Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers

Nakamura, James; Liang, Shuang; Gardner, G. C.; Manfra, Michael J.

doi:10.1038/s41467-022-27958-w

Cited by 19 publications

(8 citation statements)

References 69 publications

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“…4c and 4d. The voltage 𝑉 𝑃𝐺 values at which the phase jumps occur do not depend on the magnetic field, unlike what is observed for the GaAs FPIs 10,11 . Focusing on the constant density trajectory, , (Fig.…”

Section: Tunability Between Constant Filling and Constant Densitymentioning

confidence: 61%

“…Electron-based interferometry in the framework of the FQHE has advanced considerably during the last two decades in the GaAs/AlGaAs heterostructure platform grown by Molecular beam epitaxial (MBE) [10][11][12][13][14][15] . The two main interferometers are the Mach-Zehnder interferometer (MZI) 13,[16][17][18][19] and the Fabry-Pérot interferometer (FPI) 8,[10][11][12][20][21][22][23] .…”

Section: Introductionmentioning

confidence: 99%

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Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene

Ronen,

Kim,

Dev

et al. 2024

Preprint

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Quasi-particles in fractional quantum Hall states are collective excitations that carry fractional charge and anyonic statistics. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, the anyonic statistics is most notable in quantum interference phenomena. In this study, we utilize a versatile bilayer graphene-based Fabry-Pérot Interferometer (FPI) that facilitates the study of a broad spectrum of operating regimes, from Coulomb-dominated to Aharonov-Bohm, for both integer and fractional quantum Hall states. Focusing on the ν=1⁄3 fractional quantum Hall state, we study the Aharonov-Bohm interference of quasi-particles when the magnetic flux through an interference loop and the charge density within the loop are independently varied. When their combined variation is such that the Landau filling remains 1/3 we observe pristine Aharonov-Bohm oscillations with a period of three flux quanta, as is expected from the interference of quasi-particles of one-third of the electron charge. When the combined variation is such that it leads to quasi-particles addition or removal from the loop, phase jumps emerge, and alter the phase evolution. Notably, across all cases, the average phase consistently increases by 2π with each addition of one electron to the loop.

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Section: Tunability Between Constant Filling and Constant Densitymentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene

Ronen,

Kim,

Dev

et al. 2024

Preprint

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“…The experiment of Nakamura et al 68,69 is a kind of Fabry-Perot interferometer. It central idea is depicted schematically in Figure 7.…”

Section: Experimental Observations Of Anyonsmentioning

confidence: 99%

Fractional Statistics

Greiter¹,

Wilczek²

2022

Preprint

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The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θ (i.e., a complex number e iθ of unit magnitude). θ = 0, π correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, θ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group (or a discrete subgroup thereof) realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Mutual statistics associates non-trivial transformations with winding of distinguishable particles. Anyons of all kinds are described by quantum field theories that include Chern-Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the ν = 1/3 fractional quantum Hall state has been observed both in scattering and in interferometric experiments. The latter demonstrate the defining feature of anyons, i.e. phase accumulation by braiding, quite directly. Anyons are also predicted to occur in spin liquids and other hypothetical states of matter. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.

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“…Today, the FQHE provides the only experimentally accessible system for observing anyons-quasiparticles with non-Fermi and non-Bose statistics. The pioneering works on the experimental detection of quasiparticles with abelian anyonic statistics π/3 in the FQHE state of 1/3 [1,2] opened fundamentally new prospects for incorporating anyons into applied physics. At present, the FQHE states with non-abelian anyons in the fractional states of 5/2 and 12/5 have been the focus of intense research [3,4].…”

Section: Introductionmentioning

confidence: 99%

Birotons and “Dark” Quantum Hall Hierarchies

et al. 2022

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A computational scheme is suggested to estimate neutral excitation energies in the fractional quantum Hall effect (FQHE) states. The FQHE states are systematized according to the Farey-number hierarchy structure. We show that besides the widely known Laughlin–Jain hierarchy of fractional states, there exist other “dark” hierarchies. Although hardly observed in the highest mobility samples, they can significantly affect the thermodynamics and spectral characteristics of the FQHE states. The known problems in the interpretation of the FQHE’s experimental results are explained in terms of the coexistence of two fundamentally different transformations of the electron system, one of which is a neutral excitation in the FQHE state, whereas the other is a transition between two FQHE ground states, one of which represents the Laughlin–Jain FQHE hierarchy and the other a state of “dark” hierarchies.

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Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers

Cited by 19 publications

References 69 publications

Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene

Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene

Fractional Statistics

Birotons and “Dark” Quantum Hall Hierarchies

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