1
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Mao D, Zhang K, Kim EA. Fractionalization in Fractional Correlated Insulating States at n±1/3 Filled Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:106801. [PMID: 37739384 DOI: 10.1103/physrevlett.131.106801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Revised: 07/13/2023] [Accepted: 08/17/2023] [Indexed: 09/24/2023]
Abstract
Fractionalization without time-reversal symmetry breaking is a long-sought-after goal in the study of correlated phenomena. The earlier proposal of correlated insulating states at n±1/3 filling in twisted bilayer graphene and recent experimental observations of insulating states at those fillings strongly suggest that moiré graphene systems provide a new platform to realize time-reversal symmetric fractionalized states. However, the nature of fractional excitations and the effect of quantum fluctuation on the fractional correlated insulating states are unknown. We show that excitations of the fractional correlated insulator phases in the strong coupling limit carry fractional charges and exhibit fractonic restricted mobility. Upon introduction of quantum fluctuations, the resonance of "lemniscate" structured operators drives the system into quantum lemniscate liquid (QLL) or quantum lemniscate solid (QLS). We find an emergent U(1)×U(1) 1-form symmetry unifies distinct motions of the fractionally charged excitations in the strong coupling limit and in the QLL phase, while providing a new mechanism for fractional excitations in two dimensions. We predict emergent Luttinger liquid behavior upon dilute doping in the strong coupling limit due to restricted mobility and discuss implications at a general n±1/3 filling.
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Affiliation(s)
- Dan Mao
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
| | - Kevin Zhang
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
| | - Eun-Ah Kim
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
- Radcliffe Institute for Advanced Study at Harvard, Harvard University, 10 Garden Street, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
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2
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Majorana Anyon Composites in Magneto-Photoluminescence Spectra of Natural Quantum Hall Puddles. NANOMATERIALS 2022; 12:nano12061016. [PMID: 35335829 PMCID: PMC8956118 DOI: 10.3390/nano12061016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Revised: 03/10/2022] [Accepted: 03/17/2022] [Indexed: 11/23/2022]
Abstract
In magneto-photoluminescence (magneto-PL) spectra of quasi two-dimensional islands (quantum dots) having seven electrons and Wigner−Seitz radius rs~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts, and jumps of the energy of the emission components for filling factors ν > 1 (B < 10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on rs. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock−Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the rs-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having an equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ν~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and rs. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, the Majorana anyon origin of the states having even ν, i.e., composite fermions, which provide new opportunities for topological quantum computing.
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3
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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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4
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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: 5] [Impact Index Per Article: 1.7] [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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5
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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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6
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Mintairov A, Lebedev D, Vlasov A, Bogdanov A, Ramezanpour S, Blundell S. Fractional Charge States in the Magneto-Photoluminescence Spectra of Single-Electron InP/GaInP 2 Quantum Dots. NANOMATERIALS 2021; 11:nano11020493. [PMID: 33669253 PMCID: PMC7920047 DOI: 10.3390/nano11020493] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/24/2021] [Revised: 02/09/2021] [Accepted: 02/13/2021] [Indexed: 11/17/2022]
Abstract
We used photoluminescence spectra of single electron quasi-two-dimensional InP/GaInP2 islands having Wigner-Seitz radius ~4 to measure the magnetic-field dispersion of the lowest s, p, and d single-particle states in the range 0–10 T. The measured dispersion revealed up to a nine-fold reduction of the cyclotron frequency, indicating the formation of nano-superconducting anyon or magneto-electron (em) states, in which the corresponding number of magnetic-flux-quanta vortexes and fractional charge were self-generated. We observed a linear increase in the number of vortexes versus the island size, which corresponded to a critical vortex radius equal to the Bohr radius and closed-packed topological vortex arrangements. Our observation explains the microscopic mechanism of vortex attachment in composite fermion theory of the fractional quantum Hall effect, allows its description in terms of self-localization of ems and represents progress towards the goal of engineering anyon properties for fault-tolerant topological quantum gates.
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Affiliation(s)
- Alexander Mintairov
- Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 194021 St. Petersburg, Russia; (D.L.); (A.V.)
- Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
- Correspondence:
| | - Dmitrii Lebedev
- Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 194021 St. Petersburg, Russia; (D.L.); (A.V.)
| | - Alexei Vlasov
- Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 194021 St. Petersburg, Russia; (D.L.); (A.V.)
| | - Andrey Bogdanov
- Department of Physics and Engineering, ITMO University, 197101 St. Petersburg, Russia; (A.B.); (S.R.)
| | - Shahab Ramezanpour
- Department of Physics and Engineering, ITMO University, 197101 St. Petersburg, Russia; (A.B.); (S.R.)
| | - Steven Blundell
- SyMMES, IRIG, University Grenoble Alpes, CEA, CNRS, F-38000 Grenoble, France;
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7
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Trapped fractional charges at bulk defects in topological insulators. Nature 2021; 589:376-380. [PMID: 33473226 DOI: 10.1038/s41586-020-03117-3] [Citation(s) in RCA: 29] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 10/22/2020] [Indexed: 11/08/2022]
Abstract
Topological crystalline insulators (TCIs) can exhibit unusual, quantized electric phenomena such as fractional electric polarization and boundary-localized fractional charge1-6. This quantized fractional charge is the generic observable for identification of TCIs that lack clear spectral features5-7, including ones with higher-order topology8-11. It has been predicted that fractional charges can also manifest where crystallographic defects disrupt the lattice structure of TCIs, potentially providing a bulk probe of crystalline topology10,12-14. However, this capability has not yet been confirmed in experiments, given that measurements of charge distributions in TCIs have not been accessible until recently11. Here we experimentally demonstrate that disclination defects can robustly trap fractional charges in TCI metamaterials, and show that this trapped charge can indicate non-trivial, higher-order crystalline topology even in the absence of any spectral signatures. Furthermore, we uncover a connection between the trapped charge and the existence of topological bound states localized at these defects. We test the robustness of these topological features when the protective crystalline symmetry is broken, and find that a single robust bound state can be localized at each disclination alongside the fractional charge. Our results conclusively show that disclination defects in TCIs can strongly trap fractional charges as well as topological bound states, and demonstrate the primacy of fractional charge as a probe of crystalline topology.
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8
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Rosenow B, Stern A. Flux Superperiods and Periodicity Transitions in Quantum Hall Interferometers. PHYSICAL REVIEW LETTERS 2020; 124:106805. [PMID: 32216381 DOI: 10.1103/physrevlett.124.106805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Revised: 12/26/2019] [Accepted: 01/31/2020] [Indexed: 06/10/2023]
Abstract
For strongly screened Coulomb interactions, quantum Hall interferometers can operate in a novel regime: the intrinsic energy gap can be larger than the charging energy, and addition of flux quanta can occur without adding quasiparticles. We show that flux superperiods are possible and reconcile their appearance with the Byers-Yang theorem. We explain that the observation of anyonic statistical phases is possible by tuning to the transition from a regime with constant chemical potential to a regime with constant particle density, where a flux superperiod changes to a periodicity with one flux quantum at a critical magnetic field strength.
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Affiliation(s)
- Bernd Rosenow
- Institut für Theoretische Physik, Universität Leipzig, Brüderstrasse 16, 04103 Leipzig, Germany
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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9
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Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z. ATOMS 2019. [DOI: 10.3390/atoms7020053] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system ( Z e + , e − , e − ) with Yukawa potentials is studied using correlated exponential wavefunctions based on the Ritz variational method. We obtained the critical screening parameter μ C as a function of the continuously varied nuclear charge Z , the critical nuclear charge Z C as a function of the screening parameter μ , and the ionization energies in terms of the screening parameter μ and Z . The critical nuclear charge for the bare Coulomb system ( Z e + , e − , e − ) obtained using 700-term correlated exponential wavefunctions is in accord with the reported results. The ionization energy, μ C , and Z C for the Yukawa system ( Z e + , e − , e − ) exhibit interesting behaviors. The present study describes the possible nonexistence of Borromean binding as well as Efimov states. The possible existence of quasi-bound resonances states for the negatively charged screened Ps-like ions is briefly discussed.
