Influence of Interactions on Flux and Back-Gate Period of Quantum Hall Interferometers

“…Furthermore, the size of the interferometers was not varied, nor was a Fourier analysis performed of the AB oscillations that could yield an estimation of l ϕ [12]. Quantum dot systems also implicate the possible interplay of Coulomb Blockade effects [13]. The Mach-Zender interferometers (MZI) [2,4,6] used in the present study do not suffer from the same limitations.…”

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confidence: 99%

Direct Measurement of the Coherence Length of Edge States in the Integer Quantum Hall Regime

et al. 2008

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We have determined the finite temperature coherence length of edge states in the Integer Quantum Hall Effect (IQHE) regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at filling factor 2. The visibility shows an exponential decay with the temperature. The characteristic temperature scale is found inversely proportional to the length of the interferometer arm, allowing to define a coherence length lϕ. The variations of lϕ with magnetic field are the same for all samples, with a maximum located at the upper end of the quantum hall plateau. Our results provide the first accurate determination of lϕ in the quantum Hall regime.PACS numbers: 03.65. Yz, 73.43.Fj, 73.23.Ad The understanding of the decoherence process is a major issue in solid state physics, especially in view of controlling entangled states for quantum information purposes. The edge states of the quantum Hall effect are known to present an extremely long coherence length l ϕ at low temperature [1], providing a useful tool for quantum interference experiments [2,3,4,5,6]. Surprisingly, very little is known on the exact value of this length and the mechanisms which reduce the coherence of edge states. This is in strong contrast with diffusive conductors, where weak localisation gives a powerful way to probe l ϕ . It has been shown, in this case, that electronelectron interactions are responsible for the finite coherence length at low temperatures. In the IQHE regime, the presence of a high magnetic field destroys any time reversal symmetry needed for weak localisation corrections, making such an investigation difficult. Furthermore, due to the uni-dimensionality of the edge states, electron-electron interactions may strongly modify the single particle picture and one can ask wether the notion of phase coherence length is still relevant and how it depends on temperature. In this letter, we show for the first time that one can define a phase coherence length, and that it is inversely proportional to the temperature. Though the energy redistribution length has been studied in the past [7,8],these scattering experiments do not measure the phase coherence, which requires observation of electron interference effects. So far, experiments have only been able to put a lower bound on l ϕ at low temperatures [2, 9, 10, 11]. The electronic Fabry-Pérot interferences occurring in ballistic quantum dots have been used since the early days of mesoscopic physics [9]. These first studies showed an exponential decay of the amplitude of the Aharonov-Bohm (AB) oscillations with temperature [10]. However, this decay was attributed to thermal smearing due to the contribution of thermally activated one particle energy levels of the dot. Furthermore, the size of the interferometers was not varied, nor was a Fourier analysis performed of the AB oscillations that could yield an estimation of l ϕ [12]. Quantum dot systems also implicate the possible interplay of Coulomb Blockade effects [13]. The Mach-Zender interf...

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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.…”

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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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Influence of Interactions on Flux and Back-Gate Period of Quantum Hall Interferometers

Cited by 120 publications

References 16 publications

Edge reconstruction in fractional quantum Hall states

Edge reconstruction in fractional quantum Hall states

Direct Measurement of the Coherence Length of Edge States in the Integer Quantum Hall Regime

Coulomb Blockade of Anyons in Quantum Antidots

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