Resonant Tunneling in the Quantum Hall Regime: Measurement of Fractional Charge

Goldman, V. J.; Su, Bo

doi:10.1126/science.267.5200.1010

Cited by 288 publications

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“…The fractional quasiparticle charge was observed in experiments on antidot tunneling [4] and shot-noise measurements [5,6]. The situation with fractional statistics is so far less certain even in the case of the abelian statistics, which is the subject of this work.…”

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confidence: 97%

“…In this work, we show that coherent quasiparticle dynamics in multiantidot structures should provide clear signatures of the exchange statistics in dc transport. Most notably, in tunneling through a line of three antidots, fractional statistics leads to a non-vanishing peak of the tunnel conductance which would vanish for integer statistics.These effects rely on the ability of quantum antidots to localize individual quasiparticles of the QH liq- uids [4,14,15]. The resulting transport phenomena in antidots are very similar to those associated with the Coulomb blockade [16] in tunneling of individual electrons in dots.…”

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confidence: 99%

“…These effects rely on the ability of quantum antidots to localize individual quasiparticles of the QH liq- uids [4,14,15]. The resulting transport phenomena in antidots are very similar to those associated with the Coulomb blockade [16] in tunneling of individual electrons in dots.…”

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confidence: 99%

“…The resulting transport phenomena in antidots are very similar to those associated with the Coulomb blockade [16] in tunneling of individual electrons in dots. For instance, similarly to a quantum dot [19], the linear conductance of one antidot shows periodic oscillations with each period corresponding to the addition of one quasiparticle [4,14,15,17,18]. Recently, we have developed a theory of such Coulomb-blockade-type tunneling for a double-antidot system [20], where quasiparticle exchange statistics does not affect the transport.…”

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Coulomb Blockade of Anyons in Quantum Antidots

Averin

Nesteroff

2007

Phys. Rev. Lett.

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Coulomb interaction turns anyonic quasiparticles of a primary quantum Hall liquid with filling factor ν = 1/(2m + 1) into hard-core anyons. We have developed a model of coherent transport of such quasiparticles in systems of multiple antidots by extending the Wigner-Jordan description of 1D abelian anyons to tunneling problems. We show that the anyonic exchange statistics manifests itself in tunneling conductance even in the absence of quasiparticle exchanges. In particular, it can be seen as a non-vanishing resonant peak associated with quasiparticle tunneling through a line of three antidots. [5,6]. The situation with fractional statistics is so far less certain even in the case of the abelian statistics, which is the subject of this work. Although the recent experiments [7] demonstrating unusual flux periodicity of conductance of a quasiparticle interferometer can be interpreted as a manifestation of the fractional statistics [8,9], this interpretation is not universally accepted [10,11]. There is a number of theoretical proposals (see, e.g., [12,13]) suggesting tunnel structures where the statistics manifests itself through noise properties. Partly due to complexity of noise measurements, such experiments have not been performed successfully up to now. In this work, we show that coherent quasiparticle dynamics in multiantidot structures should provide clear signatures of the exchange statistics in dc transport. Most notably, in tunneling through a line of three antidots, fractional statistics leads to a non-vanishing peak of the tunnel conductance which would vanish for integer statistics.These effects rely on the ability of quantum antidots to localize individual quasiparticles of the QH liq- uids [4,14,15]. The resulting transport phenomena in antidots are very similar to those associated with the Coulomb blockade [16] in tunneling of individual electrons in dots. For instance, similarly to a quantum dot [19], the linear conductance of one antidot shows periodic oscillations with each period corresponding to the addition of one quasiparticle [4,14,15,17,18]. Recently, we have developed a theory of such Coulomb-blockade-type tunneling for a double-antidot system [20], where quasiparticle exchange statistics does not affect the transport. The goal of this work is to extend this theory to antidot structures where the statistics does affect the conductance. The two simplest structures with this property consist of three antidots and have quasi-1D geometries with either periodic or open boundary conditions (Fig. 1). A technical issue that needed to be resolved to calculate the tunnel conductance is that the anyonic field operators defined through the Wigner-Jordan transformation [21,22,23,24], are not fully sufficient in the situations of tunneling. As we show below, to obtain correct matrix elements for anyon tunneling, one needs to keep track of the appropriate boundary conditions of the wavefunctions which are not accounted for in the field operators.Specifically, we consider the antidots coupled by tunneli...

