Integer Quantum Hall Edge Research Articles

Nonlocal transport of heat in equilibrium drift-diffusion systems

The amount of heat an integer quantum Hall edge state can carry in equilibrium is quantized in universal units of the heat flux quantum ${J}_{q}=\frac{\ensuremath{\pi}{k}_{B}^{2}}{12\ensuremath{\hbar}}{T}^{2}$ per edge state. We address the question of how heat transport in realistic one-dimensional devices can differ from the usual chiral Luttinger liquid theory. We show that a local measurement can reveal a nonquantized amount of heat carried by the edge states, despite a globally equilibrium situation. More specifically, we report a heat enhancement effect in edge states interacting with Ohmic reservoirs in the presence of nonlocal interactions or chirality-breaking diffusive currents. In contrast to a nonequilibrium, nonlinear drag effect, we report an equilibrium, linear phenomenon. The chirality of the edge states creates additional correlations between the reservoirs, reflected in a higher-than-quantum heat flux in the chiral channel. We show that for different types of coupling the enhancement can be understood as static or dynamical back action of the reservoirs on the chiral channel. We show that our results qualitatively hold by replacing the dissipative Ohmic reservoirs by an energy-conserving mesoscopic capacitor and consider the respective transmission lines for different types of interaction.

Vortex-enabled Andreev processes in quantum Hall–superconductor hybrids

Quantum Hall--superconductor heterostructures provide possible platforms for intrinsically fault-tolerant quantum computing. Motivated by several recent experiments that successfully integrated these phases, we investigate transport through a proximitized integer quantum Hall edge---paying particular attention to the impact of vortices in the superconductor. By examining the downstream conductance, we identify regimes in which subgap vortex levels mediate Andreev processes that would otherwise be frozen out in a vortex-free setup. Moreover, we show that at finite temperature, and in the limit of a large number of vortices, the downstream conductance can average to zero, indicating that the superconductor effectively behaves like a normal contact. Our results highlight the importance of considering vortices when using transport measurements to study superconducting correlations in quantum Hall--superconductor hybrids.

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.

Induced Superconducting Pairing in Integer Quantum Hall Edge States.

Indium arsenide (InAs) near surface quantum wells (QWs) are promising for the fabrication of semiconductor-superconductor heterostructures given that they allow for a strong hybridization between the two-dimensional states in the quantum well and the ones in the superconductor. In this work, we present results for InAs QWs in the quantum Hall regime placed in proximity of superconducting NbTiN. We observe a negative downstream resistance with a corresponding reduction of Hall (upstream) resistance, consistent with a very high Andreev conversion. We analyze the experimental data using the Landauer-Büttiker formalism, generalized to allow for Andreev reflection processes. We attribute the high efficiency of Andreev conversion in our devices to the large transparency of the InAs/NbTiN interface and the consequent strong hybridization of the QH edge modes with the states in the superconductor.

Transmission line approach to transport of heat in chiral systems with dissipation

Measurements of the energy relaxation in the integer quantum Hall edge at filling factor $\ensuremath{\nu}=2$ suggest the breakdown of heat current quantization [H. le Sueur et al., Phys. Rev. Lett. 105, 056803 (2010)]. It was shown in a hydrodynamic model that dissipative neutral modes contributing apparently less than a quantum of heat can be an explanation for the missing heat flux [A. Goremykina et al., arXiv:1908.01213]. This hydrodynamic model relies on the introduction of an artificial high-energy cutoff and lacks a way of a priori obtaining the correct definition of the heat flux. In this work we overcome these limitations and present a formalism, effectively modeling dissipation in the quantum Hall edge, proving the quantization of heat flux for all modes. We mapped the quantum Hall edge to a transmission line by analogy and used the Langevin equations and scattering theory to extract the heat current in the presence of dissipation.

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.

Fractional Mutual Statistics on Integer Quantum Hall Edges.

Fractional charge and statistics are hallmarks of low-dimensional interacting systems such as fractional quantum Hall (QH) systems. Integer QH systems are regarded as noninteracting, yet they can have fractional charge excitations when they couple to another interacting system or time-dependent voltages. Here, we notice Abelian fractional mutual statistics between such a fractional excitation and an electron, and propose a setup for detection of the statistics in which a fractional excitation is generated at a source and injected to a Mach-Zehnder interferometer (MZI) in the integer QH regime. In a parameter regime, the dominant interference process involves braiding, via double exchange, between an electron excited at an MZI beam splitter and the fractional excitation. The braiding results in the interference phase shift by the phase angle of the mutual statistics. This proposal for directly observing the fractional mutual statistics is within experimental reach.

