1
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Freeman ML, Madathil PT, Pfeiffer LN, Baldwin KW, Chung YJ, Winkler R, Shayegan M, Engel LW. Origin of Pinning Disorder in Magnetic-Field-Induced Wigner Solids. PHYSICAL REVIEW LETTERS 2024; 132:176301. [PMID: 38728701 DOI: 10.1103/physrevlett.132.176301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Revised: 02/28/2024] [Accepted: 03/29/2024] [Indexed: 05/12/2024]
Abstract
At low Landau level filling factors (ν), Wigner solid phases of two-dimensional electron systems in GaAs are pinned by disorder and exhibit a pinning mode, whose frequency is a measure of the disorder that pins the Wigner solid. Despite numerous studies spanning the past three decades, the origin of the disorder that causes the pinning and determines the pinning mode frequency remains unknown. Here, we present a study of the pinning mode resonance in the low-ν Wigner solid phases of a series of ultralow-disorder GaAs quantum wells which are similar except for their varying well widths d. The pinning mode frequencies f_{p} decrease strongly as d increases, with the widest well exhibiting f_{p} as low as ≃35 MHz. The amount of reduction of f_{p} with increasing d can be explained remarkably well by tails of the wave function impinging into the alloy-disordered Al_{x}Ga_{1-x}As barriers that contain the electrons. However, it is imperative that the model for the confinement and wave function includes the Coulomb repulsion in the growth direction between the electrons as they occupy the quantum well.
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Affiliation(s)
- Matthew L Freeman
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - P T Madathil
- 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
| | - K W Baldwin
- 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
| | - R Winkler
- Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
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2
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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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3
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Villegas Rosales KA, Madathil PT, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Fractional Quantum Hall Effect Energy Gaps: Role of Electron Layer Thickness. PHYSICAL REVIEW LETTERS 2021; 127:056801. [PMID: 34397247 DOI: 10.1103/physrevlett.127.056801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
The fractional quantum Hall effect stands as a quintessential manifestation of an interacting two-dimensional electron system. One of the fractional quantum Hall effect's most fundamental characteristics is the energy gap separating the incompressible ground state from its excitations. Yet, despite nearly four decades of investigations, a quantitative agreement between the theoretically calculated and experimentally measured energy gaps is lacking. Here we report a systematic experimental study that incorporates very high-quality two-dimensional electron systems confined to GaAs quantum wells with fixed density and varying well widths. The results demonstrate a clear decrease of the energy gap as the electron layer is made thicker and the short-range component of the Coulomb interaction is weakened. We also provide a quantitative comparison between the measured energy gaps and the available theoretical calculations that takes into account the role of finite layer thickness and Landau level mixing. All the measured energy gaps fall below the calculations, but as the electron layer thickness increases, the results of experiments and calculations come closer. Accounting for the role of disorder in a phenomenological manner, we find better overall agreement between the measured and calculated energy gaps, although some puzzling discrepancies remain.
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Affiliation(s)
- K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - P T Madathil
- 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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4
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Paul J, Stevens CE, Smith RP, Dey P, Mapara V, Semenov D, McGill SA, Kaindl RA, Hilton DJ, Karaiskaj D. Coherent two-dimensional Fourier transform spectroscopy using a 25 Tesla resistive magnet. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:063901. [PMID: 31255018 DOI: 10.1063/1.5055891] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Accepted: 05/12/2019] [Indexed: 06/09/2023]
Abstract
We performed nonlinear optical two-dimensional Fourier transform spectroscopy measurements using an optical resistive high-field magnet on GaAs quantum wells. Magnetic fields up to 25 T can be achieved using the split helix resistive magnet. Two-dimensional spectroscopy measurements based on the coherent four-wave mixing signal require phase stability. Therefore, these measurements are difficult to perform in environments prone to mechanical vibrations. Large resistive magnets use extensive quantities of cooling water, which causes mechanical vibrations, making two-dimensional Fourier transform spectroscopy very challenging. Here, we report on the strategies we used to overcome these challenges and maintain the required phase-stability throughout the measurement. A self-contained portable platform was used to set up the experiments within the time frame provided by a user facility. Furthermore, this platform was floated above the optical table in order to isolate it from vibrations originating from the resistive magnet. Finally, we present two-dimensional Fourier transform spectra obtained from GaAs quantum wells at magnetic fields up to 25 T and demonstrate the utility of this technique in providing important details, which are obscured in one dimensional spectroscopy.
