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Huang H, Hussain W, Myers SA, Pfeiffer LN, West KW, Baldwin KW, Csáthy GA. Evidence for Topological Protection Derived from Six-Flux Composite Fermions. Nat Commun 2024; 15:1461. [PMID: 38368413 PMCID: PMC10874392 DOI: 10.1038/s41467-024-45860-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 02/05/2024] [Indexed: 02/19/2024] Open
Abstract
The composite fermion theory opened a new chapter in understanding many-body correlations through the formation of emergent particles. The formation of two-flux and four-flux composite fermions is well established. While there are limited data linked to the formation of six-flux composite fermions, topological protection associated with them is conspicuously lacking. Here we report evidence for the formation of a quantized and gapped fractional quantum Hall state at the filling factor ν = 9/11, which we associate with the formation of six-flux composite fermions. Our result provides evidence for the most intricate composite fermion with six fluxes and expands the already diverse family of highly correlated topological phases with a new member that cannot be characterized by correlations present in other known members. Our observations pave the way towards the study of higher order correlations in the fractional quantum Hall regime.
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Affiliation(s)
- Haoyun Huang
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Waseem Hussain
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - S A Myers
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, 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
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
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2
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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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3
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Chen B, Wang X, Mi W. Dirac semimetallic Janus Ni-trihalide monolayer with strain-tunable magnetic anisotropy and electronic properties. Phys Chem Chem Phys 2023; 25:28638-28650. [PMID: 37874663 DOI: 10.1039/d3cp04261h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2023]
Abstract
Two-dimensional (2D) ferromagnetic (FM) semiconductors have been paid much attention due to the potential applications in spintronics. Here, the electronic and magnetic properties of 2D Janus Ni-trihalide monolayer Ni2X3Y3 (X, Y = I, Br, Cl; X ≠ Y) are investigated by first-principle calculations. The properties of Ni2X3Y3 (X, Y = I, Br, Cl; X ≠ Y) monolayers are compared by selecting the NiCl3 monolayer as the reference material. Ni2X3Y3 monolayers have two distinct magnetic ground states of ferromagnetic (FM) and antiferromagnetic (AFM). In the Ni2X3Y3 monolayer, two different orbital splits were observed, one semiconductor state and the other semimetal state. The semimetal state of Ni2X3Y3 can be tuned to semiconductor or metallic state when biaxial strain is applied. The magnetic anisotropy energy (MAE) of the Ni2X3Y3 monolayer can display variations compared to that of the NiCl3 monolayer, with the direction of easy magnetization being influenced by the specific halogen elements present. The easy magnetization direction of Ni2X3Y3 can also be changed by applying biaxial strain. The Tc of Ni2X3Y3 is predicted to be about 100 K according to the calculation of the EAFM-EFM model. The design of the Janus Ni2X3Y3 structure has expanded the range of 2D magnetic materials, a significant contribution has been made to the advancement of spintronics and its applications.
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Affiliation(s)
- Bo Chen
- Tianjin Key Laboratory of Film Electronic & Communicate Devices, School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin 300384, China.
| | - Xiaocha Wang
- Tianjin Key Laboratory of Film Electronic & Communicate Devices, School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin 300384, China.
| | - Wenbo Mi
- Department of Applied Physics, School of Science, Tianjin University, Tianjin 300354, China.
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4
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Das S, Das S, Mandal SS. Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength. PHYSICAL REVIEW LETTERS 2023; 131:056202. [PMID: 37595232 DOI: 10.1103/physrevlett.131.056202] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 06/26/2023] [Indexed: 08/20/2023]
Abstract
A successful probing of the neutral Majorana mode in recent thermal Hall conductivity measurements opines in favor of the particle-hole symmetric Pfaffian (PH-Pf) topological order, contrasting the theoretical predictions of Pfaffian or anti-Pfaffian phases. Here we report a reentrant anomalous quantized phase that is found to be gapped in the thermodynamic limit, distinct from the conventional Pfaffian, anti-Pfaffian, or PH-Pf phases, at an intermediate strength of Landau level mixing. Our proposed wave function consistent with the PH-Pf shift in spherical geometry rightly captures the topological order of this phase, as its overlap with the exact ground state is very high and it reproduces low-lying entanglement spectra. A unique topological order, irrespective of the flux shifts, found for this phase, possibly corroborates the experimentally found topological order.
