1
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Manna S, Das A, Goldstein M, Gefen Y. Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise. PHYSICAL REVIEW LETTERS 2024; 132:136502. [PMID: 38613281 DOI: 10.1103/physrevlett.132.136502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Revised: 12/01/2023] [Accepted: 02/26/2024] [Indexed: 04/14/2024]
Abstract
The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations (electrical shot noise) in order to distinguish among the Pf, APf, and PHPf candidate states, as well as to determine their edge thermal equilibration regimes: full vs partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, is based on fully electrical measurements.
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Affiliation(s)
- Sourav Manna
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel Aviv 6997801, Israel
| | - Ankur Das
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Moshe Goldstein
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel Aviv 6997801, Israel
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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2
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Das S, Das S, Mandal SS. Fractional Quantum Hall States of the A Phase in the Second Landau Level. PHYSICAL REVIEW LETTERS 2024; 132:106501. [PMID: 38518319 DOI: 10.1103/physrevlett.132.106501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 01/19/2024] [Indexed: 03/24/2024]
Abstract
A proposal of the existence of an Anomalous phase (A phase) [Das et al., Phys. Rev. Lett. 131, 056202 (2023)PRLTAO0031-900710.1103/PhysRevLett.131.056202] at the experimental range of moderate Landau-level-mixing strength has recently been made for the 5/2 state. We here report that the gapped A phase is generic to the sequence of spin-polarized fractional quantum Hall states with filling fractions ν=n/(nm-1) and ν=1-n/(nm-1), (n≥1,m≥3), that exhausts almost all the observed states and also predicts some states in the second Landau level for GaAs systems. Our proposed trial wave functions for all these states have remarkably high overlaps with the corresponding exact ground states and can support non-Abelian quasiparticle excitations with charge e/[2(nm-1)]. By analyzing edge modes, we predict experimentally verifiable thermal Hall conductance 2.5(π^{2}k_{B}^{2}T/3h) for all the states in these sequences.
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Affiliation(s)
- Sudipto Das
- Department of Physics, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Sahana Das
- Department of Physics, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Sudhansu S Mandal
- Department of Physics, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
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3
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Le Breton G, Delagrange R, Hong Y, Garg M, Watanabe K, Taniguchi T, Ribeiro-Palau R, Roulleau P, Roche P, Parmentier FD. Heat Equilibration of Integer and Fractional Quantum Hall Edge Modes in Graphene. PHYSICAL REVIEW LETTERS 2022; 129:116803. [PMID: 36154417 DOI: 10.1103/physrevlett.129.116803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Accepted: 08/01/2022] [Indexed: 06/16/2023]
Abstract
Hole-conjugate states of the fractional quantum Hall effect host counterpropagating edge channels which are thought to exchange charge and energy. These exchanges have been the subject of extensive theoretical and experimental works; in particular, it is yet unclear if the presence of integer quantum Hall edge channels stemming from fully filled Landau levels affects heat equilibration along the edge. In this Letter, we present heat transport measurements in quantum Hall states of graphene demonstrating that the integer channels can strongly equilibrate with the fractional ones, leading to markedly different regimes of quantized heat transport that depend on edge electrostatics. Our results allow for a better comprehension of the complex edge physics in the fractional quantum Hall regime.
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Affiliation(s)
- G Le Breton
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette cedex, France
| | - R Delagrange
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette cedex, France
| | - Y Hong
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120 Palaiseau, France
| | - M Garg
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette cedex, France
| | - K Watanabe
- National Institute for Materials Science, 1-1 Namiki, 305-0044 Tsukuba, Japan
| | - T Taniguchi
- National Institute for Materials Science, 1-1 Namiki, 305-0044 Tsukuba, Japan
| | - R Ribeiro-Palau
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120 Palaiseau, France
| | - P Roulleau
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette cedex, France
| | - P Roche
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette cedex, France
| | - F D Parmentier
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette cedex, France
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4
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Melcer RA, Dutta B, Spånslätt C, Park J, Mirlin AD, Umansky V. Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale. Nat Commun 2022; 13:376. [PMID: 35046393 PMCID: PMC8770503 DOI: 10.1038/s41467-022-28009-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Accepted: 11/11/2021] [Indexed: 11/25/2022] Open
Abstract
Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream propagating edge modes, which leads to complex transport behavior. Here, we combine two measurement techniques, local noise thermometry and thermal conductance, to study thermal properties of states with counter-propagating edge modes. We find that, while charge equilibration between counter-propagating edge modes is very fast, the equilibration of heat is extremely inefficient, leading to an almost ballistic heat transport over macroscopic distances. Moreover, we observe an emergent quantization of the heat conductance associated with a strong interaction fixed point of the edge modes. Such understanding of the thermal equilibration on edges with counter-propagating modes is a natural route towards extracting the topological order of the exotic 5/2 state. The transport behaviour of counter-propagating edge modes in the hole-conjugate fractional quantum Hall state is not fully understood. Here, by combining local noise thermometry and thermal conductance measurements, the authors show the absence of thermal equilibration on the edge at macroscopic distances.