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Affiliation(s)
- Jagannath Paul
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | | | - Ryan P Smith
- Department of Physics, California State University-East Bay, Hayward, California 94542, USA
| | - Prasenjit Dey
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Varun Mapara
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Dimitry Semenov
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 30201, USA
| | - Steven A McGill
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 30201, USA
| | - Robert A Kaindl
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - David J Hilton
- Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA
| | - Denis Karaiskaj
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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5
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Zhao J, Zhang Y, Jain JK. Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing. PHYSICAL REVIEW LETTERS 2018; 121:116802. [PMID: 30265120 DOI: 10.1103/physrevlett.121.116802] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2018] [Indexed: 06/08/2023]
Abstract
The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the nonperturbative fixed-phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the ν-κ plane, where ν is the filling factor and κ is the strength of Landau-level (LL) mixing. The phase boundary is seen to exhibit a striking ν dependence, with the states away from the magic filling factors ν=n/(2pn+1) being much more susceptible to crystallization due to Landau-level mixing than those at ν=n/(2pn+1). Our results explain the qualitative difference between the experimental behaviors observed in n- and p-doped gallium arsenide quantum wells and, in particular, the existence of an insulating state for ν<1/3 and also for 1/3<ν<2/5 in low-density p-doped systems. We predict that, in the vicinity of ν=1/5 and ν=2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal, but rather into a strongly correlated crystal of composite fermions carrying two vortices.
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Affiliation(s)
- Jianyun Zhao
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Yuhe Zhang
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - J K Jain
- Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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6
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Tran S, Yang J, Gillgren N, Espiritu T, Shi Y, Watanabe K, Taniguchi T, Moon S, Baek H, Smirnov D, Bockrath M, Chen R, Lau CN. Surface transport and quantum Hall effect in ambipolar black phosphorus double quantum wells. SCIENCE ADVANCES 2017; 3:e1603179. [PMID: 28630916 PMCID: PMC5457033 DOI: 10.1126/sciadv.1603179] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2016] [Accepted: 04/05/2017] [Indexed: 06/07/2023]
Abstract
Quantum wells (QWs) constitute one of the most important classes of devices in the study of two-dimensional (2D) systems. In a double-layer QW, the additional "which-layer" degree of freedom gives rise to celebrated phenomena, such as Coulomb drag, Hall drag, and exciton condensation. We demonstrate facile formation of wide QWs in few-layer black phosphorus devices that host double layers of charge carriers. In contrast to traditional QWs, each 2D layer is ambipolar and can be tuned into n-doped, p-doped, or intrinsic regimes. Fully spin-polarized quantum Hall states are observed on each layer, with an enhanced Landé g factor that is attributed to exchange interactions. Our work opens the door for using 2D semiconductors as ambipolar single, double, or wide QWs with unusual properties, such as high anisotropy.
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Affiliation(s)
- Son Tran
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
- Department of Physics, Ohio State University, Columbus, OH 43220, USA
| | - Jiawei Yang
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
- Department of Physics, Ohio State University, Columbus, OH 43220, USA
| | - Nathaniel Gillgren
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
| | - Timothy Espiritu
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
| | - Yanmeng Shi
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Seongphill Moon
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA
- Department of Physics, Florida State University, Tallahassee, FL 32306, USA
| | - Hongwoo Baek
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA
| | - Dmitry Smirnov
- National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA
| | - Marc Bockrath
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
- Department of Physics, Ohio State University, Columbus, OH 43220, USA
| | - Ruoyu Chen
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
- Department of Physics, Ohio State University, Columbus, OH 43220, USA
| | - Chun Ning Lau
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
- Department of Physics, Ohio State University, Columbus, OH 43220, USA
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7
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Mueed MA, Kamburov D, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States. PHYSICAL REVIEW LETTERS 2016; 117:246801. [PMID: 28009213 DOI: 10.1103/physrevlett.117.246801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 06/06/2023]
Abstract
Via the application of a parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors ν=1 and 1/2. Near ν=1, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to ν=1/2, CFs appear single-layer-like (single component) as their resonance features correspond to the total density.
