Scattering of bunched fractionally charged quasiparticles

Fractional charge and fractional statistics in the quantum Hall effects

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.

Progress in Cooling Nanoelectronic Devices to Ultra-Low Temperatures

Here we review recent progress in cooling micro-/nanoelectronic devices significantly below 10 mK. A number of groups worldwide are working to produce sub-millikelvin on-chip electron temperatures, motivated by the possibility of observing new physical effects and improving the performance of quantum technologies, sensors and metrological standards. The challenge is a longstanding one, with the lowest reported on-chip electron temperature having remained around 4 mK for more than 15 years. This is despite the fact that microkelvin temperatures have been accessible in bulk materials since the mid-twentieth century. In this review, we describe progress made in the last 5 years using new cooling techniques. Developments have been driven by improvements in the understanding of nanoscale physics, material properties and heat flow in electronic devices at ultralow temperatures and have involved collaboration between universities and institutes, physicists and engineers. We hope that this review will serve as a summary of the current state of the art and provide a roadmap for future developments. We focus on techniques that have shown, in experiment, the potential to reach sub-millikelvin electron temperatures. In particular, we focus on on-chip demagnetisation refrigeration. Multiple groups have used this technique to reach temperatures around 1 mK, with a current lowest temperature below 0.5 mK.

Microwave photons emitted by fractionally charged quasiparticles

Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge q and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage Vdc. We observe that only photons at frequencies f below qVdc/h are emitted. This threshold provides a direct and unambiguous determination of the charge q, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements.

Noise of a Chargeless Fermi Liquid

We construct a Fermi liquid theory to describe transport in a superconductor-quantum dot-normal metal junction close to the singlet-doublet (parity changing) transition of the dot. Though quasiparticles do not have a definite charge in this chargeless Fermi liquid, in the case of particle-hole symmetry, a mapping to the Anderson model unveils a hidden U(1) symmetry and a corresponding pseudocharge. In contrast to other correlated Fermi liquids, the back scattering noise reveals an effective charge equal to the charge of Cooper pairs, e^{*}=2e. In addition, we find a strong suppression of noise when the linear conductance is unitary, even for its nonlinear part.

Primary thermometry triad at 6 mK in mesoscopic circuits

Quantum physics emerge and develop as temperature is reduced. Although mesoscopic electrical circuits constitute an outstanding platform to explore quantum behaviour, the challenge in cooling the electrons impedes their potential. The strong coupling of such micrometre-scale devices with the measurement lines, combined with the weak coupling to the substrate, makes them extremely difficult to thermalize below 10 mK and imposes in situ thermometers. Here we demonstrate electronic quantum transport at 6 mK in micrometre-scale mesoscopic circuits. The thermometry methods are established by the comparison of three in situ primary thermometers, each involving a different underlying physics. The employed combination of quantum shot noise, quantum back action of a resistive circuit and conductance oscillations of a single-electron transistor covers a remarkably broad spectrum of mesoscopic phenomena. The experiment, performed in vacuum using a standard cryogen-free dilution refrigerator, paves the way towards the sub-millikelvin range with additional thermalization and refrigeration techniques.

Mesoscopic electrical circuits are an ideal platform to explore quantum phenomena, but this requires cooling the electrons to very low temperature, which is challenging. Here, the authors employ three different in situ thermometers to report electronic quantum transport at 6mK in a micrometer-scale circuit.

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.

The quantum Hall effect at 5/2 filling factor

Experimental discovery of a quantized Hall state at 5/2 filling factor presented an enigmatic finding in an established field of study that has remained an open issue for more than twenty years. In this review we first examine the experimental requirements for observing this state and outline the initial theoretical implications and predictions. We will then follow the chronology of experimental studies over the years and present the theoretical developments as they pertain to experiments, directed at sets of issues. These topics will include theoretical and experimental examination of the spin properties at 5/2; is the state spin polarized? What properties of the higher Landau levels promote development of the 5/2 state, what other correlation effects are observed there, and what are their interactions with the 5/2 state? The 5/2 state is not a robust example of the fractional quantum Hall effect: what experimental and material developments have allowed enhancement of the effect? Theoretical developments from initial pictures have promoted the possibility that 5/2 excitations are exceptional; do they obey non-abelian statistics? The proposed experiments to determine this and their executions in various forms will be presented: this is the heart of this review. Experimental examination of the 5/2 excitations through interference measurements will be reviewed in some detail, focusing on recent results that demonstrate consistency with the picture of non-abelian charges. The implications of this in the more general physics picture is that the 5/2 excitations, shown to be non-abelian, should exhibit the properties of Majorana operators. This will be the topic of the last review section.

