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Nakamura J, Liang S, Gardner GC, Manfra MJ. Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers. Nat Commun 2022; 13:344. [PMID: 35039497 PMCID: PMC8763912 DOI: 10.1038/s41467-022-27958-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 12/20/2021] [Indexed: 11/29/2022] Open
Abstract
Quantum Hall interferometers have been used to probe fractional charge and statistics of quasiparticles. We present measurements of a small Fabry-Perot interferometer in which the electrostatic coupling constants which affect interferometer behavior can be determined experimentally. Near the center of the ν = 1/3 state this device exhibits Aharonov-Bohm interference interrupted by a few discrete phase jumps, and Φ0 oscillations at higher and lower magnetic fields, consistent with theoretical predictions for detection of anyonic statistics. We estimate the electrostatic parameters KI and KIL by two methods: using the ratio of oscillation periods in compressible versus incompressible regions, and from finite-bias conductance measurements. We find that the extracted KI and KIL can account for the deviation of the phase jumps from the theoretical anyonic phase θa = 2π/3. At integer states, we find that KI and KIL can account for the Aharonov-Bohm and Coulomb-dominated behavior of different edge states.
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Affiliation(s)
- J Nakamura
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
| | - S Liang
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
| | - G C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
- Microsoft Quantum Lab West Lafayette, West Lafayette, IN, USA
| | - M J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA.
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA.
- Microsoft Quantum Lab West Lafayette, West Lafayette, IN, USA.
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA.
- School of Materials Engineering, Purdue University, West Lafayette, IN, USA.
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Feldman DE, Halperin BI. Fractional charge and fractional statistics in the quantum Hall effects. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:076501. [PMID: 34015771 DOI: 10.1088/1361-6633/ac03aa] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 05/20/2021] [Indexed: 06/12/2023]
Abstract
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.
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Affiliation(s)
- D E Feldman
- Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, RI 02912, United States of America
| | - Bertrand I Halperin
- Department of Physics, Harvard University, Cambridge, MA 02138, United States of America
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3
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Röösli MP, Hug M, Nicolí G, Märki P, Reichl C, Rosenow B, Wegscheider W, Ensslin K, Ihn T. Fractional Coulomb blockade for quasi-particle tunneling between edge channels. SCIENCE ADVANCES 2021; 7:eabf5547. [PMID: 33962947 PMCID: PMC8104872 DOI: 10.1126/sciadv.abf5547] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Accepted: 03/10/2021] [Indexed: 06/12/2023]
Abstract
In the fractional quantum Hall effect, the elementary excitations are quasi-particles with fractional charges as predicted by theory and demonstrated by noise and interference experiments. We observe Coulomb blockade of fractional charges in the measured magneto-conductance of a 1.4-micron-wide quantum dot. Interaction-driven edge reconstruction separates the dot into concentric compressible regions with fractionally charged excitations and incompressible regions acting as tunnel barriers for quasi-particles. Our data show the formation of incompressible regions of filling factors 2/3 and 1/3. Comparing data at fractional filling factors to filling factor 2, we extract the fractional quasi-particle charge e */e = 0.32 ± 0.03 and 0.35 ± 0.05. Our investigations extend and complement quantum Hall Fabry-Pérot interference experiments investigating the nature of anyonic fractional quasi-particles.
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Affiliation(s)
- Marc P Röösli
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland.
| | - Michael Hug
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Giorgio Nicolí
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Peter Märki
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Christian Reichl
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Bernd Rosenow
- Institute for Theoretical Physics, Leipzig University Leipzig D-04009, Germany
| | - Werner Wegscheider
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Klaus Ensslin
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Thomas Ihn
- Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
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Matveev KA, Pustilnik M. Viscous Dissipation in One-Dimensional Quantum Liquids. PHYSICAL REVIEW LETTERS 2017; 119:036801. [PMID: 28777639 DOI: 10.1103/physrevlett.119.036801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2017] [Indexed: 06/07/2023]
Abstract
We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zero-temperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. Our consideration is applicable to all single-component Galilean-invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.
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Affiliation(s)
- K A Matveev
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M Pustilnik
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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von Keyserlingk CW, Simon SH, Rosenow B. Enhanced Bulk-Edge Coulomb Coupling in Fractional Fabry-Perot Interferometers. PHYSICAL REVIEW LETTERS 2015; 115:126807. [PMID: 26431008 DOI: 10.1103/physrevlett.115.126807] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2014] [Indexed: 06/05/2023]
Abstract
Recent experiments use Fabry-Perot (FP) interferometry to claim that the ν=5/2 quantum Hall state exhibits non-Abelian topological order. We note that the experiments appear inconsistent with a model neglecting bulk-edge Coulomb coupling and Majorana tunneling, so we reexamine the theory of FP devices. Even a moderate Coulomb coupling may strongly affect some fractional plateaus, but very weakly affect others, allowing us to model the data over a wide range of plateaus. While experiments are consistent with the ν=5/2 state harboring Moore-Read topological order, they may have measured Coulomb effects rather than an "even-odd effect" due to non-Abelian braiding.
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Affiliation(s)
- C W von Keyserlingk
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom
| | - S H Simon
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom
| | - Bernd Rosenow
- Institut für Theoretische Physik, Universität Leipzig, D-04103, Leipzig, Germany
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Robust electron pairing in the integer quantum hall effect regime. Nat Commun 2015; 6:7435. [DOI: 10.1038/ncomms8435] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2014] [Accepted: 05/08/2015] [Indexed: 11/08/2022] Open
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