Optimization of edge state velocity in the integer quantum Hall regime

Sahasrabudhe, Harshad; Novaković, Božidar; Nakamura, James; Fallahi, Saeed; Povolotskyi, Michael; Klimeck, Gerhard; Rahman, Rajib; Manfra, Michael J.

doi:10.1103/physrevb.97.085302

Cited by 14 publications

(11 citation statements)

References 56 publications

(76 reference statements)

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“…An SEM image of the device is shown in Fig. 1b; the device has a nominal area of 1.0µm × 1.0 µm, and measurements suggest that lateral depletion of the 2DES makes the interferometer area smaller by approximately 200nm on each side, similar to the experimental and numerical results in [58] (see also [61]). Note that the length scale of the interferometer is much greater than the magnetic length l B ≡ hc eB in the regime investigated, with l B ≈9nm at ν = 1/3, so the condition that the interfering quasiparticles be well separated from the localized quasiparticles inside the interferometer which they may braid around should hold [10,11].…”

Section: Device Designsupporting

confidence: 72%

Direct observation of anyonic braiding statistics at the $ν$=1/3 fractional quantum Hall state

Nakamura,

Liang,

Gardner

et al. 2020

Preprint

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Utilizing an electronic Fabry-Perot interferometer in which Coulomb charging effects are suppressed, we report experimental observation of anyonic braiding statistics for the ν = 1/3 fractional quantum Hall state. Strong Aharonov-Bohm interference of the ν = 1/3 edge mode is punctuated by discrete phase slips consistent with an anyonic phase of θanyon = 2π 3 . Our results are consistent with a recent theory of a Fabry-Perot interferometer operated in a regime in which device charging energy is small compared to the energy of formation of charged quasiparticles [17]. Close correspondence between device operation and theoretical predictions substantiates our claim of observation of anyonic braiding.

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Section: Device Designsupporting

confidence: 72%

Direct observation of anyonic braiding statistics at the $ν$=1/3 fractional quantum Hall state

Nakamura,

Liang,

Gardner

et al. 2020

Preprint

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“…The self-consistent problem can also be tackled directly in presence of a finite temperature [31]. More recent works improved on Thomas-Fermi by incorporating a Gaussian broadening of the Landau levels [32][33][34]. Solving the full self-consistent electrostatic-quantum problem, beyond the above approximations and at low temperature, is a difficult task however, as the presence of the Landau levels (and the associated Dirac comb for the density of states) makes the set of equations highly nonlinear.…”

mentioning

confidence: 99%

Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor

Armagnat

Waintal

2020

J. Phys. Mater.

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The well-known Landauer-Buttiker (LB) picture used to explain the quantum Hall effect uses the concept of (chiral) edge states that carry the current. In their seminal 1992 article, Chklovskii, Shklovskii and Glazman (CSG) showed that the LB picture does not account for some very basic properties of the gas, such as its density profile, as it lacks a proper treatment of the electrostatic energy. They showed that, instead, one should consider alternated stripes of compressible and incompressible phases. In this letter, we revisit this issue using a full solution of the quantum-electrostatic problem of a narrow ballistic conductor, beyond the CSG approach. We recover the LB channels at low field and the CSG compressible/incompressible stripes at high field. Our calculations reveal the existence of a third 'hybrid' phase at intermediate field. This hybrid phase has well defined LB type edge states, yet possesses a Landau level pinned at the Fermi energy as in the CSG picture. We calculate the magnetoconductance which reveals the interplay between the LB and CSG regimes. Our results have important implications for the propagation of edge magneto-plasmons.Electrostatic energy is very often the largest energy scale in a physical situation. Yet, the electrostatic landscape is equally often taken for granted as an external potential, which may result in a wrong physical picture. A well known example is the quantum Hall effect [1] (QHE) that has been largely discussed using the concept of edge states in a non-interacting Landauer-Buttiker (LB) picture [2, 3]. Despite being very successful for the understanding of e.g. the quantification of the Hall resistance and the vanishing longitudinal resistance, the LB picture also fails spectacularly to describe basic physics such as the density profile of the electron gas. In a series of articles [4-6] that culminated with the work of Chklovskii, Shklovskii and Glazman (CSG) [7-9], it was recognized that the LB picture should be revisited. It was shown that the interplay between quantum mechanics and electrostatics leads to the emergence of compressible and incompressible stripes, a concept related, yet somehow different, to the original edge states. An important effort has been devoted to the experimental observation of these stripes [10][11][12][13][14][15][16][17][18][19][20]. CSG work, as well as a large fraction of the subsequent litterature [21][22][23][24][25][26][27][28][29][30] was based on the Thomas-Fermi approximation which is suitable at high magnetic field but inadequate at low field where the LB approach is expected to work well. The self-consistent problem can also be tackled directly in presence of a finite temperature [31]. More recent works improved on Thomas-Fermi by incorporating a Gaussian broadening of the Landau levels [32][33][34]. Solving the full self-consistent electrostatic-quantum problem, beyond the above approximations and at low temperature, is a difficult task however, as the presence of the Landau levels (and the associated Dirac comb for the den...

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“…These fabrication advances allowed the study of FPIs in the extreme AB regime for small interferometer areas of the order of ∼ 1 µm 2 . Structures utilizing screening layers resulted in charging energies, and hence mutual bulk edge coupling, lower by more than one order of magnitude with respect to devices of the same size with conventional gating schemes [22,109,124,125]. Remarkably, these new devices allowed to observe, for the first time, oscillations with negatively sloped lines of constant phase in the B − V g plane, hallmark of the AB operating regime, also in the FQH regime.…”

Section: Screening Unwanted Coulomb Interactionsmentioning

confidence: 93%

Anyons in Quantum Hall Interferometry

Carrega,

Chirolli,

Heun

et al. 2021

Preprint

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The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers, able to reveal the coherence and statistical properties of the interfering constituents. Here, we review the two main geometries developed in the QH regime, the Mach-Zehnder and the Fabry-Perot interferometers. We present their basic working principles, fabrication methods, and the main results obtained both in the integer and fractional QH regime. We will also show how recent technological advances led to the direct experimental demonstration of fractional statistics for Laughlin quasiparticles in a Fabry-Perot interferometric setup.

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Optimization of edge state velocity in the integer quantum Hall regime

Cited by 14 publications

References 56 publications

Direct observation of anyonic braiding statistics at the $ν$=1/3 fractional quantum Hall state

Direct observation of anyonic braiding statistics at the $ν$=1/3 fractional quantum Hall state

Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor

Anyons in Quantum Hall Interferometry

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