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10
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Hatke AT, Deng H, Liu Y, Engel LW, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Wigner solid pinning modes tuned by fractional quantum Hall states of a nearby layer. SCIENCE ADVANCES 2019; 5:eaao2848. [PMID: 30899780 PMCID: PMC6420311 DOI: 10.1126/sciadv.aao2848] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/11/2018] [Accepted: 01/29/2019] [Indexed: 06/09/2023]
Abstract
We studied a bilayer system hosting two-dimensional electron systems (2DESs) in close proximity but isolated from one another by a thin barrier. One 2DES has low electron density and forms a Wigner solid (WS) at high magnetic fields. The other has much higher density and, in the same field, exhibits fractional quantum Hall states (FQHSs). The WS spectrum has resonances which are understood as pinning modes, oscillations of the WS within the residual disorder. We found the pinning mode frequencies of the WS are strongly affected by the FQHSs in the nearby layer. Analysis of the spectra indicates that the majority layer screens like a dielectric medium even when its Landau filling is ~1/2, at which the layer is essentially a composite fermion (CF) metal. Although the majority layer is only ~ one WS lattice constant away, a WS site only induces an image charge of ~0.1e in the CF metal.
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Affiliation(s)
- A. T. Hatke
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA
| | - H. Deng
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - L. W. Engel
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA
| | - L. N. Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - K. W. West
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - K. W. Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - M. Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
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11
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Kumar M, Laitinen A, Hakonen P. Unconventional fractional quantum Hall states and Wigner crystallization in suspended Corbino graphene. Nat Commun 2018; 9:2776. [PMID: 30018365 PMCID: PMC6050265 DOI: 10.1038/s41467-018-05094-8] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Accepted: 06/11/2018] [Indexed: 11/08/2022] Open
Abstract
Competition between liquid and solid states in two-dimensional electron systems is an intriguing problem in condensed matter physics. We have investigated competing Wigner crystal and fractional quantum Hall (FQH) liquid phases in atomically thin suspended graphene devices in Corbino geometry. Low-temperature magnetoconductance and transconductance measurements along with IV characteristics all indicate strong charge density dependent modulation of electron transport. Our results show unconventional FQH phases which do not fit the standard Jain's series for conventional FQH states, instead they appear to originate from residual interactions of composite fermions in partially filled Landau levels. Also at very low charge density with filling factors [Formula: see text], electrons crystallize into an ordered Wigner solid which eventually transforms into an incompressible Hall liquid at filling factors around ν ≤ 1/7. Building on the unique Corbino sample structure, our experiments pave the way for enhanced understanding of the ordered phases of interacting electrons.
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Affiliation(s)
- Manohar Kumar
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland
- Laboratoire Pierre Aigrain, Département de Physique de l'École Normale Supérieure -PSL Research University, CNRS Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, Paris, France
| | - Antti Laitinen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland
| | - Pertti Hakonen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland.
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12
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Umucalılar RO, Macaluso E, Comparin T, Carusotto I. Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics. PHYSICAL REVIEW LETTERS 2018; 120:230403. [PMID: 29932690 DOI: 10.1103/physrevlett.120.230403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2017] [Indexed: 06/08/2023]
Abstract
We propose a standard time-of-flight experiment as a method for observing the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. Our proposed method is validated by Monte Carlo calculations for ν=1/2 and 1/3 fractional quantum Hall liquids containing a realistic number of particles. Extensions to quantum Hall liquids of light and to non-Abelian anyons are briefly discussed.
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Affiliation(s)
- R O Umucalılar
- Deparment of Physics, Mimar Sinan Fine Arts University, 34380 Sisli, Istanbul, Turkey
| | - E Macaluso
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
| | - T Comparin
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
| | - I Carusotto
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
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13
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Wölfle P. Quasiparticles in condensed matter systems. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:032501. [PMID: 29155414 DOI: 10.1088/1361-6633/aa9bc4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed.
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Affiliation(s)
- Peter Wölfle
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology, 76049 Karlsruhe, Germany. Institute for Nanotechnology, Karlsruhe Institute of Technology, 76031 Karlsruhe, Germany
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14
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Fatin GL, Matos-Abiague A, Scharf B, Žutić I. Wireless Majorana Bound States: From Magnetic Tunability to Braiding. PHYSICAL REVIEW LETTERS 2016; 117:077002. [PMID: 27563991 DOI: 10.1103/physrevlett.117.077002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2015] [Indexed: 06/06/2023]
Abstract
We propose a versatile platform to investigate the existence of Majorana bound states (MBSs) and their non-Abelian statistics through braiding. This implementation combines a two-dimensional electron gas formed in a semiconductor quantum well grown on the surface of an s-wave superconductor with a nearby array of magnetic tunnel junctions (MTJs). The underlying magnetic textures produced by MTJs provide highly controllable topological phase transitions to confine and transport MBSs in two dimensions, overcoming the requirement for a network of wires. Obtained scaling relations confirm that various semiconductor quantum well materials are suitable for this proposal.
