions, but the weaker quantum coherence in conventional semiconductors has hindered their realization. In this work, we engineered on-demand injection of a single electronic flying qubit state and its manipulation over the Bloch sphere. The flying qubit is a Leviton propagating in quantum Hall edge channels of a high-mobility graphene monolayer. Although single-shot qubit readout and two-qubit operations are still needed for a viable manipulation of flying qubits, the coherent manipulation of an itinerant electronic state at the single-electron level presents a highly promising alternative to conventional qubits.

Evidence for chiral supercurrent in quantum Hall Josephson junctions.

Hybridizing superconductivity with the quantum Hall (QH) effect has notable potential for designing circuits capable of inducing and manipulating non-Abelian states for topological quantum computation1-3. However, despite recent experimental progress towards this hybridization4-15, concrete evidence for a chiral QH Josephson junction16-the elemental building block for coherent superconducting QH circuits-is still lacking. Its expected signature is an unusual chiral supercurrent flowing in QH edge channels, which oscillates with a specific 2ϕ0 magnetic flux periodicity16-19 (ϕ0 = h/2e is the superconducting flux quantum, where h is the Planck constant and e is the electron charge). Here we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit a chiral supercurrent, visible up to 8 T and carried by the spin-degenerate edge channel of the QH plateau of resistance h/2e2 ≈ 12.9 kΩ. We observe reproducible 2ϕ0-periodic oscillations of the supercurrent, which emerge at a constant filling factor when the area of the loop formed by the QH edge channel is constant, within a magnetic-length correction that we resolve in the data. Furthermore, by varying the junction geometry, we show that reducing the superconductor/normal interface length is crucial in obtaining a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface19-22. Our findings are important for the exploration of correlated and fractional QH-based superconducting devices that host non-Abelian Majorana and parafermion zero modes23-32.

Absence of edge reconstruction for quantum Hall edge channels in graphene devices.

Quantum Hall (QH) edge channels propagating along the periphery of two-dimensional (2D) electron gases under perpendicular magnetic field are a major paradigm in physics. However, groundbreaking experiments that could use them in graphene are hampered by the conjecture that QH edge channels undergo a reconstruction with additional nontopological upstream modes. By performing scanning tunneling spectroscopy up to the edge of a graphene flake on hexagonal boron nitride, we show that QH edge channels are confined to a few magnetic lengths at the crystal edges. This implies that they are ideal 1D chiral channels defined by boundary conditions of vanishing electronic wave functions at the crystal edges, hence free of electrostatic reconstruction. We further evidence a uniform charge carrier density at the edges, incompatible with the existence of upstream modes. This work has profound implications for electron and heat transport experiments in graphene-based systems and other 2D crystalline materials.

Non-thermal Tomonaga-Luttinger liquid eventually emerging from hot electrons in the quantum Hall regime

Dynamics of integrable systems, such as Tomonaga-Luttinger (TL) liquids, is deterministic, and the absence of stochastic thermalization processes provides unique characteristics, such as long-lived non-thermal metastable states with many conserved quantities. Here, we show such non-thermal states can emerge even when the TL liquid is excited with extremely high-energy hot electrons in chiral quantum-Hall edge channels. This demonstrates the robustness of the integrable model against the excitation energy. Crossover from the single-particle hot electrons to the many-body TL liquid is investigated by using on-chip detectors with a quantum point contact and a quantum dot. The charge dynamics can be understood with a single-particle picture only for hot electrons. The resulting electron-hole plasma in the TL liquid shows a non-thermal metastable state, in which warm and cold electrons coexist without further thermalization. The multi-temperature constituents are attractive for transporting information with conserved quantities along the channels.

Thermal transport imaging in the quantum Hall edge channel

Research focused on heat transport in the quantum Hall (QH) edge channel has successfully addressed fundamental theoretical questions surrounding the QH physics. However, the picture of the edge channel is complicated by the phenomenon of energy dissipation out of the edge, and theories treating this dissipation are lacking. More experimental data is also needed to determine the coupling mechanism by which energy leaves the edge channel. We developed a method to map the heat transport in the QH edge to study the dissipation of heat. We locally heated the QH edge and locally detected the temperature increase while continuously varying the distance between heater and thermometer. We thereby obtained the thermal decay length of the edge state.

Half-Mirror for Electrons in Quantum Hall Copropagating Edge Channels in a Mach-Zehnder Interferometer

A half-mirror that divides a spin-polarized electron into two parallel copropagating spin-resolved quantum Hall edge channels one half each is presented in this study. The partition process is coherent, as confirmed by observing the Aharonov-Bohm oscillation at high visibility of up to 85% in a Mach-Zehnder interferometer, which comprises two such half-mirrors. The coherence length of the interferometer exceeds $200\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$, which reflects the robust nature of the copropagating channels against the decoherence caused by the coupling to the environment. In addition, the device characteristics are highly stable, making the device promising in the application of quantum information processing. The beam-splitting process is theoretically modeled, and the numerical simulation successfully reproduces the experimental observation. The partition of the electron accompanied by the spin rotation is explained by the angular momentum transfer from the orbital to the spin via spin-orbit interactions.