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Affiliation(s)
- Ron Aharon Melcer
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 761001, Israel.
| | - Bivas Dutta
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 761001, Israel
| | - Christian Spånslätt
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, S-412 96, Göteborg, Sweden.,Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany.,Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
| | - Jinhong Park
- Institute for Theoretical Physics, University of Cologne, Zülpicher Str. 77, 50937, Köln, Germany
| | - Alexander D Mirlin
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany.,Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany.,Petersburg Nuclear Physics Institute, 188300 St, Petersburg, Russia.,L. D. Landau Institute for Theoretical Physics RAS, 119334, Moscow, Russia
| | - Vladimir Umansky
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 761001, Israel
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5
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Kumar R, Srivastav SK, Spånslätt C, Watanabe K, Taniguchi T, Gefen Y, Mirlin AD, Das A. Observation of ballistic upstream modes at fractional quantum Hall edges of graphene. Nat Commun 2022; 13:213. [PMID: 35017473 PMCID: PMC8752686 DOI: 10.1038/s41467-021-27805-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 12/07/2021] [Indexed: 11/27/2022] Open
Abstract
The presence of "upstream" modes, moving against the direction of charge current flow in the fractional quantum Hall (FQH) phases, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here, we report noise measurements at the edges of FQH states realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at length, L = 4 μm and 10 μm away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for "hole-conjugate" FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remains independent of length, which matches our theoretical analysis demonstrating the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems.
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Affiliation(s)
- Ravi Kumar
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | | | - Christian Spånslätt
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96, Göteborg, Sweden
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany
- Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
| | - K Watanabe
- National Institute of Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - T Taniguchi
- National Institute of Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Alexander D Mirlin
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany
- Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
- Petersburg Nuclear Physics Institute, 188300, St. Petersburg, Russia
- L. D. Landau Institute for Theoretical Physics RAS, 119334, Moscow, Russia
| | - Anindya Das
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
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6
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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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7
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Bhattacharyya R, Banerjee M, Heiblum M, Mahalu D, Umansky V. Melting of Interference in the Fractional Quantum Hall Effect: Appearance of Neutral Modes. PHYSICAL REVIEW LETTERS 2019; 122:246801. [PMID: 31322402 DOI: 10.1103/physrevlett.122.246801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2019] [Revised: 04/08/2019] [Indexed: 06/10/2023]
Abstract
We attempted to measure interference of the outer edge mode in the fractional quantum hall regime with an electronic Mach-zehnder interferometer. The visibility of the interferometer wore off as we approached ν_{B}=1 and the transmission of the quantum point contacts (QPCs) of the interferometer simultaneously developed a v=1/3 conductance plateau accompanied by shot noise. The appearance of shot noise on this plateau indicates the appearance of nontopological neutral modes resulting from edge reconstruction. We have confirmed the presence of upstream neutral modes measuring upstream noise emanating from the QPC. The lack of interference throughout the lowest Landau level was correlated with a proliferation of neutral modes.
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Affiliation(s)
- Rajarshi Bhattacharyya
- Braun Center of Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 761001, Israel
| | - Mitali Banerjee
- Braun Center of Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 761001, Israel
| | - Moty Heiblum
- Braun Center of Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 761001, Israel
| | - Diana Mahalu
- Braun Center of Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 761001, Israel
| | - Vladimir Umansky
- Braun Center of Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 761001, Israel
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8
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Balram AC, Mukherjee S, Park K, Barkeshli M, Rudner MS, Jain JK. Fractional Quantum Hall Effect at ν=2+6/13: The Parton Paradigm for the Second Landau Level. PHYSICAL REVIEW LETTERS 2018; 121:186601. [PMID: 30444400 DOI: 10.1103/physrevlett.121.186601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Indexed: 06/09/2023]
Abstract
The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν=2+6/13 [A. Kumar et al., Phys. Rev. Lett. 105, 246808 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.246808] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a "3[over ¯]2[over ¯]111" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the 3[over ¯]2[over ¯]111 state to be a good candidate for the ν=2+6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the "n[over ¯]2[over ¯]111" family of parton states naturally describes many observed SLL FQHE plateaus.