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Coulomb Blockade of Anyons in Quantum Antidots

Averin

Nesteroff

2007

Phys. Rev. Lett.

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“…1. In this geometry, the tunneling processes at two point contacts interfere and statistics of tunneling quasiparticles directly affects the dc current.If the two filling factors are equal, ν 0 = ν 1 ≡ ν, as in experiments [4], strong tunneling leads to formation of a closed edge between the points x 1 and x 2 encircling the antidot and separated from external edges of the surrounding uniform QHL [10]. Quasiparticles of charge νe can then tunnel between the external edges * on leave from St. Petersburg State Polytechnical University, Center for Advanced Studies, St. Petersburg 195251, Russia.…”

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Antidot tunneling between quantum Hall liquids with different filling factors

Ponomarenko

Averin

2005

Phys. Rev. B

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We consider tunneling through two point contacts between two edges of Quantum Hall liquids of different filling factors ν0,1 = 1/(2m0,1 + 1) with m0 − m1 ≡ m > 0. Properties of the antidot formed between the point contacts in the strong-tunneling limit are shown to be very different from the ν0 = ν1 case, and include vanishing average total current in the two contacts and quasiparticles of charge e/m. For m > 1, quasiparticle tunneling leads to non-trivial m-state dynamics of effective flux through the antidot which restores the regular "electron" periodicity of the current in flux despite the fractional charge and statistics of quasiparticles. [2]. Although the quasiparticles are defined most simply in the incompressible bulk of the FQHL, in the lowenergy transport experiments, quasiparticles are created typically at the liquid edges, e.g. by tunneling between them. In the simplest case of FQHL with the filling factor ν = 1/odd, the quasiparticles that tunnel through the liquid between its edges coincide with the quasiparticles in the bulk [3] and their fractional charge νe can be measured experimentally [4,5]. So far, fractional statistics of quasiparticle has not been directly observed in experiments, although there is experimental [6] and theoretical [7] interest to manifestations of this statistics in the noise correlators of the tunnel currents.Strong tunneling between edges of FQHLs with different filling factors should create quasiparticles which are different from those in the bulk of the liquids but still have fractional charge and statistics [8,9]. Untill now, such tunneling has been considered only in the geometry of a single point contact [8] or multiple contacts [9] for which the interference between different contacts is not important (i.e., the edges do not form closed loops). The purpose of this work is to study an "antidot" tunnel junction: two separate point contacts at points x 1 , x 2 along the x-axis between two single-mode edges of QHLs with different filling factors ν 0,1 = 1/(2m 0,1 + 1) with m 0 > m 1 ≥ 0 -see Fig. 1. In this geometry, the tunneling processes at two point contacts interfere and statistics of tunneling quasiparticles directly affects the dc current.If the two filling factors are equal, ν 0 = ν 1 ≡ ν, as in experiments [4], strong tunneling leads to formation of a closed edge between the points x 1 and x 2 encircling the antidot and separated from external edges of the surrounding uniform QHL [10]. Quasiparticles of charge νe can then tunnel between the external edges * on leave from St. Petersburg State Polytechnical University, Center for Advanced Studies, St. Petersburg 195251, Russia. through the antidot. As shown below, the situation is very different for ν 0 = ν 1 , and the antidot formed between the point contacts does not decouple completely from external edges even in the limit of strong tunneling. As a result, the total tunnel current between the two QHLs vanishes in this limit. Also, interference between the two contacts produces the quasiparticles of charge e...

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Electronic correlation in the quantum Hall regime

Kasner¹

2002

Ann. Phys.

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Two-dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many-particle ground state and its excitations are studied in detail at fractional filling factors for spin-polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.

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Resonant Tunneling in the Quantum Hall Regime: Measurement of Fractional Charge

Cited by 288 publications

References 27 publications

Coulomb Blockade of Anyons in Quantum Antidots

Coulomb Blockade of Anyons in Quantum Antidots

Antidot tunneling between quantum Hall liquids with different filling factors

Electronic correlation in the quantum Hall regime

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