Fractional charges on an integer quantum Hall edge

Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime

Fractionalization is a phenomenon where an elementary excitation partitions into several pieces. This picture explains non-trivial transport through a junction of one-dimensional edge channels defined by topologically distinct quantum Hall states, for example, a hole-conjugate state at Landau-level filling factor ν = 2/3. Here we employ a time-resolved scheme to identify an elementary fractionalization process; injection of charge q from a non-interaction region into an interacting and scattering region of one-dimensional channels results in the formation of a collective excitation with charge (1-r)q by reflecting fractionalized charge rq. The fractionalization factors, r = 0.34 ± 0.03 for ν = 2/3 and r = 0.49 ± 0.03 for ν = 2, are consistent with the quantized values of 1/3 and 1/2, respectively, which are expected in the disorder dominated regime. The scheme can be used for generating and transporting fractionalized charges with a well-defined time course along a well-defined path.

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.

Superconducting Correlations Out of Repulsive Interactions on a Fractional Quantum Hall Edge

We consider a fractional quantum Hall bilayer system with an interface between quantum Hall states of filling fractions (ν_{top},ν_{bottom})=(1,1) and (1/3,2), motivated by a recent approach to engineering artificial edges [Y. Ronen et al., Nat. Phys. 14, 411 (2018)NPAHAX1745-247310.1038/s41567-017-0035-2]. We show that random tunneling and strong repulsive interactions within one of the layers will drive the system to a stable fixed point with two counterpropagating charge modes which have attractive interactions. As a result, slowly decaying correlations on the edge become predominantly superconducting. We discuss the resulting observable effects and derive general requirements for electron attraction in Abelian quantum Hall states. The broader interest in fractional quantum Hall edge with quasi-long-range superconducting order lies in the prospects of hosting exotic anyonic boundary excitations, which may serve as a platform for topological quantum computation.

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.

Signatures of a Nonthermal Metastable State in Copropagating Quantum Hall Edge Channels

A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a nonequilibrium many-body state survives without relaxing to a thermalized state. This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor ν=2. The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states. The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer. We find strong evidence for a nonthermal metastable state in agreement with the TL theory before the system relaxes to thermal equilibrium with coupling to the environment.

Coherent control of single electrons: a review of current progress

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

Minimal Excitations in the Fractional Quantum Hall Regime

We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury Brown-Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.

Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization

Coulomb interaction has a striking effect on electronic propagation in one-dimensional conductors. The interaction of an elementary excitation with neighbouring conductors favours the emergence of collective modes, which eventually leads to the destruction of the Landau quasiparticle. In this process, an injected electron tends to fractionalize into separated pulses carrying a fraction of the electron charge. Here we use two-particle interferences in the electronic analogue of the Hong-Ou-Mandel experiment in a quantum Hall conductor at filling factor 2 to probe the fate of a single electron emitted in the outer edge channel and interacting with the inner one. By studying both channels, we analyse the propagation of the single electron and the generation of interaction-induced collective excitations in the inner channel. These complementary pieces of information reveal the fractionalization process in the time domain and establish its relevance for the destruction of the quasiparticle, which degrades into the collective modes.

A charge injected into the edge of a correlated one-dimensional system can split into separate charge packages. Freulon et al. now study this electron fractionalization on the picosecond timescale using Hong-Ou-Mandel interferometry.

Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state

We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T(1)(1-T(1)) over a wide range of T(1), where T(1) is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.

Real-time decoherence of Landau and Levitov quasiparticles in quantum Hall edge channels

Quantum Hall edge channels at integer filling factor provide a unique test bench to understand the decoherence and relaxation of single-electron excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoherence scenario of energy (Landau)- and time (Levitov)-resolved single-electron excitations at filling factor ν = 2. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel-type experiments to probe specific signatures of these different scenarios.

Charge fractionalization in the integer quantum Hall effect

We report an observation, via sensitive shot noise measurements, of charge fractionalization of chiral edge electrons in the integer quantum Hall effect regime. Such fractionalization results solely from interchannel Coulomb interaction, leading electrons to decompose to excitations carrying fractional charges. The experiment was performed by guiding a partitioned current carrying edge channel in proximity to another unbiased edge channel, leading to shot noise in the unbiased edge channel without net current, which exhibited an unconventional dependence on the partitioning. The determination of the fractional excitations, as well as the relative velocities of the two original (prior to the interaction) channels, relied on a recent theory pertaining to this measurement. Our result exemplifies the correlated nature of multiple chiral edge channels in the integer quantum Hall effect regime.

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* (refs 6, 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.