Electric-dipole spin resonance and spin orbit coupling effects in odd-integer quantum Hall edge channels

Structural-inversion-asymmetry effects on charge carriers can be described by a spin-orbit (Rashba) effective magnetic field. The direction of this field is fixed by the carrier momentum and axis of asymmetry - properties that form the basis of the spin transistor. The authors have used a sensitive terahertz magnetophotoresponse method to probe electrons in an asymmetric quantum well of InAs in the integer quantum-Hall-effect regime. Remarkable multiple-line spin-resonance spectra are attributed to oppositely directed Rashba fields of electrons in counterpropagating quasi-one-dimensional channels on opposite sample edges. Similar effects might lead to ultrafast electric-field control of spins for any spin-polarized topological edge channels.

In-flight detection of few electrons using a singlet-triplet spin qubit

We investigate experimentally the capacitive coupling between a two-electron singlet-triplet spin qubit and flying electrons propagating in quantum Hall edge channels. After calibration of the spin qubit detector, we assess its charge sensibility and demonstrate experimentally the detection of less than five flying electrons with average measurement. This experiment demonstrates that the spin qubit is an ultrasensitive and fast charge detector with the perspective of a future single shot-detection of a single flying electron. This work opens the route toward quantum electron optics experiments at the single electron level in semiconductor circuits.

Heat Equilibration of Integer and Fractional Quantum Hall Edge Modes in Graphene.

Hole-conjugate states of the fractional quantum Hall effect host counterpropagating edge channels which are thought to exchange charge and energy. These exchanges have been the subject of extensive theoretical and experimental works; in particular, it is yet unclear if the presence of integer quantum Hall edge channels stemming from fully filled Landau levels affects heat equilibration along the edge. In this Letter, we present heat transport measurements in quantum Hall states of graphene demonstrating that the integer channels can strongly equilibrate with the fractional ones, leading to markedly different regimes of quantized heat transport that depend on edge electrostatics. Our results allow for a better comprehension of the complex edge physics in the fractional quantum Hall regime.

Interplay between topological valley and quantum Hall edge transport

An established way of realising topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene intriguingly, even in the absence of a magnetic field, topologically protected electronic states can emerge at naturally occurring stacking domain walls. While individually both types of topologically protected states have been investigated, their intriguing interplay remains poorly understood. Here, we focus on the interplay between topological domain wall states and quantum Hall edge transport within the eight-fold degenerate zeroth Landau level of high-quality suspended bilayer graphene. We find that the two-terminal conductance remains approximately constant for low magnetic fields throughout the distinct quantum Hall states since the conduction channels are traded between domain wall and device edges. For high magnetic fields, however, we observe evidence of transport suppression at the domain wall, which can be attributed to the emergence of spectral minigaps. This indicates that stacking domain walls potentially do not correspond to a topological domain wall in the order parameter.

Double-charge quantum island in the quasiballistic regime

Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device that has been experimentally achieved quite recently, with two floating islands connected to three edge channels via quantum point contacts in the integer quantum Hall regime. At high transparency of the quantum point contacts, we establish a mapping to the boundary sine-Gordon model and thereby reveal the nature of the quantum critical point. We deduce from this mapping universal expressions for the conductance and noise, in agreement with the experimental findings, and discuss the competition between Kondo-like screening of each individual island and the cooperative transfer of electrons between them. We further predict that the device operated at finite voltage bias produces fractional charges ${e}^{*}=e/3$ and propose a generalization to $N$ islands with the fractional charge ${e}^{*}=e/(N+1)$.

Nonuniform heat redistribution among multiple channels in the integer quantum Hall regime

Heat transport in multiple quantum-Hall edge channels at Landau-level filling factor nu = 2, 4, and 8 is investigated with a quantum point contact as a heat generator and a quantum dot as a local thermometer. Heat distribution among the channels remains highly non-uniform, which can be understood with the plasmon eigenmodes of the multiple channels. The heat transport can be controlled with another quantum point contact as a quantized heat valve, as manifested by stepwise increases of heat current at the thermometer. This encourages developing integrated heat circuits with quantum-Hall edge channels.