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Affiliation(s)
- Geoffrey L Fatin
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Alex Matos-Abiague
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Benedikt Scharf
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Igor Žutić
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
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15
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Mironov OA, d'Ambrumenil N, Dobbie A, Leadley DR, Suslov AV, Green E. Fractional Quantum Hall States in a Ge Quantum Well. PHYSICAL REVIEW LETTERS 2016; 116:176802. [PMID: 27176531 DOI: 10.1103/physrevlett.116.176802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Indexed: 06/05/2023]
Abstract
Measurements of the Hall and dissipative conductivity of a strained Ge quantum well on a SiGe/(001)Si substrate in the quantum Hall regime are reported. We analyze the results in terms of thermally activated quantum tunneling of carriers from one internal edge state to another across saddle points in the long-range impurity potential. This shows that the gaps for different filling fractions closely follow the dependence predicted by theory. We also find that the estimates of the separation of the edge states at the saddle are in line with the expectations of an electrostatic model in the lowest spin-polarized Landau level (LL), but not in the spin-reversed LL where the density of quasiparticle states is not high enough to accommodate the carriers required.
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Affiliation(s)
- O A Mironov
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom and International Laboratory of High Magnetic Fields and Low Temperatures, 95 Gajowicka Street, 53-421 Wroclaw, Poland
| | - N d'Ambrumenil
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - A Dobbie
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - D R Leadley
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - A V Suslov
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - E Green
- Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany
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16
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Kim Y, Lee DS, Jung S, Skákalová V, Taniguchi T, Watanabe K, Kim JS, Smet JH. Fractional Quantum Hall States in Bilayer Graphene Probed by Transconductance Fluctuations. NANO LETTERS 2015; 15:7445-7451. [PMID: 26479836 DOI: 10.1021/acs.nanolett.5b02876] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We have investigated fractional quantum Hall (QH) states in Bernal-stacked bilayer graphene using transconductance fluctuation measurements. A variety of odd-denominator fractional QH states with νQH → νQH + 2 symmetry, as previously reported, are observed. However, surprising is that also particle-hole symmetric states are clearly resolved in the same measurement set. We attribute their emergence to the reversal of orbital states in the octet level scheme induced by a strong local charge imbalance, which can be captured by the transconductance fluctuations. Also the even-denominator fractional QH state at filling -1/2 is observed. However, contrary to a previous study on a suspended graphene layer [ Ki et al. Nano Lett. 2014, 14 , 2135 ], the particle-hole symmetric state at filling 1/2 is detected as well. These observations suggest that the stability of both odd and even denominator fractional QH states is very sensitive to local transverse electric fields in bilayer graphene.
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Affiliation(s)
- Youngwook Kim
- Department of Physics, Pohang University of Science and Technology , Pohang 790-784, Korea
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
| | - Dong Su Lee
- KIST Jeonbuk Institute of Advanced Composite Materials , Jeonbuk 565-905, Korea
| | - Suyong Jung
- Center for Quantum Measurement Science, Korea Research Institute of Standards and Science , Daejeon, 305-340, Korea
| | - Viera Skákalová
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, 1090 Vienna, Austria
- STU Center for Nanodiagnostics , Vazovova 5, 812 43 Bratislava, Slovakia
| | - T Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - K Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Jun Sung Kim
- Department of Physics, Pohang University of Science and Technology , Pohang 790-784, Korea
| | - Jurgen H Smet
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
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17
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Cooper NR, Simon SH. Signatures of fractional exclusion statistics in the spectroscopy of quantum Hall droplets. PHYSICAL REVIEW LETTERS 2015; 114:106802. [PMID: 25815953 DOI: 10.1103/physrevlett.114.106802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2014] [Indexed: 06/04/2023]
Abstract
We show how spectroscopic experiments on a small Laughlin droplet of rotating bosons can directly demonstrate Haldane fractional exclusion statistics of quasihole excitations. The characteristic signatures appear in the single-particle excitation spectrum. We show that the transitions are governed by a "many-body selection rule" which allows one to relate the number of allowed transitions to the number of quasihole states on a finite geometry. We illustrate the theory with numerically exact simulations of small numbers of particles.