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Affiliation(s)
- Ajit C Balram
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Sutirtha Mukherjee
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Kwon Park
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Maissam Barkeshli
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20472, USA
| | - Mark S Rudner
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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9
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Observation of half-integer thermal Hall conductance. Nature 2018; 559:205-210. [DOI: 10.1038/s41586-018-0184-1] [Citation(s) in RCA: 191] [Impact Index Per Article: 31.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2017] [Accepted: 03/26/2018] [Indexed: 11/08/2022]
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10
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Goldstein M, Gefen Y. Suppression of Interference in Quantum Hall Mach-Zehnder Geometry by Upstream Neutral Modes. PHYSICAL REVIEW LETTERS 2016; 117:276804. [PMID: 28084761 DOI: 10.1103/physrevlett.117.276804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2016] [Indexed: 06/06/2023]
Abstract
Mach-Zehnder interferometry has been proposed as a probe for detecting the statistics of anyonic quasiparticles in fractional quantum Hall (FQH) states. Here, we focus on interferometers made of multimode edge states with upstream modes. We find that the interference visibility is suppressed due to downstream-upstream mode entanglement; the latter serves as a "which path" detector to the downstream interfering trajectories. Our analysis tackles a concrete realization of a filling factor of ν=2/3, but its applicability goes beyond that specific case, and encompasses the recent observation of the ubiquitous emergence of upstream neutral modes in FQH states. The latter, according to our analysis, goes hand in hand with the failure to observe Mach-Zehnder anyonic interference in fractional states. We point out how charge-neutral mode disentanglement will resuscitate the interference signal.
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Affiliation(s)
- Moshe Goldstein
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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11
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Jacak J, Jacak L. Unconventional fractional quantum Hall effect in monolayer and bilayer graphene. SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS 2016; 17:149-165. [PMID: 27877866 PMCID: PMC5102017 DOI: 10.1080/14686996.2016.1145531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Revised: 12/20/2015] [Accepted: 12/22/2015] [Indexed: 06/06/2023]
Abstract
The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition.
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Affiliation(s)
- Janusz Jacak
- Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
| | - Lucjan Jacak
- Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
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12
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Łydżba P, Jacak L, Jacak J. Hierarchy of fillings for the FQHE in monolayer graphene. Sci Rep 2015; 5:14287. [PMID: 26392385 PMCID: PMC4585763 DOI: 10.1038/srep14287] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2015] [Accepted: 08/21/2015] [Indexed: 12/03/2022] Open
Abstract
In this paper, the commensurability conditions, which originated from the unique topology of two-dimensional systems, are applied to determine the quantum Hall effect hierarchy in the case of a monolayer graphene. The fundamental difference in a definition of a typical semiconductor and a monolayer graphene filling factor is pointed out. The calculations are undertaken for all spin-valley branches of two lowest Landau levels, since only they are currently experimentally accessible. The obtained filling factors are compared with the experimental data and a very good agreement is achieved. The work also introduces a concept of the single-loop fractional quantum Hall effect.
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Affiliation(s)
- Patrycja Łydżba
- Faculty of Fundamental Problems of Technology, Wroclaw University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
| | - Lucjan Jacak
- Faculty of Fundamental Problems of Technology, Wroclaw University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
| | - Janusz Jacak
- Faculty of Fundamental Problems of Technology, Wroclaw University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
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13
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Kleinbaum E, Kumar A, Pfeiffer LN, West KW, Csáthy GA. Gap reversal at filling factors 3+1/3 and 3+1/5: towards novel topological order in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 2015; 114:076801. [PMID: 25763967 DOI: 10.1103/physrevlett.114.076801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Indexed: 06/04/2023]
Abstract
In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor ν=3+1/3, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν=3+1/3 and 3+1/5 states from the upper spin branch are reversed when compared to the ν=2+1/3 and 2+1/5 counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.
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Affiliation(s)
- Ethan Kleinbaum
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Ashwani Kumar
- Department of Physics, Monmouth College, Monmouth, Illinois 61462, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
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14
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Grivnin A, Inoue H, Ronen Y, Baum Y, Heiblum M, Umansky V, Mahalu D. Nonequilibrated counterpropagating edge modes in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 2014; 113:266803. [PMID: 25615371 DOI: 10.1103/physrevlett.113.266803] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2014] [Indexed: 06/04/2023]
Abstract
It is well established that density reconstruction at the edge of a two-dimensional electron gas takes place for hole-conjugate states in the fractional quantum Hall effect (such as v=2/3, 3/5, etc.). Such reconstruction leads, after equilibration between counterpropagating edge channels, to a downstream chiral current edge mode accompanied by upstream chiral neutral modes (carrying energy without net charge). Short equilibration length prevented thus far observation of the counterpropagating current channels-the hallmark of density reconstruction. Here, we provide evidence for such nonequilibrated counterpropagating current channels, in short regions (l=4 μm and l=0.4 μm) of fractional filling v=2/3 and, unexpectedly, v=1/3, sandwiched between two regions of integer filling v=1. Rather than a two-terminal fractional conductance, the conductance exhibited a significant ascension towards unity quantum conductance (GQ=e(2)/h) at or near the fractional plateaus. We attribute this conductance rise to the presence of a nonequilibrated channel in the fractional short regions.
