1
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Wu M, Liu X, Wang R, Chung YJ, Gupta A, Baldwin KW, Pfeiffer L, Lin X, Liu Y. Probing Quantum Phases in Ultra-High-Mobility Two-Dimensional Electron Systems Using Surface Acoustic Waves. PHYSICAL REVIEW LETTERS 2024; 132:076501. [PMID: 38427873 DOI: 10.1103/physrevlett.132.076501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Revised: 11/21/2023] [Accepted: 01/16/2024] [Indexed: 03/03/2024]
Abstract
Transport measurement, which applies an electric field and studies the migration of charged particles, i.e., the current, is the most widely used technique in condensed matter studies. It is generally assumed that the quantum phase remains unchanged when it hosts a sufficiently small probing current, which is, surprisingly, rarely examined experimentally. In this Letter, we study the ultra-high-mobility two-dimensional electron system using a propagating surface acoustic wave, whose traveling speed is affected by the electrons' compressibility. The acoustic power used in our Letter is several orders of magnitude lower than previous reports, and its induced perturbation to the system is smaller than the transport current. Therefore we are able to observe the quantum phases become more incompressible when hosting a perturbative current.
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Affiliation(s)
- Mengmeng Wu
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
| | - Xiao Liu
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
| | - Renfei Wang
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
| | - Yoon Jang Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Adbhut Gupta
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Kirk W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Loren Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Haidian, Beijing 100871, China
| | - Yang Liu
- International Center for Quantum Materials, Peking University, Haidian, Beijing 100871, China
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2
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Yan J, Wu Y, Yuan S, Liu X, Pfeiffer LN, West KW, Liu Y, Fu H, Xie XC, Lin X. Anomalous quantized plateaus in two-dimensional electron gas with gate confinement. Nat Commun 2023; 14:1758. [PMID: 36997525 PMCID: PMC10064851 DOI: 10.1038/s41467-023-37495-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2022] [Accepted: 03/16/2023] [Indexed: 04/01/2023] Open
Abstract
AbstractQuantum information can be coded by the topologically protected edges of fractional quantum Hall (FQH) states. Investigation on FQH edges in the hope of searching and utilizing non-Abelian statistics has been a focused challenge for years. Manipulating the edges, e.g. to bring edges close to each other or to separate edges spatially, is a common and essential step for such studies. The FQH edge structures in a confined region are typically presupposed to be the same as that in the open region in analysis of experimental results, but whether they remain unchanged with extra confinement is obscure. In this work, we present a series of unexpected plateaus in a confined single-layer two-dimensional electron gas (2DEG), which are quantized at anomalous fractions such as 9/4, 17/11, 16/13 and the reported 3/2. We explain all the plateaus by assuming surprisingly larger filling factors in the confined region. Our findings enrich the understanding of edge states in the confined region and in the applications of gate manipulation, which is crucial for the experiments with quantum point contact and interferometer.
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3
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Hossain MS, Ma MK, Chung YJ, Singh SK, Gupta A, West KW, Baldwin KW, Pfeiffer LN, Winkler R, Shayegan M. Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System. PHYSICAL REVIEW LETTERS 2023; 130:126301. [PMID: 37027870 DOI: 10.1103/physrevlett.130.126301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 02/22/2023] [Indexed: 06/19/2023]
Abstract
Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν=1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the ν=1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν=1/2 FQHS depend strongly on valley occupancy.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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4
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Yutushui M, Stern A, Mross DF. Identifying the ν=5/2 Topological Order through Charge Transport Measurements. PHYSICAL REVIEW LETTERS 2022; 128:016401. [PMID: 35061467 DOI: 10.1103/physrevlett.128.016401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Accepted: 10/27/2021] [Indexed: 06/14/2023]
Abstract
We propose an experiment to identify the topological order of the ν=5/2 state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing ν=2,5/2, and 3 in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the Moore-Read and anti-Pfaffian topological orders, which are favored by numerical calculations.