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Affiliation(s)
- Nigel R Cooper
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Steven H Simon
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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18
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Lin X, Du R, Xie X. Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene. Natl Sci Rev 2014. [DOI: 10.1093/nsr/nwu071] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Abstract
The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.
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Affiliation(s)
- Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Du
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xincheng Xie
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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19
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Zhang D, Huang X, Dietsche W, von Klitzing K, Smet JH. Signatures for Wigner crystal formation in the chemical potential of a two-dimensional electron system. PHYSICAL REVIEW LETTERS 2014; 113:076804. [PMID: 25170727 DOI: 10.1103/physrevlett.113.076804] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2014] [Indexed: 06/03/2023]
Abstract
We investigate the evolution of the chemical potential of a two-dimensional electron system (2DES) as a function of density at a fixed magnetic field. By using a bilayer system, changes in the chemical potential of one 2DES are determined from the density variation induced in the second, nearby 2DES. At high magnetic fields around a filling factor of ν=1 or ν=2, the chemical potential jump associated with the condensation in a quantum Hall state exhibits two anomalies symmetrically located around these integer filling factors. They are attributed to the formation of a 2D Wigner crystal of quasiparticles.
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Affiliation(s)
- Ding Zhang
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Xuting Huang
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Werner Dietsche
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Klaus von Klitzing
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Jurgen H Smet
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
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20
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Inoue H, Grivnin A, Ofek N, Neder I, Heiblum M, Umansky V, Mahalu D. Charge fractionalization in the integer quantum Hall effect. PHYSICAL REVIEW LETTERS 2014; 112:166801. [PMID: 24815662 DOI: 10.1103/physrevlett.112.166801] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2014] [Indexed: 06/03/2023]
Abstract
We report an observation, via sensitive shot noise measurements, of charge fractionalization of chiral edge electrons in the integer quantum Hall effect regime. Such fractionalization results solely from interchannel Coulomb interaction, leading electrons to decompose to excitations carrying fractional charges. The experiment was performed by guiding a partitioned current carrying edge channel in proximity to another unbiased edge channel, leading to shot noise in the unbiased edge channel without net current, which exhibited an unconventional dependence on the partitioning. The determination of the fractional excitations, as well as the relative velocities of the two original (prior to the interaction) channels, relied on a recent theory pertaining to this measurement. Our result exemplifies the correlated nature of multiple chiral edge channels in the integer quantum Hall effect regime.
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Affiliation(s)
- Hiroyuki Inoue
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Anna Grivnin
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Nissim Ofek
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Izhar Neder
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, 69978 Tel Aviv, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Vladimir Umansky
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
| | - Diana Mahalu
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
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21
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d'Ambrumenil N, Morf RH. Thermopower in the quantum Hall regime. PHYSICAL REVIEW LETTERS 2013; 111:136805. [PMID: 24116804 DOI: 10.1103/physrevlett.111.136805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Indexed: 06/02/2023]
Abstract
We consider the effect of disorder on the themopower in quantum Hall systems. For a sample in the Corbino geometry, where dissipative currents are not carried by edge states, we find that thermopower behaves at high temperatures like a system with a gap and has a maximum which increases as the temperature is reduced. At lower temperatures this maximum reduces as a function of temperature as a result of tunneling across saddle points in the background potential. Our model assumes that the mean saddle point height varies linearly with the deviation in filling factor from the quantized value. We test this hypothesis against observations for the dissipative electrical conductance as a function of temperature and field and find good agreement with experiment around the minimum.
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Affiliation(s)
- N d'Ambrumenil
- Physics Department, University of Warwick, Coventry CV4 7AL, United Kingdom
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22
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Ben-Shach G, Laumann CR, Neder I, Yacoby A, Halperin BI. Detecting non-Abelian anyons by charging spectroscopy. PHYSICAL REVIEW LETTERS 2013; 110:106805. [PMID: 23521280 DOI: 10.1103/physrevlett.110.106805] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2012] [Indexed: 06/01/2023]
Abstract
Observation of non-Abelian statistics for the e/4 quasiparticles in the ν = 5/2 fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states in a system with localized quasiparticles, and, hence, an additional low temperature entropy. Recent experiments, which detect changes in the number of quasiparticles trapped in a local potential well as a function of an applied gate voltage, V(G), provide a possibility for measuring this entropy, if carried out over a suitable range of temperatures, T. We present a microscopic model for quasiparticles in a potential well and study the effects of non-Abelian statistics on the charge stability diagram in the V(G)-T plane, including broadening at finite temperature. We predict a measurable slope for the first quasiparticle charging line and an even-odd effect in the diagram, which is a signature of non-Abelian statistics.
