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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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Niu C, Qiu G, Wang Y, Si M, Wu W, Ye PD. Bilayer Quantum Hall States in an n-Type Wide Tellurium Quantum Well. NANO LETTERS 2021; 21:7527-7533. [PMID: 34514803 DOI: 10.1021/acs.nanolett.1c01705] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Tellurium (Te) is a narrow bandgap semiconductor with a unique chiral crystal structure. The topological nature of electrons in the Te conduction band can be studied by realizing n-type doping using atomic layer deposition (ALD) technique on two-dimensional (2D) Te film. In this work, we fabricated and measured the double-gated n-type Te Hall-bar devices, which can operate as two separate or coupled electron layers controlled by the top gate and back gate. Profound Shubnikov-de Haas (SdH) oscillations are observed in both top and bottom electron layers. Landau level hybridization between two layers, compound and charge-transferable bilayer quantum Hall states at filling factor ν = 4, 6, and 8, are analyzed. Our work opens the door for the study of Weyl physics in coupled bilayer systems of 2D materials.
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Affiliation(s)
- Chang Niu
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Gang Qiu
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Yixiu Wang
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Mengwei Si
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Wenzhuo Wu
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Peide D Ye
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
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3
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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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4
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Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene. Sci Rep 2016; 6:38068. [PMID: 27905496 PMCID: PMC5131475 DOI: 10.1038/srep38068] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2016] [Accepted: 11/04/2016] [Indexed: 01/29/2023] Open
Abstract
Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.
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5
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Teo JCY. Globally symmetric topological phase: from anyonic symmetry to twist defect. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:143001. [PMID: 26953520 DOI: 10.1088/0953-8984/28/14/143001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Topological phases in two dimensions support anyonic quasiparticle excitations that obey neither bosonic nor fermionic statistics. These anyon structures often carry global symmetries that relate distinct anyons with similar fusion and statistical properties. Anyonic symmetries associate topological defects or fluxes in topological phases. As the symmetries are global and static, these extrinsic defects are semiclassical objects that behave disparately from conventional quantum anyons. Remarkably, even when the topological states supporting them are Abelian, they are generically non-Abelian and powerful enough for topological quantum computation. In this article, I review the most recent theoretical developments on symmetries and defects in topological phases.
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Affiliation(s)
- Jeffrey C Y Teo
- Department of Physics, University of Virginia, VA 22904, USA
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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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7
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Liu G, Zhang C, Tsui DC, Knez I, Levine A, Du RR, Pfeiffer LN, West KW. Enhancement of the ν = 5/2 fractional quantum Hall state in a small in-plane magnetic field. PHYSICAL REVIEW LETTERS 2012; 108:196805. [PMID: 23003074 DOI: 10.1103/physrevlett.108.196805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2011] [Indexed: 06/01/2023]
Abstract
Using a 50-nm-width ultraclean GaAs/AlGaAs quantum well, we have studied the Landau level filling factor ν=5/2 fractional quantum Hall effect in a perpendicular magnetic field B∼1.7 T and determined its dependence on tilted magnetic fields. Contrary to all previous results, the 5/2 resistance minimum and the Hall plateau are found to strengthen continuously under an increasing tilt angle 0<θ<25° (corresponding to an in-plane magnetic field 0<B(∥)<0.8 T). In the same range of θ, the activation gaps of both the 7/3 and the 8/3 states are found to increase with tilt. The 5/2 state transforms into a compressible Fermi liquid upon tilt angle θ>60°, and the composite fermion series [2+p/(2p±1), p=1,2] can be identified. Based on our results, we discuss the relevance of a Skyrmion spin texture at ν=5/2 associated with small Zeeman energy in wide quantum wells, as proposed by Wójs et al. [Phys. Rev. Lett. 104, 086801 (2010)].
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Affiliation(s)
- Guangtong Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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8
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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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9
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Spielman IB, Eisenstein JP, Pfeiffer LN, West KW. Resonantly enhanced tunneling in a double layer quantum hall ferromagnet. PHYSICAL REVIEW LETTERS 2000; 84:5808-5811. [PMID: 10991060 DOI: 10.1103/physrevlett.84.5808] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2000] [Indexed: 05/23/2023]
Abstract
The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling nuT=1 the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed.