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Affiliation(s)
- Misha Yutushui
- 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
| | - David F Mross
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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5
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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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6
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Yan J, Yao J, Shvarts V, Du RR, Lin X. Cryogen-free one hundred microkelvin refrigerator. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:025120. [PMID: 33648063 DOI: 10.1063/5.0036497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 02/04/2021] [Indexed: 06/12/2023]
Abstract
A temperature below 100 µK is achieved in a customized cryogen-free dilution refrigerator with a copper-nuclear demagnetization stage. The lowest temperature of conduction electrons of the demagnetization stage is below 100 µK as measured by using a pulsed platinum nuclear magnetic resonance thermometer, and the temperature can remain below 100 µK for over 10 h. A demagnetization magnetic field of up to 9 T and a research magnetic field of up to 12 T can be controlled independently, provided by a coaxial room-temperature-bore cryogen-free magnet.
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Affiliation(s)
- Jiaojie Yan
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jianing Yao
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Vladimir Shvarts
- Janis Research Company LLC, Wilmington, Massachusetts 01887, USA
| | - Rui-Rui Du
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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7
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Yang B. Fractional Quantum Hall Effect from Frustration-Free Hamiltonians. PHYSICAL REVIEW LETTERS 2020; 125:176402. [PMID: 33156656 DOI: 10.1103/physrevlett.125.176402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 09/24/2020] [Indexed: 05/06/2023]
Abstract
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalized set of few-body coherent states. In particular, model Hamiltonians of the FQH effect (FQHE) are equivalent to the real-space von Neumann lattice of local projection operators imposed on a continuous system in the thermodynamic limit. It can be analytically derived that tuning local one-body potentials in such lattices amounts to the tuning of individual two- or few-body pseudopotentials. For some cases, we can realize pure few-body pseudopotentials important for stabilizing exotic non-Abelian topological phases. Thus, this new approach can potentially lead to the experimental realization of coveted non-Abelian quantum fluids including the Moore-Read state and the Fibonacci state. The reformulation of the FQHE as a sum of local projections opens up new paths for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit.
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Affiliation(s)
- Bo Yang
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371 and Institute of High Performance Computing, A*STAR, Singapore, 138632
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8
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Fei F, Zhang S, Zhang M, Shah SA, Song F, Wang X, Wang B. The Material Efforts for Quantized Hall Devices Based on Topological Insulators. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1904593. [PMID: 31840308 DOI: 10.1002/adma.201904593] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Revised: 09/09/2019] [Indexed: 06/10/2023]
Abstract
A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.
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Affiliation(s)
- Fucong Fei
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Shuai Zhang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Minhao Zhang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Syed Adil Shah
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Fengqi Song
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Xuefeng Wang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Baigeng Wang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
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9
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Jacak JE. Homotopy Phases of FQHE with Long-Range Quantum Entanglement in Monolayer and Bilayer Hall Systems. NANOMATERIALS (BASEL, SWITZERLAND) 2020; 10:E1286. [PMID: 32629942 PMCID: PMC7408279 DOI: 10.3390/nano10071286] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/09/2020] [Revised: 06/08/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
Correlated phases in Hall systems have topological character. Multilayer configurations of planar electron systems create the opportunity to change topological phases on demand using macroscopic factors, such as vertical voltage. We present an analysis of such phenomena in close relation to recent experiments with multilayer Hall setups including GaAs and graphene multi-layers. The consequences of the blocking or not of the inter-layer electron tunneling in stacked Hall configurations are analyzed and presented in detail. Multilayer Hall systems are thus tunable topological composite nanomaterials, in the case of graphene-stacked systems by both intra- and inter-layer voltage.