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Affiliation(s)
- G Ben-Shach
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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23
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Lee DS, Skákalová V, Weitz RT, von Klitzing K, Smet JH. Transconductance fluctuations as a probe for interaction-induced quantum Hall states in graphene. PHYSICAL REVIEW LETTERS 2012; 109:056602. [PMID: 23006193 DOI: 10.1103/physrevlett.109.056602] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2012] [Indexed: 06/01/2023]
Abstract
Transport measurements normally provide a macroscopic, averaged view of the sample so that disorder prevents the observation of fragile interaction-induced states. Here, we demonstrate that transconductance fluctuations in a graphene field effect transistor reflect charge localization phenomena on the nanometer scale due to the formation of a dot network which forms near incompressible quantum states. These fluctuations give access to fragile broken symmetry and fractional quantum Hall states even though these states remain hidden in conventional magnetotransport quantities.
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Affiliation(s)
- Dong Su Lee
- Max-Planck-Institut für Festköperforschung, Stuttgart, Germany
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24
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Kou A, Marcus CM, Pfeiffer LN, West KW. Coulomb oscillations in antidots in the integer and fractional quantum Hall regimes. PHYSICAL REVIEW LETTERS 2012; 108:256803. [PMID: 23004632 DOI: 10.1103/physrevlett.108.256803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2012] [Indexed: 06/01/2023]
Abstract
We report measurements of resistance oscillations in micron-scale antidots in both the integer and fractional quantum Hall regimes. In the integer regime, we conclude that oscillations are of the Coulomb type from the scaling of magnetic field period with the number of edges bound to the antidot. Based on both gate-voltage and field periods, we find at filling factor ν = 2 a tunneling charge of e and two charged edges. Generalizing this picture to the fractional regime, we find (again, based on field and gate-voltage periods) at ν = 2/3 a tunneling charge of (2/3)e and a single charged edge.
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Affiliation(s)
- A Kou
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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25
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Venkatachalam V, Yacoby A, Pfeiffer L, West K. Local charge of the ν = 5/2 fractional quantum Hall state. Nature 2011; 469:185-8. [PMID: 21228871 DOI: 10.1038/nature09680] [Citation(s) in RCA: 82] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2010] [Accepted: 11/16/2010] [Indexed: 11/09/2022]
Abstract
Electrons moving in two dimensions under the influence of strong magnetic fields effectively lose their kinetic energy and display exotic behaviour dominated by Coulomb forces. When the ratio of electrons to magnetic flux quanta in the system (ν) is near 5/2, the electrons are predicted to condense into a correlated phase with fractionally charged quasiparticles and a ground-state degeneracy that grows exponentially as these quasiparticles are introduced. The only way for electrons to transform between the many ground states would be to braid the fractional excitations around each other. This property has been proposed as the basis of a fault-tolerant quantum computer. Here we present observations of localized quasiparticles at ν = 5/2, confined to puddles by disorder. Using a local electrometer to compare how quasiparticles at ν = 5/2 and ν = 7/3 charge these puddles, we were able to extract the ratio of local charges for these states. Averaged over several disorder configurations and samples, we found the ratio to be 4/3, suggesting that the local charges are = e/3 and = e/4, where e is the charge of an electron. This is in agreement with theoretical predictions for a paired state at ν = 5/2. Confirming the existence of localized e/4 quasiparticles shows that proposed interferometry experiments to test statistics and computational ability of the state at ν = 5/2 would be possible.
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Affiliation(s)
- Vivek Venkatachalam
- Department of Physics, Harvard University, 11 Oxford Street, Cambridge, Massachusetts 02138, USA
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26
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Maclean K, Mentzel TS, Kastner MA. The effect of electrostatic screening on a nanometer scale electrometer. NANO LETTERS 2011; 11:30-34. [PMID: 21155560 DOI: 10.1021/nl102121e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We investigate the effect of electrostatic screening on a nanoscale silicon MOSFET electrometer. We find that screening by the lightly doped p-type substrate, on which the MOSFET is fabricated, significantly affects the sensitivity of the device. We are able to tune the rate and magnitude of the screening effect by varying the temperature and the voltages applied to the device, respectively. We show that despite this screening effect, the electrometer is still very sensitive to its electrostatic environment, even at room temperature.