Fabry-Perot interferometry with fractional charges

Resistance oscillations in electronic Fabry-Perot interferometers near fractional quantum Hall (FQH) filling factors 1/3, 2/3, 4/3, and 5/3 in the constrictions are compared to those near integer quantum Hall (IQH) filling factors in the same devices and at the same gate voltages. Two-dimensional plots of resistance versus gate voltage and magnetic field indicate that all oscillations are Coulomb dominated. A charging-model analysis of gate-voltage periods yields an effective tunneling charge e* ≈ e/3 for all FQH states and e* ≈ e for IQH states. Temperature decay of the oscillations appears exponential, qualitatively consistent with a recent prediction, and the surprising filling-factor dependence of the associated energy scale may shed light on edge structure.

Anomalous charge tunneling in fractional quantum Hall edge states at a filling factor ν=5/2

We explain effective charge anomalies recently observed for fractional quantum Hall edge states at ν=5/2 [M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Phys. Rev. B 81, 161303(R) (2010)]. The experimental data of differential conductance and excess noise are fitted, using the anti-Pfaffian model, by properly taking into account renormalizations of the Luttinger parameters induced by the coupling of the system with an intrinsic 1/f noise. We demonstrate that a peculiar agglomerate excitation with charge e/2, double the expected e/4 charge, dominates the transport properties at low energies.

Characterizing neutral modes of fractional states in the second Landau level

Fractionally charged quasiparticles, which obey non-abelian statistics, were predicted to exist in the ν=8/3, ν=5/2, and ν=7/3 fractional quantum Hall states (in the second Landau level). Here we present measurements of charge and neutral modes in these states. For both ν=7/3 and ν=8/3 states, we found a quasiparticle charge e=1/3 and an upstream neutral mode only in ν=8/3-excluding the possibility of non-abelian Read-Rezayi states and supporting Laughlin-like states. The absence of an upstream neutral mode in the ν=7/3 state also proves that edge reconstruction was not present in the ν=7/3 state, suggesting its absence also in ν=5/2 state, and thus may provide further support for the non-abelian anti-pfaffian nature of the ν=5/2 state.

Method for cooling nanostructures to microkelvin temperatures

We propose a new scheme aimed at cooling nanostructures to microkelvin temperature based on the well established technique of adiabatic nuclear demagnetization: we attach each device measurement lead to an individual nuclear refrigerator, allowing efficient thermal contact to a microkelvin bath. On a prototype consisting of a parallel network of nuclear refrigerators, temperatures of ∼1 mK simultaneously on ten measurement leads have been reached upon demagnetization, thus completing the first steps toward ultracold nanostructures.

Tuning nonlinear charge transport between integer and fractional quantum Hall states

Controllable point junctions between different quantum Hall phases are a necessary building block for the development of mesoscopic circuits based on fractionally charged quasiparticles. We demonstrate how particle-hole duality can be exploited to realize such point-contact junctions. We show an implementation for the case of two quantum Hall liquids at filling factors nu=1 and nu*<or=1 in which both the fractional filling nu* and the coupling strength can be finely and independently tuned. A peculiar crossover from insulating to conducting behavior as nu* goes from 1/3 to 1 is observed. These results highlight the key role played on interedge tunneling by local charge depletion at the point contact.

Electronic refrigeration of a two-dimensional electron gas

Measurements are presented of a device designed to cool a 6 microm;{2} region of 2D electron gas using quantum dots. Electrostatic effects are found to be significant in the device, and a model that accounts for them is developed. At ambient electron temperatures above 120 mK the results are consistent with the model and the base temperature of the cooled region is estimated. At an ambient electron temperature of 280 mK, the 6 microm;{2} region is found to be cooled below 190 mK. Below 120 mK the results deviate from predictions, which is attributed to reduced electron-electron scattering rates.