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Affiliation(s)
- Janusz Edward Jacak
- Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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10
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Kumar S, Pepper M, Holmes SN, Montagu H, Gul Y, Ritchie DA, Farrer I. Zero-Magnetic Field Fractional Quantum States. PHYSICAL REVIEW LETTERS 2019; 122:086803. [PMID: 30932620 DOI: 10.1103/physrevlett.122.086803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Indexed: 06/09/2023]
Abstract
Since the discovery of the fractional quantum Hall effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing magnetic field. Although various situations have been theoretically envisaged, particularly lattice models in which band flattening resembles Landau levels, the predicted fractions have never been observed. In this Letter, we show that odd and even denominator fractions can be observed, and manipulated, in the absence of a quantizing magnetic field, when a low-density electron system in a GaAs based one-dimensional quantum wire is allowed to relax in the second dimension. It is suggested that such a relaxation results in formation of a zigzag array of electrons with ring paths which establish a cyclic current and a resultant lowering of energy. The behavior has been observed for both symmetric and asymmetric confinement but increasing the asymmetry of the confinement potential, to result in a flattening of confinement, enhances the appearance of new fractional states. We find that an in-plane magnetic field induces new even denominator fractions possibly indicative of electron pairing. The new quantum states described here have implications both for the physics of low dimensional electron systems and also for quantum technologies. This work will enable further development of structures which are designed to electrostatically manipulate the electrons for the formation of particular configurations. In turn, this could result in a designer tailoring of fractional states to amplify particular properties of importance in future quantum computation.
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Affiliation(s)
- S Kumar
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - M Pepper
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - S N Holmes
- Toshiba Research Europe Limited, Cambridge Research Laboratory, 208 Cambridge Science Park, Milton Road, Cambridge CB4 0GZ, United Kingdom
| | - H Montagu
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - Y Gul
- London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - D A Ritchie
- Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom
| | - I Farrer
- Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom
- Now at Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
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11
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Wang P, Huang K, Sun J, Hu J, Fu H, Lin X. Piezo-driven sample rotation system with ultra-low electron temperature. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:023905. [PMID: 30831686 DOI: 10.1063/1.5083994] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Accepted: 01/19/2019] [Indexed: 06/09/2023]
Abstract
Piezo-driven rotator is convenient for tilted magnetic field experiments due to its precise angle control. However, the rotator itself and the sample mounted on it are difficult to be cooled down because of extra heat leaks and presumably bad thermal contacts from the piezo. Here, we report a piezo-driven sample rotation system designed for ultra-low temperature environment. The sample, as well as the rotating sample holder, can be cooled to as low as 25 mK by customized thermal links and thermal contacts. More importantly, the electron temperature in the electrical transport measurements can also be cooled down to 25 mK with the help of home-made filters. To demonstrate the application of our rotation system at ultra-low electron temperature, a measurement revealing tilt-induced localization and delocalization in the second Landau level of two-dimensional electron gas is provided.
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Affiliation(s)
- Pengjie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ke Huang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jian Sun
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jingjin Hu
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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12
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Hossain MS, Ma MK, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Unconventional Anisotropic Even-Denominator Fractional Quantum Hall State in a System with Mass Anisotropy. PHYSICAL REVIEW LETTERS 2018; 121:256601. [PMID: 30608773 DOI: 10.1103/physrevlett.121.256601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Indexed: 06/09/2023]
Abstract
The fractional quantum Hall state (FQHS) observed at a half-filled Landau level in an interacting two-dimensional electron system (2DES) is among the most exotic states of matter as its quasiparticles are expected to be Majorana excitations with non-Abelian statistics. We demonstrate here the unexpected presence of such a state in a novel 2DES with a strong band-mass anisotropy. The FQHS we observe has unusual characteristics. While its Hall resistance is well quantized at low temperatures, it exhibits highly anisotropic in-plane transport resembling compressible stripe or nematic charge-density-wave phases. More striking, the anisotropy sets in suddenly below a critical temperature, suggesting a finite-temperature phase transition. Our observations highlight how anisotropy modifies the many-body phases of a 2DES, and should further fuel the discussion surrounding the enigmatic even-denominator FQHS.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, 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
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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13
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Hossain MS, Ma MK, Mueed MA, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Direct Observation of Composite Fermions and Their Fully-Spin-Polarized Fermi Sea near ν=5/2. PHYSICAL REVIEW LETTERS 2018; 120:256601. [PMID: 29979050 DOI: 10.1103/physrevlett.120.256601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2018] [Indexed: 06/08/2023]
Abstract
The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor ν=5/2 is arguably the most promising candidate for harboring Majorana quasiparticles with non-Abelian statistics and, thus, of potential use for topological quantum computing. The theoretical description of the ν=5/2 state is generally believed to involve a topological p-wave pairing of fully-spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near ν=5/2 or for an underlying fully-spin-polarized Fermi sea. Here, we report the observation of composite fermions very near ν=5/2 through geometric resonance measurements and find that the measured Fermi wave vector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of 5/2 fractional quantum Hall effect as a topological p-wave paired state of composite fermions.