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Affiliation(s)
- Kenneth Maclean
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
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27
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Zhu H, Chen YP, Jiang P, Engel LW, Tsui DC, Pfeiffer LN, West KW. Observation of a pinning mode in a Wigner solid with ν=1/3 fractional quantum Hall excitations. PHYSICAL REVIEW LETTERS 2010; 105:126803. [PMID: 20867666 DOI: 10.1103/physrevlett.105.126803] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2010] [Indexed: 05/29/2023]
Abstract
We report the observation of a resonance in the microwave spectra of the real diagonal conductivities of a two-dimensional electron system within a range of ∼ ± 0.015 from filling factor ν = 1/3. The resonance is remarkably similar to resonances previously observed near integer ν, and is interpreted as the collective pinning mode of a disorder-pinned Wigner solid phase of e/3-charged carriers.
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Affiliation(s)
- Han Zhu
- Princeton University, Princeton, New Jersey 08544, USA
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28
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Role of interactions in an electronic Fabry-Perot interferometer operating in the quantum Hall effect regime. Proc Natl Acad Sci U S A 2010; 107:5276-81. [PMID: 20212147 DOI: 10.1073/pnas.0912624107] [Citation(s) in RCA: 93] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Interference of edge channels is expected to be a prominent tool for studying statistics of charged quasiparticles in the quantum Hall effect (QHE). We present here a detailed study of an electronic Fabry-Perot interferometer (FPI) operating in the QHE regime [C. Chamon, et al. (1997) Phys Rev B 55:2331-2334], with the phase of the interfering quasiparticles controlled by the Aharonov-Bohm effect. Our main finding is that Coulomb interactions among the electrons dominate the interference, even in a relatively large area FPI, leading to a strong dependence of the area enclosed by the interference loop on the magnetic field. In particular, for a composite edge structure, with a few independent edge channels propagating along the edge, interference of the outmost edge channel (belonging to the lowest Landau level) was insensitive to magnetic field-suggesting a constant enclosed flux. However, when any of the inner edge channels interfered, the enclosed flux decreased when the magnetic field increased. By intentionally varying the enclosed area with a biased metallic gate and observing the periodicity of the interference pattern, charges e (for integer filling factors) and e/3 (for a fractional filling factor) were found to be expelled from the FPI. Moreover, these observations provided also a novel way of detecting the charge of the interfering quasiparticles.
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29
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Groshaus JG, Dujovne I, Gallais Y, Hirjibehedin CF, Pinczuk A, Tan YW, Stormer H, Dennis BS, Pfeiffer LN, West KW. Spin texture and magnetoroton excitations at nu=1/3. PHYSICAL REVIEW LETTERS 2008; 100:046804. [PMID: 18352317 DOI: 10.1103/physrevlett.100.046804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2007] [Indexed: 05/26/2023]
Abstract
Neutral spin texture (ST) excitations at nu=1/3 are directly observed for the first time by resonant inelastic light scattering. They are determined to involve two simultaneous spin flips. At low magnetic fields, the ST energy is below that of the magnetoroton minimum. With increasing in-plane magnetic field these mode energies cross at a critical ratio of the Zeeman and Coulomb energies of eta(c)=0.020+/-0.001. Surprisingly, the intensity of the ST mode grows with temperature in the range in which the magnetoroton modes collapse. The temperature dependence is interpreted in terms of a competition between coexisting phases supporting different excitations. We consider the role of the ST excitations in activated transport at nu=1/3.
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Affiliation(s)
- Javier G Groshaus
- Physics & Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA.
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30
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Luin S, Pellegrini V, Pinczuk A, Dennis BS, Pfeiffer LN, West KW. Resonant rayleigh scattering from bilayer quantum Hall phases. PHYSICAL REVIEW LETTERS 2006; 97:216802. [PMID: 17155764 DOI: 10.1103/physrevlett.97.216802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2006] [Indexed: 05/12/2023]
Abstract
We observe resonant Rayleigh scattering of light from quantum Hall bilayers at Landau level filling factor nu = 1. The effect arises below 1 Kelvin when electrons are in the incompressible quantum Hall phase with strong interlayer correlations. Marked changes in the Rayleigh scattering signal in response to application of an in-plane magnetic field indicate that the unexpected temperature dependence is linked to formation of a nonuniform electron fluid close to the phase transition towards the compressible state. These results demonstrate a new realm of study in which resonant Rayleigh scattering methods probe quantum phases of electrons in semiconductor heterostructures.
