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Wijewardena UK, Nanayakkara TR, Kriisa A, Reichl C, Wegscheider W, Mani RG. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields. Sci Rep 2022; 12:19204. [PMID: 36357438 PMCID: PMC9649807 DOI: 10.1038/s41598-022-22812-x] [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: 08/21/2022] [Accepted: 10/19/2022] [Indexed: 11/12/2022] Open
Abstract
Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, \documentclass[12pt]{minimal}
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\begin{document}$$g \mu _B B$$\end{document}gμBB, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in \documentclass[12pt]{minimal}
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\begin{document}$$R_{xx}$$\end{document}Rxx minimum, e.g., from \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 11/7$$\end{document}ν=11/7 to \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 8/5$$\end{document}ν=8/5, and a corresponding change in the \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}$$\end{document}Rxy, e.g., from \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}/R_{K} = (11/7)^{-1}$$\end{document}Rxy/RK=(11/7)-1 to \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}/R_{K} = (8/5)^{-1}$$\end{document}Rxy/RK=(8/5)-1, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 4/3$$\end{document}ν=4/3 and \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 7/5$$\end{document}ν=7/5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}$$\end{document}Rxy at the \documentclass[12pt]{minimal}
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\begin{document}$$R_{xx}$$\end{document}Rxx minima- the latter occurring for \documentclass[12pt]{minimal}
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\begin{document}$$\nu = 4/3, 7/5$$\end{document}ν=4/3,7/5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}$$\end{document}Rxy, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.
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2
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Mani RG, Wijewardena UK, Nanayakkara TR, Kriisa A, Reichl C, Wegscheider W. Marginal metallic state at a fractional filling of '8/5' and '4/3' of Landau levels in the GaAs/AlGaAs 2D electron system. Sci Rep 2021; 11:15003. [PMID: 34294839 PMCID: PMC8298480 DOI: 10.1038/s41598-021-94563-0] [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: 03/22/2021] [Accepted: 07/08/2021] [Indexed: 11/09/2022] Open
Abstract
A metallic state with a vanishing activation gap, at a filling factor [Formula: see text] in the untilted specimen with [Formula: see text], and at [Formula: see text] at [Formula: see text] under a [Formula: see text] tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest, remarkably, that at the possible degeneracy point of states with different spin polarization, where the 8/5 or 4/3 FQHE vanish, there occurs a peculiar marginal metallic state that differs qualitatively from a quantum Hall insulating state and the usual quantum Hall metallic state. Such a marginal metallic state occurs most prominently at [Formula: see text], and at [Formula: see text] under tilt as mentioned above, over the interval [Formula: see text], that also includes the [Formula: see text] state, which appears perceptibly gapped in the first instance.
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Affiliation(s)
- R G Mani
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA.
| | - U K Wijewardena
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
| | - T R Nanayakkara
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
| | - Annika Kriisa
- Dept. of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
| | - C Reichl
- Department of Physics, ETH Zurich, 8093, Zurich, Switzerland
| | - W Wegscheider
- Department of Physics, ETH Zurich, 8093, Zurich, Switzerland
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3
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Huang K, Wang P, Pfeiffer LN, West KW, Baldwin KW, Liu Y, Lin X. Resymmetrizing Broken Symmetry with Hydraulic Pressure. PHYSICAL REVIEW LETTERS 2019; 123:206602. [PMID: 31809100 DOI: 10.1103/physrevlett.123.206602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2019] [Indexed: 06/10/2023]
Abstract
Recent progress in condensed matter physics, such as for graphene, topological insulators, and Weyl semimetals, often originate from the specific topological symmetries of their lattice structures. Quantum states with different degrees of freedom, e.g., spin, valley, layer, etc., arise from these symmetries, and the coherent superposition of these states form multiple energy subbands. The pseudospin, a concept analogous to the Dirac spinor matrices, is a successful description of such multisubband systems. When the electron-electron interaction dominates, many-body quantum phases arise. They usually have discrete pseudospin polarizations and exhibit sharp phase transitions at certain universal critical pseudospin energy splittings. In this Letter, we present our discovery of hydrostatic-pressure-induced degeneracy between the two lowest Landau levels. This degeneracy is evidenced by the pseudospin polarization transitions of the fragile correlated quantum liquid phases near the Landau level filling factor ν=3/2. Benefitting from the constant hole concentration and the sensitive nature of these transitions, we study the fine-tuning effect of the hydrostatic pressure at the order of 10 μeV, well beyond the meV-level state-of-the-art resolution of other techniques.