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Affiliation(s)
- M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Kamburov
- 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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8
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Liu Y, Hasdemir S, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Observation of an Anisotropic Wigner Crystal. PHYSICAL REVIEW LETTERS 2016; 117:106802. [PMID: 27636486 DOI: 10.1103/physrevlett.117.106802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2016] [Indexed: 06/06/2023]
Abstract
We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears in a large range of low Landau level fillings 1/3≲ν≲2/3 in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component (B_{∥}) leads to a crossing of the lowest two Landau levels, and an elongated hole wave function in the direction of B_{∥}. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along B_{∥} about 10 times smaller than the resistance perpendicular to B_{∥}. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal.
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Affiliation(s)
- Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S Hasdemir
- 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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9
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Hatke AT, Liu Y, Engel LW, Shayegan M, Pfeiffer LN, West KW, Baldwin KW. Microwave spectroscopy of the low-filling-factor bilayer electron solid in a wide quantum well. Nat Commun 2015; 6:7071. [PMID: 25947282 PMCID: PMC4432649 DOI: 10.1038/ncomms8071] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2014] [Accepted: 03/28/2015] [Indexed: 11/30/2022] Open
Abstract
At the low Landau filling factor termination of the fractional quantum Hall effect series, two-dimensional electron systems exhibit an insulating phase that is understood as a form of pinned Wigner solid. Here we use microwave spectroscopy to probe the transition to the insulator for a wide quantum well sample that can support single-layer or bilayer states depending on its overall carrier density. We find that the insulator exhibits a resonance which is characteristic of a bilayer solid. The resonance also reveals a pair of transitions within the solid, which are not accessible to dc transport measurements. As density is biased deeper into the bilayer solid regime, the resonance grows in specific intensity, and the transitions within the insulator disappear. These behaviours are suggestive of a picture of the insulating phase as an emulsion of liquid and solid components. In 2D electron gases, insulating behaviour at low fractional quantum Hall filling factors is understood by the formation of an electronic Wigner solid. Here, the authors use microwave spectroscopy to evidence an electron liquid–solid mixed phase in bilayer states of GaAs/AlGaAs wide quantum wells.
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Affiliation(s)
- A T Hatke
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - Y Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - M Shayegan
- 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
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10
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Vaezi A, Barkeshli M. Fibonacci anyons from Abelian bilayer quantum Hall states. PHYSICAL REVIEW LETTERS 2014; 113:236804. [PMID: 25526149 DOI: 10.1103/physrevlett.113.236804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2014] [Indexed: 06/04/2023]
Abstract
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.
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Affiliation(s)
- Abolhassan Vaezi
- Department of Physics, Cornell University, Ithaca, New York 14850, USA
| | - Maissam Barkeshli
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
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11
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12
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Microwave spectroscopic observation of distinct electron solid phases in wide quantum wells. Nat Commun 2014; 5:4154. [PMID: 24948190 PMCID: PMC4083423 DOI: 10.1038/ncomms5154] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2014] [Accepted: 05/19/2014] [Indexed: 11/08/2022] Open
Abstract
In high magnetic fields, two-dimensional electron systems can form a number of phases in which interelectron repulsion plays the central role, since the kinetic energy is frozen out by Landau quantization. These phases include the well-known liquids of the fractional quantum Hall effect, as well as solid phases with broken spatial symmetry and crystalline order. Solids can occur at the low Landau-filling termination of the fractional quantum Hall effect series but also within integer quantum Hall effects. Here we present microwave spectroscopy studies of wide quantum wells that clearly reveal two distinct solid phases, hidden within what in d.c. transport would be the zero diagonal conductivity of an integer quantum-Hall-effect state. Explanation of these solids is not possible with the simple picture of a Wigner solid of ordinary (quasi) electrons or holes.
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13
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Liu Y, Graninger AL, Hasdemir S, Shayegan M, Pfeiffer LN, West KW, Baldwin KW, Winkler R. Fractional quantum Hall effect at ν=1/2 in hole systems confined to GaAs quantum wells. PHYSICAL REVIEW LETTERS 2014; 112:046804. [PMID: 24580479 DOI: 10.1103/physrevlett.112.046804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2013] [Indexed: 06/03/2023]
Abstract
We observe the fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor ν=1/2 in two-dimensional hole systems confined to GaAs quantum wells of width 30 to 50 nm and having bilayerlike charge distributions. The ν=1/2 FQHE is stable when the charge distribution is symmetric and only in a range of intermediate densities, qualitatively similar to what is seen in two-dimensional electron systems confined to approximately twice wider GaAs quantum wells. Despite the complexity of the hole Landau level structure, originating from the coexistence and mixing of the heavy- and light-hole states, we find the hole ν=1/2 FQHE to be consistent with a two-component, Halperin-Laughlin (Ψ331) state.