Anyons in multichannel Kondo systems

Fractionalized quasiparticles - anyons - bear a special role in present-day physics. At the same time, they display properties of interest both foundational, with quantum numbers that transcend the spin-statistics laws, and applied, providing a cornerstone for decoherence-free quantum computation. The development of platforms for realization and manipulation of these objects, however, remains a challenge. Typically these entail the zero-temperature ground-state of incompressible, gapped fluids. Here, we establish a strikingly different approach: the development and probing of anyon physics in a gapless fluid. The platform of choice is a chiral, multichannel, multi-impurity realization of the Kondo effect. We discuss how, in the proper limit, anyons appear at magnetic impurities, protected by an asymptotic decoupling from the fluid and by the emerging Kondo length scale. We discuss possible experimental realization schemes using integer quantum Hall edges. The gapless and charged degrees of freedom coexistent with the anyons suggest the possibility of extracting quantum information data by transport and simple correlation functions. To show that this is the case, we generalize the fusion ansatz of Cardy's boundary conformal field theory, now in the presence of multiple localized perturbations. The generalized fusion ansatz captures the idea that multiple impurities share quantum information non-locally, in a way formally identical to anyonic zero modes. We display several examples supporting and illustrating this generalization and the extraction of quantum information data out of two-point correlation functions. With the recent advances in mesoscopic realizations of multichannel Kondo devices, our results imply that exotic anyon physics may be closer to reach than presently imagined.

Disordered contacts can localize chiral edge electrons

Chiral integer quantum Hall (QH) edge modes are immune to backscattering and therefore are non-localized and show a vanishing longitudinal as well as non-local resistance along with quantized 2-terminal and Hall resistance even in presence of sample disorder. However, this is not the case for contact disorder, which refers to the possibility that a contact can reflect edge modes either partially or fully. This paper shows that when all contacts are disordered in a N-terminal quantum Hall bar, then transport via chiral QH edge modes can have a significant localization correction. The Hall and 2-terminal resistance in an N-terminal quantum Hall sample deviate from their values derived while neglecting the phase acquired at disordered contacts, and this deviation is called the quantum localization correction. This correction term increases with the increase of disorderedness of contacts but decreases with the increase in number of contacts in an N-terminal Hall bar. The presence of inelastic scattering, however, can completely destroy the quantum localization correction.

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.

Interaction Effects and Charge Quantization in Single-Particle Quantum Dot Emitters.

We discuss a theoretical model of an on-demand single-particle emitter that employs a quantum dot, attached to an integer or fractional quantum Hall edge state. Via an exact mapping of the model onto the spin-boson problem we show that Coulomb interactions between the dot and the chiral quantum Hall edge state, unavoidable in this setting, lead to a destruction of precise charge quantization in the emitted wave packet. Our findings cast doubt on the viability of this setup as a single-particle source of quantized charge pulses. We further show how to use a spin-boson master equation approach to explicitly calculate the current pulse shape in this setup.

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.

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.

Two-terminal transport along a proximity-induced superconducting quantum Hall edge

We study electric transport along an integer quantum Hall edge where the proximity effect is induced due to a coupling to a superconductor. Such an edge exhibits two Majorana-Weyl fermions with different group velocities set by the induced superconducting pairing. We show that this structure of the spectrum results in interference fringes that can be observed in both the two-terminal conductance and shot noise. We develop a complete analytical theory of such fringes for an arbitrary smooth profile of the induced pairing.

Tunable transmission of quantum Hall edge channels with full degeneracy lifting in split-gated graphene devices

Charge carriers in the quantum Hall regime propagate via one-dimensional conducting channels that form along the edges of a two-dimensional electron gas. Controlling their transmission through a gate-tunable constriction, also called quantum point contact, is fundamental for many coherent transport experiments. However, in graphene, tailoring a constriction with electrostatic gates remains challenging due to the formation of p–n junctions below gate electrodes along which electron and hole edge channels co-propagate and mix, short circuiting the constriction. Here we show that this electron–hole mixing is drastically reduced in high-mobility graphene van der Waals heterostructures thanks to the full degeneracy lifting of the Landau levels, enabling quantum point contact operation with full channel pinch-off. We demonstrate gate-tunable selective transmission of integer and fractional quantum Hall edge channels through the quantum point contact. This gate control of edge channels opens the door to quantum Hall interferometry and electron quantum optics experiments in the integer and fractional quantum Hall regimes of graphene.