Relevance of multiple quasiparticle tunneling between edge states at nu=p/(2np+1)

We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series nu=p/(2np+1), for extremely weak backscattering and low temperatures [Y. C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. 91, 216804 (2003)10.1103/PhysRevLett.91.216804]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticle tunneling at low energies becomes the most relevant process. This result will be used to explain the experimental data on current noise where tunneling particles have a charge that can reach p times the single-quasiparticle charge. In this Letter, we analyze the conductance and the shot noise to substantiate quantitatively the proposed scenario.

Electron bunching in transport through quantum dots in a high magnetic field

Shot noise measurements provide information on particle charge and its correlations. We report on shot noise measurements in a generic quantum dot under a quantized magnetic field. The measured noise at the peaks of a sequence of conductance resonances was some 9 times higher than expected, suggesting bunching of electrons as they traverse through the dot. This enhancement might be mediated by an additional level, weakly coupled to the leads or an excited state. Note that in the absence of a magnetic filed no bunching had been observed.

Metal-insulator transition tuned by external gates in Hall systems with constrictions

The nature of a metal-insulator transition tuned by external gates in quantum Hall systems with point constrictions, as reported in recent experiments [S. Roddaro, Phys. Rev. Lett. 95, 156804 (2005)10.1103/PhysRevLett.95.156804], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Interchannel impurity scattering and interchannel Coulomb interactions do not destabilize this picture.

Signatures of fractional statistics in noise experiments in quantum Hall fluids

The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an "antibunching" effect.

Particle-hole symmetric Luttinger liquids in a quantum Hall circuit

We report current transmission data through a split-gate constriction fabricated onto a two-dimensional electron system in the integer quantum Hall (QH) regime. Split-gate biasing drives interedge backscattering and is shown to lead to suppressed or enhanced transmission, in marked contrast to the expected linear Fermi-liquid behavior. This evolution is described in terms of particle-hole symmetry and allows us to conclude that an unexpected class of gate-controlled particle-hole-symmetric chiral Luttinger liquids (CLLs) can exist at the edges of our QH circuit. These results highlight the role of particle-hole symmetry on the properties of CLL edge states.

Quasiparticle tunneling through a barrier in the fractional quantum hall regime

Tunneling of fractionally charged quasiparticles (QPs) through a barrier is considered in the context of a multiply connected geometry. In this geometry global constraints do not prohibit such a tunneling process. The tunneling amplitude is evaluated and the crossover from mesoscopic QP-dominated to electron-dominated tunneling as the system's size is increased is found. The presence of disorder enhances both electron and QP-tunneling rates.

Temperature dependence of the tunneling amplitude between quantum hall edges

Recent experiments have studied the tunneling current between the edges of a fractional quantum Hall liquid as a function of temperature and voltage. The results of the experiment are puzzling because at "high" temperature (600-900 mK) the behavior of the tunneling conductance is consistent with the theory of tunneling between chiral Luttinger liquids, but at low temperature it strongly deviates from that prediction dropping to zero with decreasing temperature. In this Letter we suggest a possible explanation of this behavior in terms of the strong temperature dependence of the tunneling amplitude.

Interactions suppress quasiparticle tunneling at Hall bar constrictions

Tunneling of fractionally charged quasiparticles across a two-dimensional electron system on a fractional quantum Hall plateau is expected to be strongly enhanced at low temperatures. This theoretical prediction is at odds with recent experimental studies of samples with weakly pinched quantum-point-contact constrictions in which the opposite behavior is observed. We argue here that this unexpected finding is a consequence of electron-electron interactions near the point contact.

Interedge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime

Gate-voltage control of interedge tunneling at a split-gate constriction in the fractional quantum Hall regime is reported. Quantitative agreement with the behavior predicted for out-of-equilibrium quasiparticle transport between chiral Luttinger liquids is shown at low temperatures at specific values of the backscattering strength. When the latter is lowered by changing the gate voltage, the zero-bias peak of the tunneling conductance evolves into a minimum, and a nonlinear quasiholelike characteristic emerges. Our analysis emphasizes the role of the local filling factor in the split-gate constriction region.