Proposed measurement of an effective flux quantum in the fractional quantum Hall effect

Flux Superperiods and Periodicity Transitions in Quantum Hall Interferometers

For strongly screened Coulomb interactions, quantum Hall interferometers can operate in a novel regime: the intrinsic energy gap can be larger than the charging energy, and addition of flux quanta can occur without adding quasiparticles. We show that flux superperiods are possible and reconcile their appearance with the Byers-Yang theorem. We explain that the observation of anyonic statistical phases is possible by tuning to the transition from a regime with constant chemical potential to a regime with constant particle density, where a flux superperiod changes to a periodicity with one flux quantum at a critical magnetic field strength.

Nonequilibrated counterpropagating edge modes in the fractional quantum Hall regime

It is well established that density reconstruction at the edge of a two-dimensional electron gas takes place for hole-conjugate states in the fractional quantum Hall effect (such as v=2/3, 3/5, etc.). Such reconstruction leads, after equilibration between counterpropagating edge channels, to a downstream chiral current edge mode accompanied by upstream chiral neutral modes (carrying energy without net charge). Short equilibration length prevented thus far observation of the counterpropagating current channels-the hallmark of density reconstruction. Here, we provide evidence for such nonequilibrated counterpropagating current channels, in short regions (l=4  μm and l=0.4  μm) of fractional filling v=2/3 and, unexpectedly, v=1/3, sandwiched between two regions of integer filling v=1. Rather than a two-terminal fractional conductance, the conductance exhibited a significant ascension towards unity quantum conductance (GQ=e(2)/h) at or near the fractional plateaus. We attribute this conductance rise to the presence of a nonequilibrated channel in the fractional short regions.

Resonant tunneling in the quantum Hall regime: measurement of fractional charge

In experiments on resonant tunneling through a "quantum antidot" (a potential hill) in the quantum Hall (QH) regime, periodic conductance peaks were observed as a function of both magnetic field and back gate voltage. A combination of the two periods constitutes a measurement of the charge of the tunneling particles and implies that charge deficiency on the antidot is quantized in units of the charge of quasi-particles of the surrounding QH condensate. The experimentally determined value of the electron charge e is 1.57 x 10(-19) coulomb = (0.98 +/- 0.03) e for the states v = 1 and v = 2 of the integer QH effect, and the quasi-particle charge is 5.20 x 10(-20) coulomb = (0.325 +/- 0.01)e for the state v = (1/3) of the fractional QH effect.

Correlators and fractional statistics in the quantum Hall bulk

We derive one-particle and two-particle correlators of anyons in the lowest Landau level. We show that the two-particle correlator exhibits signatures of fractional statistics which can distinguish anyons from their fermionic and bosonic counterparts. These signatures include the zeros of the two-particle correlator and its exclusion behavior. We find that the one-particle correlator in finite geometries carries valuable information relevant to experiments in which quasiparticles on the edge of a quantum Hall system tunnel through its bulk.

Universal periods in quantum Hall droplets

Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.

Why should anyone care about computing with anyons?

In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behaviour and establish their relation to quantum computation. Possible directions for the physical realization of topological systems and the detection of anyonic behaviour are elaborated.

Aharanov-Bohm interference and fractional statistics in a quantum Hall interferometer

We compute the temperature, voltage, and magnetic field dependences of the conductance oscillations of a model interferometer designed to measure the fractional statistics of the quasiparticles in the fractional quantum Hall effect. The geometry is the same as that used in recent experiments. With appropriate assumptions concerning the relative areas of the inner and outer rings of the interferometer, we find the theoretical results, including the existence of super periodic Aharonov-Bohm oscillations, to be in remarkably good agreement with experiment. We then make additional experimental predictions with no adjustable parameters which, if verified, would confirm the proposed interpretation of the experiment as a measurement of fractional statistics.

Resonant tunneling in the fractional quantum Hall effect: superperiods and braiding statistics

We study theoretically resonant tunneling of composite fermions through their quasibound states around a fractional quantum Hall island, and find a rich set of possible transitions of the island state as a function of the magnetic field or the backgate voltage. These have possible relevance to a recent experimental study, and reveal many subtleties involved in deducing fractional braiding statistics.

Aharonov-Bohm superperiod in a Laughlin quasiparticle interferometer

We report an Aharonov-Bohm superperiod of five magnetic flux quanta (5h/e) observed in a Laughlin quasiparticle interferometer, where an edge channel of the 1/3 fractional quantum Hall fluid encircles an island of the 2/5 fluid. This result does not violate the gauge invariance argument of the Byers-Yang theorem because the magnetic flux, in addition to affecting the Aharonov-Bohm phase of the encircling 1/3 quasiparticles, creates the 2/5 quasiparticles in the island. The superperiod is accordingly understood as imposed by the anyonic statistical interaction of Laughlin quasiparticles.

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.

Telegraph noise and fractional statistics in the quantum Hall effect

We study theoretically nonequilibrium noise in the fractional quantum Hall regime for an Aharonov-Bohm ring with a third contact in the middle of the ring. Because of their fractional statistics the tunneling of Laughlin quasiparticles between the inner and outer edges of the ring changes the effective Aharonov-Bohm flux experienced by quasiparticles going around the ring, leading to a change in the conductance across the ring. A small current in the middle contact, therefore, gives rise to fluctuations in the current flowing across the ring which resemble random telegraph noise. We analyze this noise using the chiral Luttinger liquid model. At low frequencies the telegraph noise varies inversely with the tunneling current and can be much larger than the shot noise. We propose that combining the Aharonov-Bohm effect with a noise measurement provides a direct method for observing fractional statistics.