Interactions and charge fractionalization in an electronic Hong-Ou-Mandel interferometer

We consider an electronic analog of the Hong-Ou-Mandel (HOM) interferometer, where two single electrons travel along opposite chiral edge states and collide at a quantum point contact. Studying the current noise, we show that because of interactions between copropagating edge states, the degree of indistinguishability between the two electron wave packets is dramatically reduced, leading to reduced contrast for the HOM signal. This decoherence phenomenon strongly depends on the energy resolution of the packets. Insofar as interactions cause charge fractionalization, we show that charge and neutral modes interfere with each other, leading to satellite dips or peaks in the current noise. Our calculations explain recent experimental results [E. Bocquillon Science 339 1054 (2013)] where an electronic HOM signal with reduced contrast was observed.

Shot-noise signatures of charge fractionalization in the ν=2 quantum Hall edge

We investigate the effect of interactions on shot noise in ν=2 quantum Hall edges, where a repulsive coupling between copropagating edge modes is expected to give rise to charge fractionalization. Using the method of nonequilibrium bosonization, we find that even asymptotically the edge distribution function depends in a sensitive way on the interaction strength between the edge modes. We compute shot noise and the Fano factor from the asymptotic distribution function, and from comparison with a reference model of fractionalized excitations, we find that the Fano factor can be close to the value of the fractionalized charge.

Charge fractionalization in biased bilayer graphene

Fractional charge may arise when fermionic zero modes exist in a topological background field. In biased bilayer graphene (BBLG), the bias plays the role of the nontrivial background field. When semi-infinite BBLG with a zigzag edge is used, the dynamics induces an odd number of zero-energy modes, which, together with the conjugation symmetry between positive- and negative-energy states, are the requisite conditions for fractionalization. Exploiting the trigonal interaction to isolate a given zero-energy mode on the zigzag edge, we consider extended and localized modes (the latter being obtained from a localized wavepacket generated by prior irradiation of the sample with an electromagnetic vortex). The valley degeneracy is lifted by a layer asymmetry, while an edge-induced spin polarization breaks the spin degeneracy. We describe scenarios for the detection of charge-1/2 edge states.

Electron quantum optics: partitioning electrons one by one

We have realized a quantum optics like Hanbury Brown-Twiss (HBT) experiment by partitioning, on an electronic beam splitter, single elementary electronic excitations produced one by one by an on-demand emitter. We show that the measurement of the output currents correlations in the HBT geometry provides a direct counting, at the single charge level, of the elementary excitations (electron-hole pairs) generated by the emitter at each cycle. We observe the antibunching of low energy excitations emitted by the source with thermal excitations of the Fermi sea already present in the input leads of the splitter, which suppresses their contribution to the partition noise. This effect is used to probe the energy distribution of the emitted wave packets.

Fractionalization noise in edge channels of integer quantum Hall states

A theoretical calculation is presented of current noise which is due charge fractionalization, in two interacting edge channels in the integer quantum Hall state at filling factor ν=2. Because of the capacitive coupling between the channels, a tunneling event, in which an electron is transferred from a biased source lead to one of the two channels, generates propagating plasma mode excitations which carry fractional charges on the other edge channel. When these excitations impinge on a quantum point contact, they induce low-frequency current fluctuations with no net average current. A perturbative treatment in the weak tunneling regime yields analytical integral expressions for the noise as a function of the bias on the source. Asymptotic expressions of the noise in the limits of high and low bias are found.

Energy partitioning of tunneling currents into Luttinger liquids

Tunneling of electrons of definite chirality into a quantum wire creates counterpropagating excitations, carrying both charge and energy. We find that the partitioning of energy is qualitatively different from that of charge. The partition ratio of energy depends on the excess energy of the tunneling electrons (controlled by the applied bias) and on the interaction strength within the wire (characterized by the Luttinger-liquid parameter κ), while the partitioning of charge is fully determined by κ. Moreover, unlike for charge currents, the partitioning of energy current should manifest itself in dc experiments on wires contacted by conventional (Fermi-liquid) leads.

Full counting statistics of a Luttinger liquid conductor

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.

Cooper-pair injection into quantum spin Hall insulators

We theoretically study tunneling of Cooper pairs from a superconductor spanning a two-dimensional topological insulator strip into its helical edge states. The coherent low-energy electron-pair tunneling sets off positive current cross correlations along the edges, which reflect an interplay of two quantum-entanglement processes. Most importantly, superconducting spin pairing dictates a Cooper pair partitioning into the helical edge liquids, which transport electrons in opposite directions for opposite spin orientations. At the same time, Luttinger-liquid correlations fractionalize electrons injected at a given edge into counterpropagating charge pulses carrying definite fractions of the elementary electron charge.