Scaling dimension of quantum Hall quasiparticles from tunneling-current noise measurements

Snizhko, Kyrylo; Cheianov, Vadim

doi:10.1103/physrevb.91.195151

Cited by 14 publications

(17 citation statements)

References 43 publications

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“…I repeat the analysis of the previous section for this case, fitting perturbative formula (27) (using the parameters corresponding to the experimental ones) with phenomenological formula (28). A typical resulting fit is shown in Fig.…”

Section: ν = 2/5: System Temperature Dependence Of the Effective mentioning

confidence: 84%

“…At the same time the Fano factor (21) stays constant since κ = κ 3 /(κ 1 + κ 2 ) is independent of I n . This suggests that the true origin of the reported effective charge dependence on I n is the use of phenomenological formula (28) for the analysis of experimental data, and is not related to the non-universal behavior of the tunneling amplitudes, nor to complications in the ν = 2/3 edge theory (for example, like the ones proposed in Refs. [12,14]).…”

Section: ν = 2/3: Neutral Mode Heating and Behavior Of The Effectimentioning

confidence: 93%

“…Therefore, the most generally applicable approach is to treat the tunneling Hamiltonian (8) as a small perturbation. Then in the lowest non-trivial order of perturbation theory one obtains the following results [15,28] where T 0 is the equilibrium system temperature, I s is the current injected into Source S, λ = λ(I n ) is related to the upper edge heating due to injection of current I n (the upper edge temperature at near the QPC is T = λT 0 ), e is the elementary charge, h = 2π is the Planck constant, k B is the Boltzmann constant, ν is the filling factor,…”

Section: Tunneling Experiments In the Fqhe: The Modelmentioning

confidence: 97%

“…1.8 nA). The red curve is a fit of these points by phenomenological formula (28). The dashed cyan curve is the large-Is asymptote of the perturbative theory.…”

Section: ν = 2/3: Neutral Mode Heating and Behavior Of The Effectimentioning

confidence: 99%

“…In some cases the latter approach allows one to describe the data for both tunneling rate and noise very well using a finite number of fitting parameters [11][12][13]. Whether it For such a case, it has been argued in [15,28] that instead of considering r andS(0) separately, it is advantageous to consider their ratio (noise to tunneling rate ratio, NtTRR)…”

Section: Tunneling Experiments In the Fqhe: The Modelmentioning

confidence: 99%

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Tunneling current noise in the fractional quantum Hall effect: When the effective charge is not what it appears to be

Snizhko

2016

Low Temperature Physics

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Fractional quantum Hall quasiparticles are famous for having fractional electric charge. Recent experiments report that the quasiparticles' effective electric charge determined through tunneling current noise measurements can depend on the system parameters such as temperature or bias voltage. Several works proposed to understand this as a signature for edge theory properties changing with energy scale. I consider two of such experiments and show that in one of them the apparent dependence of the electric charge on a system parameter is likely to be an artefact of experimental data analysis. Conversely, in the second experiment the dependence cannot be explained in such a way.

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Section: ν = 2/5: System Temperature Dependence Of the Effective mentioning

confidence: 84%

Section: ν = 2/3: Neutral Mode Heating and Behavior Of The Effectimentioning

confidence: 93%

Section: Tunneling Experiments In the Fqhe: The Modelmentioning

confidence: 97%

“…1.8 nA). The red curve is a fit of these points by phenomenological formula (28). The dashed cyan curve is the large-Is asymptote of the perturbative theory.…”

Section: ν = 2/3: Neutral Mode Heating and Behavior Of The Effectimentioning

confidence: 99%

Section: Tunneling Experiments In the Fqhe: The Modelmentioning

confidence: 99%

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Tunneling current noise in the fractional quantum Hall effect: When the effective charge is not what it appears to be

Snizhko

2016

Low Temperature Physics

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Observation of the scaling dimension of fractional quantum Hall anyons

Veillon,

Piquard,

Glidic

et al. 2024

Nature

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Unconventional quasiparticles emerging in the fractional quantum Hall regime1,2 present the challenge of observing their exotic properties unambiguously. Although the fractional charge of quasiparticles has been demonstrated for nearly three decades3–5, the first convincing evidence of their anyonic quantum statistics has only recently been obtained6,7 and, so far, the so-called scaling dimension that determines the propagation dynamics of the quasiparticles remains elusive. In particular, although the nonlinearity of the tunnelling quasiparticle current should reveal their scaling dimension, the measurements fail to match theory, arguably because this observable is not robust to non-universal complications8–12. Here we expose the scaling dimension from the thermal noise to shot noise crossover and observe an agreement with expectations. Measurements are fitted to the predicted finite-temperature expression involving both the scaling dimension of the quasiparticles and their charge12,13, in contrast to previous charge investigations focusing on the high-bias shot-noise regime14. A systematic analysis, repeated on several constrictions and experimental conditions, consistently matches the theoretical scaling dimensions for the fractional quasiparticles emerging at filling factors ν = 1/3, 2/5 and 2/3. This establishes a central property of fractional quantum Hall anyons and demonstrates a powerful and complementary window into exotic quasiparticles.

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Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

2022

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Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge Q and scaling dimension ∆. For the simplest states (such as the Laughlin series) the scaling dimension determines the quasiparticle's anyonic statistics (the statistical phase θ = 2π∆). For more complicated states (featuring counterpropagating modes or non-Abelian statistics) knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases knowing the scaling dimension facilitates distinguishing different candidate theories for describing the quantum Hall state at a particular filling (such as PH-Pfaffian and anti-Pfaffian at ν = 5/2). Here we propose a scheme for extracting the scaling dimension of quantum Hall quasiparticles from thermal tunneling noise produced at a quantum point contact. Our scheme makes only minimal assumptions about the edge structure and features the level of robustness, simplicity, and model independence comparable to extracting the quasiparticle charge from tunneling shot noise.

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Scaling dimension of quantum Hall quasiparticles from tunneling-current noise measurements

Cited by 14 publications

References 43 publications

Tunneling current noise in the fractional quantum Hall effect: When the effective charge is not what it appears to be

Tunneling current noise in the fractional quantum Hall effect: When the effective charge is not what it appears to be

Observation of the scaling dimension of fractional quantum Hall anyons

Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

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