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Affiliation(s)
- Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A L Graninger
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S Hasdemir
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- 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
| | - R Winkler
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA and Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
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14
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Graninger AL, Kamburov D, Shayegan M, Pfeiffer LN, West KW, Baldwin KW, Winkler R. Reentrant ν=1 quantum Hall state in a two-dimensional hole system. PHYSICAL REVIEW LETTERS 2011; 107:176810. [PMID: 22107562 DOI: 10.1103/physrevlett.107.176810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2011] [Indexed: 05/31/2023]
Abstract
We report the observation of a reentrant quantum Hall state at the Landau level filling factor ν=1 in a two-dimensional hole system confined to a 35-nm-wide (001) GaAs quantum well. The reentrant behavior is characterized by a weakening and eventual collapse of the ν=1 quantum Hall state in the presence of a parallel magnetic field component B(∥), followed by a strengthening and reemergence as B(∥) is further increased. The robustness of the ν=1 quantum Hall state during the transition depends strongly on the charge distribution symmetry of the quantum well, while the magnitude of B(∥) needed to invoke the transition increases with the total density of the system.
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Affiliation(s)
- A L Graninger
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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15
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Shabani J, Gokmen T, Chiu YT, Shayegan M. Evidence for developing fractional quantum Hall states at even denominator 1/2 and 1/4 fillings in asymmetric wide quantum wells. PHYSICAL REVIEW LETTERS 2009; 103:256802. [PMID: 20366273 DOI: 10.1103/physrevlett.103.256802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2009] [Indexed: 05/29/2023]
Abstract
We report the observation of developing fractional quantum Hall states at Landau level filling factors nu = 1/2 and 1/4 in electron systems confined to wide GaAs quantum wells with significantly asymmetric charge distributions. The very large electric subband separation and the highly asymmetric charge distribution at which we observe these quantum Hall states, together with the fact that they disappear when the charge distribution is made symmetric, suggest that these are one-component states, possibly described by the Moore-Read Pfaffian wave function.
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Affiliation(s)
- J Shabani
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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16
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Shabani J, Gokmen T, Shayegan M. Correlated states of electrons in wide quantum wells at low fillings: the role of charge distribution symmetry. PHYSICAL REVIEW LETTERS 2009; 103:046805. [PMID: 19659383 DOI: 10.1103/physrevlett.103.046805] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2009] [Indexed: 05/28/2023]
Abstract
Magnetotransport measurements on electrons confined to a 57-nm-wide, GaAs quantum well reveal that the correlated electron states at low Landau level fillings (nu) display a remarkable dependence on the symmetry of the electron charge distribution. At a density of 1.93 x 10;{11} cm;{-2}, a developing fractional quantum Hall state is observed at the even-denominator filling nu = 1/4 when the distribution is symmetric, but it quickly vanishes when the distribution is made asymmetric. At lower densities, as we make the charge distribution asymmetric, we observe a rapid strengthening of the insulating phases that surround the nu = 1/5 fractional quantum Hall state.
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Affiliation(s)
- J Shabani
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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17
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Wang Z, Chen YP, Engel LW, Tsui DC, Tutuc E, Shayegan M. Pinning modes and interlayer correlation in high-magnetic-field bilayer Wigner solids. PHYSICAL REVIEW LETTERS 2007; 99:136804. [PMID: 17930621 DOI: 10.1103/physrevlett.99.136804] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2006] [Indexed: 05/25/2023]
Abstract
We report studies of pinning mode resonances in the low total Landau filling (nu) Wigner solid of a series of bilayer hole samples with negligible interlayer tunneling and with varying interlayer separation d. Comparison of states with equal layer densities (p,p) to single layer states (p,0) produced in situ by biasing, indicates that there is interlayer quantum correlation in the solid at small d. Also, the resonance frequency at small d is decreased just near nu = 1/2 and 2/3, indicating the importance in the solid of correlations related to those in the fractional quantum Hall effects.