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Affiliation(s)
- Ke Huang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Pengjie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - 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
| | - Yang Liu
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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4
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Barkeshli M, Nayak C, Papić Z, Young A, Zaletel M. Topological Exciton Fermi Surfaces in Two-Component Fractional Quantized Hall Insulators. PHYSICAL REVIEW LETTERS 2018; 121:026603. [PMID: 30085706 DOI: 10.1103/physrevlett.121.026603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Indexed: 06/08/2023]
Abstract
A wide variety of two-dimensional electron systems allow for independent control of the total and relative charge density of two-component fractional quantum Hall (FQH) states. In particular, a recent experiment on bilayer graphene (BLG) observed a continuous transition between a compressible and incompressible phase at total filling ν_{T}=1/2 as charge is transferred between the layers, with the remarkable property that the incompressible phase has a finite interlayer polarizability. We argue that this occurs because the topological order of ν_{T}=1/2 systems supports a novel type of interlayer exciton that carries Fermi statistics. If the fermionic excitons are lower in energy than the conventional bosonic excitons (i.e., electron-hole pairs), they can form an emergent neutral Fermi surface, providing a possible explanation of an incompressible yet polarizable state at ν_{T}=1/2. We perform exact diagonalization studies that demonstrate that fermionic excitons are indeed lower in energy than bosonic excitons. This suggests that a "topological exciton metal" hidden inside a FQH insulator may have been realized experimentally in BLG. We discuss several detection schemes by which the topological exciton metal can be experimentally probed.
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Affiliation(s)
- Maissam Barkeshli
- Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Chetan Nayak
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Andrea Young
- Department of Physics, University of California, Santa Barbara, California 93106-6105, USA
| | - Michael Zaletel
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08540, USA
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5
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Ghazaryan A, Graß T, Gullans MJ, Ghaemi P, Hafezi M. Light-Induced Fractional Quantum Hall Phases in Graphene. PHYSICAL REVIEW LETTERS 2017; 119:247403. [PMID: 29286754 DOI: 10.1103/physrevlett.119.247403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 06/07/2023]
Abstract
We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.
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Affiliation(s)
- Areg Ghazaryan
- Department of Physics, City College, City University of New York, New York, New York 10031, USA
| | - Tobias Graß
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, College Park, Maryland 20742, USA
| | - Michael J Gullans
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Pouyan Ghaemi
- Department of Physics, City College, City University of New York, New York, New York 10031, USA
- Department of Physics, Graduate Center, City University of New York, New York, New York 10016, USA
| | - Mohammad Hafezi
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, College Park, Maryland 20742, USA
- Department of Electrical Engineering and IREAP, University of Maryland, College Park, Maryland 20742, USA
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6
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Cao X, Li H, He J, Kang L, Jiang R, Shi F, Xu H, Lei Z, Liu ZH. Preparation and formation process of α-MnS@MoS2 microcubes with hierarchical core/shell structure. J Colloid Interface Sci 2017; 507:18-26. [DOI: 10.1016/j.jcis.2017.07.102] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Revised: 07/23/2017] [Accepted: 07/28/2017] [Indexed: 10/19/2022]
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7
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Zhang Y, Wójs A, Jain JK. Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2016; 117:116803. [PMID: 27661711 DOI: 10.1103/physrevlett.117.116803] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2016] [Indexed: 06/06/2023]
Abstract
The spin transitions in the fractional quantum Hall effect provide a direct measure of the tiny energy differences between differently spin-polarized states and thereby serve as an extremely sensitive test of the quantitative accuracy of the theory of the fractional quantum Hall effect, and, in particular, of the role of Landau-level mixing in lifting the particle-hole symmetry. We report on an accurate quantitative study of this physics, evaluating the effect of Landau-level mixing in a nonperturbative manner using a fixed-phase diffusion Monte Carlo method. We find excellent agreement between our calculated critical Zeeman energies and the experimentally measured values. In particular, we find, as also do experiments, that the critical Zeeman energies for fractional quantum Hall states at filling factors ν=2-n/(2n±1) are significantly higher than those for ν=n/(2n±1), a quantitative signature of the lifting of particle-hole symmetry due to Landau-level mixing.