Counterpropagating topological and quantum Hall edge channels

The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a counterpropagating quantum Hall edge channel for magnetic fields at which the transition to the insulating regime is expected. For larger fields, we observe only the quantum Hall edge channel with transverse resistance close to h/e2. By tuning the disorder using different fabrication processes, we find evidence that this unexpected ν = 1 plateau originates from extended quantum Hall edge channels along a continuous network of charge puddles at the edges of the device.

Nonequilibrium Charge Dynamics of Tomonaga–Luttinger Liquids in Quantum Hall Edge Channels

AbstractTomonaga–Luttinger liquids exhibit unique features that cannot be seen in ordinary Fermi liquids. Recent advancement in measurement techniques on 1D quantum Hall edge channels allows to reveal unique characteristics, such as spin‐charge separation and nonthermal metastable states. In this review, an overview of nonequilibrium dynamics in quantum‐Hall Tomonaga–Luttinger liquids is presented. After the introduction of a circuit model for collective excitations (bosons) in the system, transport eigenmodes in interaction‐ and disorder‐dominated regimes are discussed with time‐resolved charge measurements for the integer and fractional quantum Hall systems. Moreover, nonthermal steady states associated with the integrable model are studied with energy distribution functions obtained with a quantum dot spectrometer. These nontrivial dynamics can be extended to other 1D systems, including 2D topological insulators.

Erratum: Plasmon modes of coupled quantum Hall edge channels in the presence of disorder-induced tunneling [Phys. Rev. B 103 , 165302 (2021)

Erratum: Plasmon modes of coupled quantum Hall edge channels in the presence of disorder-induced tunneling [Phys. Rev. B <b>103</b> , 165302 (2021)

Suppression of the radiation squeezing in interacting quantum Hall edge channels

We study the quantum fluctuations of the two quadratures of the emitted electromagnetic radiation generated by a quantum Hall device in a quantum point contact geometry. In particular, we focus our attention on the role played by the unavoidable electron–electron interactions between the two edge channels at filling factor two. We investigate quantum features of the emitted microwave radiation, such as squeezing, by studying the current fluctuations at finite frequency, accessible through a two-filters set-up placed just after the quantum point contact. We compare two different drives, respectively a cosine and a train of Lorentzian pulses, used for the injection of the excitations into the system. In both cases quantum features are reduced due to the interactions, however the Lorentzian drive is still characterized by a robust squeezing effect which can have important application on quantum information.

Quantum Hall Valley Splitters and a Tunable Mach-Zehnder Interferometer in Graphene.

Graphene is a very promising test bed for the field of electron quantum optics. However, a fully tunable and coherent electronic beam splitter is still missing. We report the demonstration of electronic beam splitters in graphene that couple quantum Hall edge channels having opposite valley polarizations. Theelectronic transmission of our beam splitters can be tuned from zero to near unity. By independently setting the beam splitters at the two corners of a graphene p-n junction to intermediate transmissions, we realize a fully tunable electronic Mach-Zehnder interferometer. This tunability allows us to unambiguously identify the quantum interferences due to the Mach-Zehnder interferometer, and to study their dependence with the beam-splitter transmission and the interferometer bias voltage. The comparison with conventional semiconductor interferometers points toward universal processes driving the quantum decoherence in those two different 2D systems, with graphene being much more robust to their effect.

Plasmon modes of coupled quantum Hall edge channels in the presence of disorder-induced tunneling

Coupled quantum Hall edge channels show intriguing non-trivial modes, for example, charge and neutral modes at Landau level filling factors 2 and 2/3. We propose an appropriate and effective model with Coulomb interaction and disorder-induced tunneling characterized by coupling capacitances and tunneling conductances, respectively. This model explains how the transport eigenmodes, within the interaction- and disorder-dominated regimes, change with the coupling capacitance, tunneling conductance, and measurement frequency. We propose frequency- and time-domain transport experiments, from which eigenmodes can be determined using this model.

A tunable Fabry-Pérot quantum Hall interferometer in graphene.

Electron interferometry with quantum Hall edge channels in semiconductor heterostructures can probe and harness the exchange statistics of anyonic excitations. However, charging effects present in semiconductors often obscured the Aharonov-Bohm interference in quantum Hall interferometers and make advanced charge screening strategies necessary. Here, we show that high-mobility monolayer graphene constitutes an alternative material system, not affected by charging effects, to perform Fabry-Pérot quantum Hall interferometry in the integer quantum Hall regime. In devices equipped with gate-tunable quantum point contacts acting on the edge channels of the zeroth Landau level, we observe high-visibility Aharonov-Bohm interference widely tunable through electrostatic gating or magnetic field, in agreement with theory. A coherence length of 10 μm at a temperature of 0.02 K allows us to further achieve coherently-coupled double Fabry-Pérot interferometry. In future, quantum Hall interferometry with graphene devices may enable investigations of anyonic excitations in fractional quantum Hall states.