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Affiliation(s)
- Stefano Luin
- NEST CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
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31
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Brenning HTA, Kubatkin SE, Erts D, Kafanov SG, Bauch T, Delsing P. A single electron transistor on an atomic force microscope probe. NANO LETTERS 2006; 6:937-41. [PMID: 16683829 DOI: 10.1021/nl052526t] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
We report fabrication as well as proof-of-concept experiments of a noninvasive sensor of weak nanoscale electric fields. The sensor is a single electron transistor (SET) placed at the tip of a noncontact atomic force microscope (AFM). This is a general technology to make any nanometer-sized lithography pattern at edges or tips of a cantilever. The height control of the AFM allows the SET to hover a few nanometers above the substrate, improving both the electric field sensitivity and lateral resolution of the electrometer. Our AFM-SET sensor is prepared by a scalable technology. It means that the probe can be routinely fabricated and replaced, if broken.
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Affiliation(s)
- Henrik T A Brenning
- Microtechnology and Nanoscience, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden.
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32
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Rossi E, Núñez AS, MacDonald AH. Interlayer transport in bilayer quantum Hall systems. PHYSICAL REVIEW LETTERS 2005; 95:266804. [PMID: 16486385 DOI: 10.1103/physrevlett.95.266804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2005] [Indexed: 05/06/2023]
Abstract
Bilayer quantum Hall systems have a broken symmetry ground state at a filling factor which can be viewed either as an excitonic superfluid or as a pseudospin ferromagnet. We present a theory of interlayer transport in quantum Hall bilayers that highlights remarkable similarities and critical differences between transport in Josephson junction and ferromagnetic metal spin-transfer devices. Our theory is able to explain the size of the large but finite low-bias interlayer conductance and the voltage width of this collective transport anomaly.
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Affiliation(s)
- Enrico Rossi
- Department of Physics, University of Texas at Austin, 78712, USA
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33
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Kim EA, Lawler M, Vishveshwara S, Fradkin E. Signatures of fractional statistics in noise experiments in quantum Hall fluids. PHYSICAL REVIEW LETTERS 2005; 95:176402. [PMID: 16383842 DOI: 10.1103/physrevlett.95.176402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2005] [Indexed: 05/05/2023]
Abstract
The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an "antibunching" effect.
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Affiliation(s)
- Eun-Ah Kim
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
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34
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Shopen E, Gefen Y, Meir Y. Quasiparticle tunneling through a barrier in the fractional quantum hall regime. PHYSICAL REVIEW LETTERS 2005; 95:136803. [PMID: 16197164 DOI: 10.1103/physrevlett.95.136803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2005] [Indexed: 05/04/2023]
Abstract
Tunneling of fractionally charged quasiparticles (QPs) through a barrier is considered in the context of a multiply connected geometry. In this geometry global constraints do not prohibit such a tunneling process. The tunneling amplitude is evaluated and the crossover from mesoscopic QP-dominated to electron-dominated tunneling as the system's size is increased is found. The presence of disorder enhances both electron and QP-tunneling rates.
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Affiliation(s)
- Elad Shopen
- Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel
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35
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Heo J, Bockrath M. Local electronic structure of single-walled carbon nanotubes from electrostatic force microscopy. NANO LETTERS 2005; 5:853-7. [PMID: 15884883 DOI: 10.1021/nl0501765] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
An atomic force microscope was used to locally perturb and detect the charge density in carbon nanotubes. Changing the tip voltage varied the Fermi level in the nanotube. The local charge density increased abruptly whenever the Fermi level was swept through a van Hove singularity in the density of states, thereby coupling the cantilever's mechanical oscillations to the nanotube's local electronic properties. By using our technique to measure the local band gap of an intratube quantum-well structure, created by a nonuniform uniaxial strain, we have estimated the nanotube chiral angle. Our technique does not require attached electrodes or a specialized substrate, yielding a unique high-resolution spectroscopic tool that facilitates the comparison between local electronic structure of nanomaterials and further transport, optical, or sensing experiments.
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Affiliation(s)
- Jinseong Heo
- Department of Applied Physics, California Institute of Technology, M/C 128-95, Pasadena, California 91125, USA
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