Mesoscopic Quantum Hall Effect

Levkivskyi, Ivan P.

doi:10.1007/978-3-642-30499-6

Cited by 9 publications

(14 citation statements)

References 91 publications

(351 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A study of phase coherence properties of matter waves propagating along a quantum circuit of TP edge states will be the subject of future work, similar to that pursued by Ref. 75 with IQHE solid-state devices [13].…”

Section: Outlook and Discussionmentioning

confidence: 93%

Robustness of topologically protected edge states in quantum walk experiments with neutral atoms

et al. 2016

View full text Add to dashboard Cite

Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one-and two-dimensional discrete-time quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental proposal based on neutral atoms in spin-dependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spin-dependent discrete shift operations in a two-dimensional optical lattice. We analyze under realistic decoherence conditions the experimental feasibility of observing unidirectional, dissipationless transport of matter waves along boundaries separating distinct topological domains.

show abstract

Section: Outlook and Discussionmentioning

confidence: 93%

Robustness of topologically protected edge states in quantum walk experiments with neutral atoms

et al. 2016

View full text Add to dashboard Cite

show abstract

“…This filling factor may take on integer values or fractional values and is described by both the electron density and the quantization of magnetic flux. When the filling factor takes on fractional values, this phenomenon is called the fractional quantum Hall effect, or, FQHE [9,19,27,32,38]. The model describing the FQHE in a two-dimensional doublelayered system was described with the use of Chern-Simons theory [3,13,17,18,22,28,30,35,36,39,40,[44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

An indefinite system of equations governing the fractional quantum Hall effect

Esposito¹

2018

Preprint

View full text Add to dashboard Cite

In this paper, we establish existence of solutions to an indefinite coupled nonlinear system. We use partial coercivity to establish existence of a critical point to an indefinite functional and thus the existence of solutions on both bounded domains and doubly-periodic domains. We then take the limit of the bounded domain to extend solutions on a bounded domain to the full-plane. We also provide asymptotic decay analysis for solutions over the full-plane. Necessary and sufficient conditions are also provided for the doubly periodic domain.

show abstract

“…In the context of electron quantum optics, such QPCs act as electron beam splitters and provide a platform for tunneling experiments in the presence of different kind of injection sources [30,31]. Particular examples are electron analogs of the photonic Hong-Ou-Mandel, Hanbury Brown and Twiss, Mach-Zehnder and Fabry-Perot experiments [32]. The current and shot noise through a QPC connecting integer and fractional QH edge states have been measured in several experiments [2].…”

mentioning

confidence: 99%

“…At low energies the characteristic length scales are much longer than the screening length of the Coulomb interaction. Therefore, one can further approximate the Coulomb potential as short-ranged, i.e., U αβ (x − y) = U αβ δ(x − y), with non-zero diagonal and off-diagonal interaction strengths U αβ [32].…”

mentioning

confidence: 99%

Current cross-correlations in a quantum Hall collider at filling factor two

Idrisov¹,

Levkivskyi²,

Sukhorukov³

et al. 2022

Preprint

View full text Add to dashboard Cite

We use the non-equilibrium bosonization technique to study the effects of Coulomb interactions in mesoscopic electron colliders based on quantum Hall (QH) edge states at filing factor ν = 2. The current cross-correlations and Fano factor, which carry the information about the exclusion statistics, are calculated. It is shown that both these quantities have a non-analytical dependence on the source transparency, which scales as log(1/Ts) at small Ts 1. This is the consequence of electron-electron interactions in the outgoing non-equilibrium states of the collider.

show abstract

Mesoscopic Quantum Hall Effect

Cited by 9 publications

References 91 publications

Robustness of topologically protected edge states in quantum walk experiments with neutral atoms

Robustness of topologically protected edge states in quantum walk experiments with neutral atoms

An indefinite system of equations governing the fractional quantum Hall effect

Current cross-correlations in a quantum Hall collider at filling factor two

Contact Info

Product

Resources

About