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Affiliation(s)
- Anna Grivnin
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Hiroyuki Inoue
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yuval Ronen
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yuval Baum
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Vladimir Umansky
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Diana Mahalu
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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15
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Abstract
The dynamics of two component-coupled vectorial Airy beams is investigated. In the linear propagation regime, a complete analytic solution describes the breather-like propagation of two components that feature nondiffracting self-accelerating Airy behavior. The superposition of two beams with different input properties opens the possibility of designing more complex nondiffracting propagation scenarios. In the strongly nonlinear regime, the dynamics remain qualitatively robust as is revealed by direct numerical simulations. Because of the Kerr effect, the two beams emit solitonic breathers whose coupling period is compatible with the remaining Airy-like beams. The results of this study are relevant for the description of photonic and plasmonic beams that propagate in coupled planar waveguides, as well as for birefrigent or multiwavelength beams.
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16
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Driben R, Meier T. Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves. OPTICS LETTERS 2014; 39:5539-5542. [PMID: 25360922 DOI: 10.1364/ol.39.005539] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse.
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17
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Proliferation of neutral modes in fractional quantum Hall states. Nat Commun 2014; 5:4067. [DOI: 10.1038/ncomms5067] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2014] [Accepted: 05/07/2014] [Indexed: 11/09/2022] Open
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18
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Balram AC, Wu YH, Sreejith GJ, Wójs A, Jain JK. Role of exciton screening in the 7/3 fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 2013; 110:186801. [PMID: 23683230 DOI: 10.1103/physrevlett.110.186801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2012] [Indexed: 06/02/2023]
Abstract
The excitations of the 7/3 fractional Hall state, one of the most prominent states in the second Landau level, are not understood. We study the effect of screening by composite fermion excitons and find that it causes a strong renormalization at 7/3, thanks to a relatively small exciton gap and a relatively large residual interaction between composite fermions. The excitations of the 7/3 state are to be viewed as composite fermions dressed by a large exciton cloud. Their wide extent has implications for experiments as well as for analysis of finite system exact diagonalization studies.
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Affiliation(s)
- Ajit C Balram
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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19
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Wurstbauer U, West KW, Pfeiffer LN, Pinczuk A. Resonant inelastic light scattering investigation of low-lying gapped excitations in the quantum fluid at ν=5/2. PHYSICAL REVIEW LETTERS 2013; 110:026801. [PMID: 23383929 DOI: 10.1103/physrevlett.110.026801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2012] [Indexed: 05/06/2023]
Abstract
The low-lying neutral excitation spectrum of the incompressible quantum Hall fluid at ν=5/2 is investigated by inelastic light scattering. Gapped modes are observable only in a very narrow filling factor range centered at 5/2 at energies that overlap estimates from transport activation gaps. The modes are interpreted as critical points in the wave-vector dispersion of excitations that preserve spin orientation. For very small changes |δν|≲0.01 the gapped modes disappear and a continuum of low-lying excitations takes over indicating the transition from an incompressible fluid at 5/2 to a compressible state. Observations of spin wave modes indicate spin polarization of the 5/2 and 2+1/3 quantum Hall fluids.
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Affiliation(s)
- U Wurstbauer
- Department of Physics, Columbia University, New York, New York 10027, USA.
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Gurman I, Sabo R, Heiblum M, Umansky V, Mahalu D. Extracting net current from an upstream neutral mode in the fractional quantum Hall regime. Nat Commun 2012; 3:1289. [DOI: 10.1038/ncomms2305] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2012] [Accepted: 11/09/2012] [Indexed: 11/09/2022] Open
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21
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Viola G, Das S, Grosfeld E, Stern A. Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 2012; 109:146801. [PMID: 23083267 DOI: 10.1103/physrevlett.109.146801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Indexed: 06/01/2023]
Abstract
The ν=5/2 anti-Pfaffian state and the ν=2/3 state are believed to have an edge composed of counterpropagating charge and neutral modes. This situation allows the generation of a pure thermal bias between two composite edge states across a quantum point contact as was experimentally established by Bid et al. [Nature 466, 585 (2010)]. We show that replacing the quantum point contact by a quantum dot provides a natural way for detecting the neutral modes via the dc current generated by the thermoelectric response of the dot. We also show that the degeneracies of the dot spectrum, dictated by the conformal field theories describing these states, induce asymmetries in the thermoelectric current peaks. This in turn provides a direct fingerprint of the corresponding conformal field theory.