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Affiliation(s)
- Zhihai Wang
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
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18
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Faniel S, Tutuc E, De Poortere EP, Gustin C, Vlad A, Melinte S, Shayegan M, Bayot V. Thermopower of interacting GaAs bilayer hole systems in the reentrant insulating phase near nu=1. PHYSICAL REVIEW LETTERS 2005; 94:046802. [PMID: 15783582 DOI: 10.1103/physrevlett.94.046802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2004] [Indexed: 05/24/2023]
Abstract
We report thermopower measurements of interacting GaAs bilayer hole systems. When the carrier densities in the two layers are equal, these systems exhibit a reentrant insulating phase near the quantum Hall state at total filling factor nu=1. Our data show that, as the temperature is decreased, the thermopower diverges in the insulating phase. This behavior indicates the opening of an energy gap at low temperature, consistent with the formation of a pinned Wigner solid. We extract an energy gap and a Wigner solid melting phase diagram.
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Affiliation(s)
- S Faniel
- Cermin, PCPM and DICE Labs, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium.
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19
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Vakili K, Shkolnikov YP, Tutuc E, De Poortere EP, Shayegan M. Realization of an interacting two-valley AlAs bilayer system. PHYSICAL REVIEW LETTERS 2004; 92:186404. [PMID: 15169516 DOI: 10.1103/physrevlett.92.186404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2003] [Indexed: 05/24/2023]
Abstract
By using different widths for two AlAs quantum wells comprising a bilayer system, we force the X-point conduction-band electrons in the two layers to occupy valleys with different Fermi contours, electron effective masses, and g factors. Since the occupied valleys are at different X points of the Brillouin zone, the interlayer tunneling is negligibly small despite the close electron layer spacing. We demonstrate the realization of this system via magnetotransport measurements and the observation of a phase-coherent, bilayer nu=1 quantum Hall state flanked by a reentrant insulating phase.
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Affiliation(s)
- K Vakili
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
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20
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Tutuc E, Melinte S, De Poortere EP, Pillarisetty R, Shayegan M. Role of density imbalance in an interacting bilayer hole system. PHYSICAL REVIEW LETTERS 2003; 91:076802. [PMID: 12935040 DOI: 10.1103/physrevlett.91.076802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2002] [Indexed: 05/24/2023]
Abstract
We study interacting GaAs hole bilayers in the limit of zero interlayer tunneling. When the layers have equal density, we observe a phase-coherent bilayer quantum Hall state (QHS) at a total filling factor nu=1, flanked by a reentrant insulating phase at nearby fillings which suggests the formation of a pinned, bilayer Wigner crystal. As we transfer charge from one layer to another, the phase-coherent QHS becomes stronger, evincing its robustness against charge imbalance, but the insulating phase disappears, suggesting that its stability requires the commensurability of the two layers.
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Affiliation(s)
- E Tutuc
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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21
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Kellogg M, Eisenstein JP, Pfeiffer LN, West KW. Bilayer quantum hall systems at nu(T)=1: coulomb drag and the transition from weak to strong interlayer coupling. PHYSICAL REVIEW LETTERS 2003; 90:246801. [PMID: 12857210 DOI: 10.1103/physrevlett.90.246801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2002] [Indexed: 05/24/2023]
Abstract
Measurements revealing anomalously large frictional drag at the transition between the weakly and strongly coupled regimes of a bilayer two-dimensional electron system at total Landau level filling factor nu(T)=1 are reported. This result suggests the existence of fluctuations, either static or dynamic, near the phase boundary separating the quantized Hall state at small layer separations from the compressible state at larger separations. Interestingly, the anomalies in drag seem to persist to larger layer separations than does interlayer phase coherence as detected in tunneling.
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Affiliation(s)
- M Kellogg
- California Institute of Technology, Pasadena, California 91125, USA
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22
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Ye PD, Engel LW, Tsui DC, Lewis RM, Pfeiffer LN, West K. Correlation lengths of the wigner-crystal order in a two-dimensional electron system at high magnetic fields. PHYSICAL REVIEW LETTERS 2002; 89:176802. [PMID: 12398694 DOI: 10.1103/physrevlett.89.176802] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2002] [Indexed: 05/24/2023]
Abstract
The insulator terminating the fractional quantum Hall series at low Landau level filling nu is generally taken to be a pinned Wigner crystal (WC), and exhibits a microwave resonance that is interpreted as a WC pinning mode. For a high quality sample at several densities, n, we find maxima in resonance peak frequency, f(pk), vs magnetic field, B. L, the correlation length of WC order, is calculated from f(pk). For each n, L vs nu tends at low nu toward a line with positive intercept; the fit is accurate over as much as a factor of 5 range of nu. The linear behavior is interpreted as due to B compressing the electron wave functions, to alter the effective electron-impurity interaction.
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Affiliation(s)
- P D Ye
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
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