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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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5
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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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Fu H, Huang K, Watanabe K, Taniguchi T, Kayyalha M, Zhu J. Aharonov-Bohm Oscillations in Bilayer Graphene Quantum Hall Edge State Fabry-Pérot Interferometers. NANO LETTERS 2023; 23:718-725. [PMID: 36622939 DOI: 10.1021/acs.nanolett.2c05004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Bernal-stacked bilayer graphene exhibits a wealth of interaction-driven phenomena, including robust even-denominator fractional quantum Hall states. We construct Fabry-Pérot interferometers using a split-gate design and present measurements of the Aharonov-Bohm oscillations. The edge state velocity is found to be approximately 6 × 104 m/s at filling factor ν = 2 and decreases with increasing filling factor. The dc bias and temperature dependence of the interference point to electron-electron interaction induced decoherence mechanisms. These results pave the way for the quest of fractional and non-Abelian braiding statistics in this promising device platform.
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Affiliation(s)
- Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania16802, United States
- School of Physics, Zhejiang University, Hangzhou310058, People's Republic of China
| | - Ke Huang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania16802, United States
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba305-0044, Japan
| | - Morteza Kayyalha
- Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania16802, United States
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania16802, United States
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania16802, United States
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7
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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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8
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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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9
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Park J, Spånslätt C, Gefen Y, Mirlin AD. Noise on the non-Abelian ν=5/2 Fractional Quantum Hall Edge. PHYSICAL REVIEW LETTERS 2020; 125:157702. [PMID: 33095623 DOI: 10.1103/physrevlett.125.157702] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
The recent measurement of a half-integer thermal conductance for the ν=5/2 fractional quantum Hall state has confirmed its non-Abelian nature, making the question of the underlying topological order highly intriguing. We analyze the shot noise at the edge of the three most prominent non-Abelian candidate states. We show that the noise scaling with respect to the edge length can, in combination with the thermal conductance, be used to experimentally distinguish between the Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian edge structures.
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Affiliation(s)
- Jinhong Park
- Institute for Theoretical Physics, University of Cologne, Zülpicher Strasse 77, 50937 Köln, Germany
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Christian Spånslätt
- 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
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021 Karlsruhe, 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
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10
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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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11
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Toyoda T. Magnetic induction dependence of Hall resistance in Fractional Quantum Hall Effect. Sci Rep 2018; 8:12741. [PMID: 30143739 PMCID: PMC6109190 DOI: 10.1038/s41598-018-31205-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Accepted: 08/14/2018] [Indexed: 11/09/2022] Open
Abstract
Quantum Hall effects (QHE) are observed in two-dimensional electron systems realised in semiconductors and graphene. In QHE the Hall resistance exhibits plateaus as a function of magnetic induction. In the fractional quantum Hall effects (FQHE) the values of the Hall resistance on plateaus are h/e2 divided by rational fractions, where -e is the electron charge and h is the Planck constant. The magnetic induction dependence of the Hall resistance is the strongest experimental evidence for FQHE. Nevertheless a quantitative theory of the magnetic induction and temperature dependence of the Hall resistance is still missing. Here we constructed a model for the Hall resistance as a function of magnetic induction, chemical potential and temperature. We assume phenomenological perturbation terms in the single-electron energy spectrum. The perturbation terms successively split a Landau level into sublevels, whose reduced degeneracies cause the fractional quantization of Hall resistance. The model yields all 75 odd-denominator fractional plateaus that have been experimentally found. The calculated magnetic induction dependence of the Hall resistance is consistent with experiments. This theory shows that the Fermi liquid theory is valid for FQHE.
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Affiliation(s)
- Tadashi Toyoda
- 0000 0001 1516 6626grid.265061.6Department of Physics, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292 Japan
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12
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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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13
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Hao T. Integer, fractional, and anomalous quantum Hall effects explained with Eyring's rate process theory and free volume concept. Phys Chem Chem Phys 2017; 19:6042-6050. [PMID: 28191574 DOI: 10.1039/c6cp08226b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The Hall effects, especially the integer, fractional and anomalous quantum Hall effects, have been addressed using Eyring's rate process theory and free volume concept. The basic assumptions are that the conduction process is a common rate controlled "reaction" process that can be described with Eyring's absolute rate process theory; the mobility of electrons should be dependent on the free volume available for conduction electrons. The obtained Hall conductivity is clearly quantized as with prefactors related to both the magnetic flux quantum number and the magnetic quantum number via the azimuthal quantum number, with and without an externally applied magnetic field. This article focuses on two dimensional (2D) systems, but the approaches developed in this article can be extended to 3D systems.
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Affiliation(s)
- Tian Hao
- 15905 Tanberry Dr., Chino Hills, CA 91709, USA.
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14
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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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