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Affiliation(s)
- Md Shafayat Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Meng K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, 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
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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14
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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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15
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James AJA, Konik RM, Lecheminant P, Robinson NJ, Tsvelik AM. Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:046002. [PMID: 29480168 DOI: 10.1088/1361-6633/aa91ea] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1 + 1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
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Affiliation(s)
- Andrew J A James
- London Centre for Nanotechnology, University College London, Gordon Street, London WC1H 0AH, United Kingdom
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16
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Li J, Wen H, Watanabe K, Taniguchi T, Zhu J. Gate-Controlled Transmission of Quantum Hall Edge States in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:057701. [PMID: 29481178 DOI: 10.1103/physrevlett.120.057701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Revised: 12/01/2017] [Indexed: 06/08/2023]
Abstract
The edge states of the quantum Hall and fractional quantum Hall effect of a two-dimensional electron gas carry key information of the bulk excitations. Here we demonstrate gate-controlled transmission of edge states in bilayer graphene through a potential barrier with tunable height. The backscattering rate is continuously varied from 0 to close to 1, with fractional quantized values corresponding to the sequential complete backscattering of individual modes. Our experiments demonstrate the feasibility to controllably manipulate edge states in bilayer graphene, thus opening the door to more complex experiments.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Hua Wen
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Li JIA, Tan C, Chen S, Zeng Y, Taniguchi T, Watanabe K, Hone J, Dean CR. Even-denominator fractional quantum Hall states in bilayer graphene. Science 2017; 358:648-652. [DOI: 10.1126/science.aao2521] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Accepted: 09/25/2017] [Indexed: 12/13/2022]
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Competing ν = 5/2 fractional quantum Hall states in confined geometry. Proc Natl Acad Sci U S A 2016; 113:12386-12390. [PMID: 27791162 DOI: 10.1073/pnas.1614543113] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.
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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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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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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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Ki DK, Fal'ko VI, Abanin DA, Morpurgo AF. Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene. NANO LETTERS 2014; 14:2135-2139. [PMID: 24611523 DOI: 10.1021/nl5003922] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate low-temperature magneto-transport in recently developed, high-quality multiterminal suspended bilayer graphene devices, enabling the independent measurement of the longitudinal and transverse resistance. We observe clear signatures of the fractional quantum Hall effect with different states that are either fully developed, and exhibit a clear plateau in the transverse resistance with a concomitant dip in longitudinal resistance or incipient, and exhibit only a longitudinal resistance minimum. All observed states scale as a function of filling factor ν, as expected. An unprecedented even-denominator fractional state is observed at ν = -1/2 on the hole side, exhibiting a clear plateau in Rxy quantized at the expected value of 2h/e(2) with a precision of ∼0.5%. Many of our observations, together with a recent electronic compressibility measurement performed in graphene bilayers on hexagonal boron-nitride (hBN) substrates, are consistent with a recent theory that accounts for the effect of the degeneracy between the N = 0 and N = 1 Landau levels in the fractional quantum Hall effect and predicts the occurrence of a Moore-Read type ν = -1/2 state. Owing to the experimental flexibility of bilayer graphene, which has a gate-dependent band structure, can be easily accessed by scanning probes, and can be contacted with materials such as superconductors, our findings offer new possibilities to explore the microscopic nature of even-denominator fractional quantum Hall effect.
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Affiliation(s)
- Dong-Keun Ki
- Départment de Physique de la Matiére Condensée (DPMC) and Group of Applied Physics (GAP), University of Geneva , 24 Quai Ernest-Ansermet, CH1211 Genéve 4 Switzerland
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