Universality and quantized response in bosonic mesoscopic tunneling

We show that tunneling involving bosonic wires and/or boson integer quantum Hall (bIQH) edges is characterized by universal features which are absent in their fermionic counterparts. Considering a pair of minimal geometries, we find a low energy enhancement and a universal high versus zero energy relation for the tunnel conductance that holds for all wire/bIQH edge combinations. Features distinguishing bIQH edges include a current imbalance to chemical potential bias ratio that is quantized despite the lack of conductance quantization in the bIQH edges themselves. The predicted phenomena require only initial states to be thermal and thus are well suited for tests with ultracold bosons forming wires and bIQH states. For the latter, we highlight a potential realization based on single component bosons in the recently observed Harper-Hofstadter bandstructure.

Equilibration in a chiral Luttinger liquid

We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with nonlinear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature $T$ or weakly interacting bosons at high $T$. We calculate the equilibration rate which is found to scale with temperature as ${T}^{5}$ and ${T}^{14}$ in the high-temperature (``bosonic'') and the low-temperature (``fermonic'') regimes, respectively. The relaxation rate of a hot particle with the momentum $k$ in the fermonic regime scales as ${k}^{7}{T}^{7}$.

Probing theν=23fractional quantum Hall edge by momentum-resolved tunneling

The nature of the fractional quantum Hall state with filling factor $\nu=2/3$ and its edge modes continues to remain an open problem in low-dimensional condensed matter physics. Here, we suggest an experimental setting to probe the $\nu=2/3$ edge by tunnel-coupling it to a $\nu=1$ integer quantum Hall edge in another layer of a two-dimensional electron gas (2DEG). In this double-layer geometry, the momentum of tunneling electrons may be boosted by an auxiliary magnetic field parallel to the two planes of 2DEGs. We evaluate the current as a function of bias voltage and the boosting magnetic field. Its threshold behavior yields information about the spectral function of the $\nu=2/3$ edge, in particular about the nature of the chiral edge modes. Our theory accounts also for the effects of Coulomb interaction and disorder.

Fractionalized wave packets from an artificial Tomonaga–Luttinger liquid

The model of interacting fermion systems in one dimension known as a Tomonaga-Luttinger liquid (TLL) provides a simple and exactly solvable theoretical framework that predicts various intriguing physical properties. Evidence of a TLL has been observed as power-law behaviour in electronic transport on various types of one-dimensional conductor. However, these measurements, which rely on d.c. transport involving electron tunneling processes, cannot identify the long-awaited hallmark of charge fractionalization, in which an injection of elementary charge e from a non-interacting lead is divided into the non-trivial effective charge e* and the remainder, e-e* (refs6, 7, 8). Here, we report time-resolved transport measurements on an artificial TLL composed of coupled integer quantum Hall edge channels, in which we successfully identify single charge fractionalization processes. A wave packet of charge q incident from a non-interacting region breaks up into several fractionalized charge wave packets at the edges of the artificial TLL, from which transport eigenmodes can be evaluated directly. These results are informative for elucidating the nature of TLLs and low-energy excitations in the edge channels.

Imaging the Conductance of Integer and Fractional Quantum Hall Edge States

We measure the conductance of a quantum point contact (QPC) while the biased tip of a scanning probe microscope induces a depleted region in the electron gas underneath. At finite magnetic field we find plateaus in the real-space maps of the conductance as a function of tip position at integer (\nu=1,2,3,4,6,8) and fractional (\nu=1/3,2/3,5/3,4/5) values of transmission. They resemble theoretically predicted compressible and incompressible stripes of quantum Hall edge states. The scanning tip allows us to shift the constriction limiting the conductance in real space over distances of many microns. The resulting stripes of integer and fractional filling factors are rugged on the micron scale, i.e. on a scale much smaller than the zero-field elastic mean free path of the electrons. Our experiments demonstrate that microscopic inhomogeneities are relevant even in high-quality samples and lead to locally strongly fluctuating widths of incompressible regions even down to their complete suppression for certain tip positions. The macroscopic quantization of the Hall resistance measured experimentally in a non-local contact configuration survives in the presence of these inhomogeneities, and the relevant local energy scale for the \nu=2 state turns out to be independent of tip position.