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Affiliation(s)
- Giovanni Viola
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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22
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Altimiras C, le Sueur H, Gennser U, Anthore A, Cavanna A, Mailly D, Pierre F. Chargeless heat transport in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 2012; 109:026803. [PMID: 23030194 DOI: 10.1103/physrevlett.109.026803] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate a direct approach to investigate heat transport in the fractional quantum Hall regime. At a filling factor of ν=4/3, we inject power at quantum point contacts and detect the related heating from the activated current through a quantum dot. The experiment reveals a chargeless heat transport from a significant heating that occurs upstream of the power injection point, in the absence of a concomitant electrical current. By tuning in situ the edge path, we show that the chargeless heat transport does not follow the reverse direction of the electrical current path along the edge. This unexpected heat conduction, whose mechanism remains to be elucidated, may play an important role in the physics of the fractional quantum Hall regime.
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Affiliation(s)
- C Altimiras
- CNRS/Université Paris Diderot (Sorbonne Paris Cité), Laboratoire de Photonique et de Nanostructures (LPN), Route de Nozay, 91460 Marcoussis, France
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23
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Gross Y, Dolev M, Heiblum M, Umansky V, Mahalu D. Upstream neutral modes in the fractional quantum Hall effect regime: heat waves or coherent dipoles. PHYSICAL REVIEW LETTERS 2012; 108:226801. [PMID: 23003636 DOI: 10.1103/physrevlett.108.226801] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2011] [Indexed: 06/01/2023]
Abstract
Counterpropagating (upstream) chiral neutral edge modes, which were predicted to be present in hole-conjugate states, were observed recently in a variety of fractional quantum Hall states (ν=2/3, ν=3/5, ν=8/3, and ν=5/2), by measuring the charge noise that resulted after partitioning the neutral mode by a constriction (denoted, as N→C). Particularly noticeable was the observation of such modes in the ν=5/2 fractional state--as it sheds light on the non-Abelian nature of the state's wave function. Yet, the nature of these unique, upstream, chargeless modes and the microscopic process in which they generate shot noise, are not understood. Here, we study the ubiquitous ν=2/3 state and report of two main observations: First, the nature of the neutral modes was tested by "colliding" two modes, emanating from two opposing sources, in a narrow constriction. The resultant charge noise was consistent with local heating of the partitioned quasiparticles. Second, partitioning of a downstream charge mode by a constriction gave birth to a dual process, namely, the appearance of an upstream neutral mode (C→N). In other words, splitting "hole conjugated" type quasiparticles will lead to an energy loss and decoherence, with energy carried away by neutral modes.
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Affiliation(s)
- Yaron Gross
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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24
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Deng N, Kumar A, Manfra MJ, Pfeiffer LN, West KW, Csáthy GA. Collective nature of the reentrant integer quantum Hall states in the second Landau level. PHYSICAL REVIEW LETTERS 2012; 108:086803. [PMID: 22463555 DOI: 10.1103/physrevlett.108.086803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2011] [Indexed: 05/31/2023]
Abstract
We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.
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Affiliation(s)
- N Deng
- Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
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25
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Tiemann L, Gamez G, Kumada N, Muraki K. Unraveling the Spin Polarization of the ν = 5/2 Fractional Quantum Hall State. Science 2012; 335:828-31. [DOI: 10.1126/science.1216697] [Citation(s) in RCA: 135] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- L. Tiemann
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi 243-0198, Japan
- ERATO Nuclear Spin Electronics Project, Japan Science and Technology Agency (JST), Kawaguchi 332-0012, Japan
| | - G. Gamez
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi 243-0198, Japan
| | - N. Kumada
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi 243-0198, Japan
| | - K. Muraki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi 243-0198, Japan
- ERATO Nuclear Spin Electronics Project, Japan Science and Technology Agency (JST), Kawaguchi 332-0012, Japan
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26
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Apalkov VM, Chakraborty T. Stable Pfaffian state in bilayer graphene. PHYSICAL REVIEW LETTERS 2011; 107:186803. [PMID: 22107662 DOI: 10.1103/physrevlett.107.186803] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2011] [Indexed: 05/31/2023]
Abstract
Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.
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Affiliation(s)
- Vadim M Apalkov
- Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA
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