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Affiliation(s)
- I B Spielman
- California Institute of Technology, Pasadena, California 91125, USA
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10
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Davies AG, Barnes CH, Zolleis KR, Nicholls JT, Simmons MY, Ritchie DA. Hybridization of single- and double-layer behavior in a double-quantum-well structure. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:R17331-R17334. [PMID: 9985950 DOI: 10.1103/physrevb.54.r17331] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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11
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Brey L, Fertig HA, Côté R, MacDonald AH. Charged pseudospin textures in double-layer quantum Hall systems: Bimerons and meron crystals. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16888-16902. [PMID: 9985817 DOI: 10.1103/physrevb.54.16888] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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12
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Manoharan HC, Suen YW, Santos MB, Shayegan M. Evidence for a Bilayer Quantum Wigner Solid. PHYSICAL REVIEW LETTERS 1996; 77:1813-1816. [PMID: 10063178 DOI: 10.1103/physrevlett.77.1813] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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13
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Huang D, Manasreh MO. Effects of the screened exchange interaction on the tunneling and Landau gaps in double quantum wells. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:2044-2048. [PMID: 9986056 DOI: 10.1103/physrevb.54.2044] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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14
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Jungwirth T, MacDonald AH. Correlations, compressibility, and capacitance in double-quantum-well systems in the quantum Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:9943-9951. [PMID: 9982558 DOI: 10.1103/physrevb.53.9943] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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15
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Simmons JA, Harff NE, Klem JF. Observation of extreme field-induced mass deviations in double quantum wells. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:11156-11159. [PMID: 9977830 DOI: 10.1103/physrevb.51.11156] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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16
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Nakajima T, Aoki H. Manifestation of spin degrees of freedom in the double fractional quantum Hall system. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:7874-7877. [PMID: 9977374 DOI: 10.1103/physrevb.51.7874] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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17
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Lopez A, Fradkin E. Fermionic Chern-Simons theory for the fractional quantum Hall effect in bilayers. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:4347-4368. [PMID: 9979279 DOI: 10.1103/physrevb.51.4347] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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18
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Arovas DP, Renn SR. Bogoliubov theory of Coulomb-coupled. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:15408-15411. [PMID: 9975897 DOI: 10.1103/physrevb.50.15408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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19
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Simmons JA, Lyo SK, Harff NE, Klem JF. Conductance modulation in double quantum wells due to magnetic field-induced anticrossing. PHYSICAL REVIEW LETTERS 1994; 73:2256-2259. [PMID: 10057012 DOI: 10.1103/physrevlett.73.2256] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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20
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Kurobe A, Castleton IM, Linfield EH, Grimshaw MP, Brown KM, Ritchie DA, Pepper M, Jones GA. Wave functions and Fermi surfaces of strongly coupled two-dimensional electron gases investigated by in-plane magnetoresistance. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:4889-4892. [PMID: 9976804 DOI: 10.1103/physrevb.50.4889] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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21
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Suen YW, Manoharan HC, Ying X, Santos MB, Shayegan M. Origin of the nu =1/2 fractional quantum Hall state in wide single quantum wells. PHYSICAL REVIEW LETTERS 1994; 72:3405-3408. [PMID: 10056190 DOI: 10.1103/physrevlett.72.3405] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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22
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Groshev A, Schön G. Work function of a 2-dimensional electron gas in flat-band heterojunctions: The role of image charges. PHYSICAL REVIEW LETTERS 1993; 71:2809-2812. [PMID: 10054781 DOI: 10.1103/physrevlett.71.2809] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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23
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Chen XM, Quinn JJ. Collective excitations of an electron Wigner lattice in double-quantum-well systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:3999-4002. [PMID: 10006516 DOI: 10.1103/physrevb.47.3999] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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24
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Brey L. Many-body effects on the symmetric-antisymmetric gap in double quantum wells in strong magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:4585-4591. [PMID: 10006606 DOI: 10.1103/physrevb.47.4585] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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25
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Xia X, Chen XM, Quinn JJ. Collapse of fractional quantum Hall states in double-quantum-well systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:15526-15529. [PMID: 10003681 DOI: 10.1103/physrevb.46.15526] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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26
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Hu J, MacDonald AH. Electronic structure of parallel two-dimensional electron systems in tilted magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:12554-12559. [PMID: 10003175 DOI: 10.1103/physrevb.46.12554] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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27
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Chen XM, Quinn JJ. Correlated charge-density-wave states of double-quantum-well systems in a strong magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:11054-11066. [PMID: 10001028 DOI: 10.1103/physrevb.45.11054] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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28
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Boebinger GS, Pfeiffer LN, West KW. Direct observation of an electronic phase transition in a double quantum well. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:11391-11394. [PMID: 10001078 DOI: 10.1103/physrevb.45.11391] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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29
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Eisenstein JP, Boebinger GS, Pfeiffer LN, West KW, He S. New fractional quantum Hall state in double-layer two-dimensional electron systems. PHYSICAL REVIEW LETTERS 1992; 68:1383-1386. [PMID: 10046152 DOI: 10.1103/physrevlett.68.1383] [Citation(s) in RCA: 131] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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30
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Suen YW, Engel LW, Santos MB, Shayegan M, Tsui DC. Observation of a nu =1/2 fractional quantum Hall state in a double-layer electron system. PHYSICAL REVIEW LETTERS 1992; 68:1379-1382. [PMID: 10046151 DOI: 10.1103/physrevlett.68.1379] [Citation(s) in RCA: 117] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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