Aharonov-Bohm Superperiod in a Laughlin Quasiparticle Interferometer

Zhou, Wei; Goldman, V. J.

doi:10.1103/physrevlett.95.246802

Cited by 111 publications

(139 citation statements)

References 26 publications

(52 reference statements)

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“…Recently, direct observation of anyonic statistics has been claimed 39,40 and much indirect experimental evidence is also available. Anyons with non-Abelian braiding are also expected to exist at filling fraction = 5 2 and predicted at a number of other filling fractions, including = 12 5 .…”

Section: Non-abelian Hall Statesmentioning

confidence: 99%

“…Experimental probes of topological systems ͑notably quantum-Hall systems͒ that have been proposed in recent years include measurements of the tunneling current at point contacts and especially interferometric measurements of tunneling currents through double point contacts. [29][30][31][32][33][34][35][36][37][38] Experiments with double point contacts have in fact recently been performed, both for Hall states with Abelian topological order 39,40 and for presumably non-Abelian Hall states. 6,7 The tunneling current at a single point contact in a Hall system is dominated at weak tunneling by the quasiparticle with the lowest scaling dimension.…”

Section: Contact With Experimentsmentioning

confidence: 99%

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Condensate-induced transitions between topologically ordered phases

2009

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We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetrybreaking phase transitions which applies to phases with topological excitations described by quantum groups or modular tensor categories. This enables us to deal with phases whose quasiparticles have noninteger quantum dimensions and obey braid statistics. Many examples of such phases can be constructed from two-dimensional rational conformal field theories, and we find that there is a beautiful connection between quantum group symmetry breaking and certain well-known constructions in conformal field theory, notably the coset construction, the construction of orbifold models, and more general conformal extensions. Besides the general framework, many representative examples are worked out in detail.

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Section: Non-abelian Hall Statesmentioning

confidence: 99%

Section: Contact With Experimentsmentioning

confidence: 99%

Condensate-induced transitions between topologically ordered phases

2009

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“…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.…”

mentioning

confidence: 99%

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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“…The "anyons" and "exclusions" result from the interaction of the original bosons and fermions and could not be found asymptotically free in the nature, like the gentileons. Recently, according to Camino [28] the existence of anyons ("Laughlin particle" with fractionary charge) has been confirmed in the context of the fractional quantum Hall effect. More information about this experimental confirmation is given by Lindley [29].…”

Section: Discussionmentioning

confidence: 99%

Quantum statistics: the indistinguishability principle and the permutation group theory

Cattani¹

2007

Rev. Bras. Ens. Fis.

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About two decades ago we have shown mathematically that besides bosons and fermions, it could exist a third kind of particles in nature that was named gentileons. Our results have been obtained rigorously within the framework of quantum mechanics and the permutation group theory. However, these papers are somewhat intricate for physicists not familiarized with the permutation group theory. In the present paper we show in details, step by step, how to obtain our theoretical predictions. This was done in order to permit a clear understanding of our approach by graduate students with a basic knowledge of group theory. Keywords: quantum statistics; bosons, fermions and gentileons.Há cerca de duas décadas passadas, mostramos matematicamente que, além de bósons e férmions, poderia existir na natureza um outro tipo de partículas que denominamos de gentileons. Os nossos resultados foram obtidos rigorosamente dentro do contexto da mecânica quântica e da teoria do grupo de permutações. Entretanto, os nossos artigos são difíceis de serem entendidos por físicos que não estão familiarizados com a teoria do grupo de permutações. Assim, no presente artigo nós vamos mostrar em detalhes, passo a passo, como obter as nossas previsões. Procedemos desse modo para permitir que estudantes de graduação de física possam entender claramente nossos cálculos com um conhecimento básico de teoria de grupos. Palavras-chave: estatística quântica; bósons, férmions, gentileons.

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Aharonov-Bohm Superperiod in a Laughlin Quasiparticle Interferometer

Cited by 111 publications

References 26 publications

Condensate-induced transitions between topologically ordered phases

Condensate-induced transitions between topologically ordered phases

Coulomb Blockade of Anyons in Quantum Antidots

Quantum statistics: the indistinguishability principle and the permutation group theory

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