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Affiliation(s)
- Yuhe Zhang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - A Wójs
- Department of Theoretical Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
| | - J K Jain
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Department of Physics, Indian Institute of Science, Bengaluru 560012, India
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8
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Balram AC, Tőke C, Jain JK. Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions. PHYSICAL REVIEW LETTERS 2015; 115:186805. [PMID: 26565489 DOI: 10.1103/physrevlett.115.186805] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2015] [Indexed: 06/05/2023]
Abstract
While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.
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Affiliation(s)
- Ajit C Balram
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Csaba Tőke
- BME-MTA Exotic Quantum Phases "Lendület" Research Group, Budapest University of Technology and Economics, Institute of Physics, Budafoki út 8, H-1111 Budapest, Hungary
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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9
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Kleinbaum E, Kumar A, Pfeiffer LN, West KW, Csáthy GA. Gap reversal at filling factors 3+1/3 and 3+1/5: towards novel topological order in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 2015; 114:076801. [PMID: 25763967 DOI: 10.1103/physrevlett.114.076801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Indexed: 06/04/2023]
Abstract
In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor ν=3+1/3, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν=3+1/3 and 3+1/5 states from the upper spin branch are reversed when compared to the ν=2+1/3 and 2+1/5 counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.
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Affiliation(s)
- Ethan Kleinbaum
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Ashwani Kumar
- Department of Physics, Monmouth College, Monmouth, Illinois 61462, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - G A Csáthy
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
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10
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Liu Y, Kamburov D, Hasdemir S, Shayegan M, Pfeiffer LN, West KW, Baldwin KW. Fractional quantum Hall effect and Wigner crystal of interacting composite fermions. PHYSICAL REVIEW LETTERS 2014; 113:246803. [PMID: 25541794 DOI: 10.1103/physrevlett.113.246803] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Indexed: 06/04/2023]
Abstract
In two-dimensional electron systems confined to GaAs quantum wells, as a function of either tilting the sample in a magnetic field or increasing density, we observe multiple spin-polarization transitions of the fractional quantum Hall states at filling factors ν=4/5 and 5/7. The number of observed transitions provides evidence that these are fractional quantum Hall states of interacting two-flux composite fermions. Moreover, the fact that the reentrant integer quantum Hall effect near ν=4/5 always develops following the transition to full spin polarization of the ν=4/5 fractional quantum Hall state links the reentrant phase to a pinned ferromagnetic Wigner crystal of composite fermions.
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Affiliation(s)
- Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Kamburov
- 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
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11
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Maher P, Wang L, Gao Y, Forsythe C, Taniguchi T, Watanabe K, Abanin D, Papić Z, Cadden-Zimansky P, Hone J, Kim P, Dean CR. Tunable fractional quantum Hall phases in bilayer graphene. Science 2014; 345:61-4. [DOI: 10.1126/science.1252875] [Citation(s) in RCA: 122] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order. Here, we report fractional QHE states in BLG that show phase transitions that can be tuned by a transverse electric field. This result provides a model platform with which to study the role of symmetry-breaking in emergent states with topological order.
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12
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Mukherjee S, Mandal SS, Wu YH, Wójs A, Jain JK. Enigmatic 4/11 state: a prototype for unconventional fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 2014; 112:016801. [PMID: 24483916 DOI: 10.1103/physrevlett.112.016801] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Indexed: 06/03/2023]
Abstract
The origin of the fractional quantum Hall effect (FQHE) at 4/11 and 5/13 has remained controversial. We make a compelling case that the FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, the FQHE here results from the suppression of pairs with a relative angular momentum of three rather than one, confirming the exotic mechanism proposed by Wójs, Yi, and Quinn [Phys. Rev. B 69, 205322 (2004)]. We predict that the 4/11 state reported a decade ago by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)] is a conventional partially spin polarized FQHE of composite fermions, and we estimate the Zeeman energy where a phase transition into the unconventional fully spin polarized state will occur.
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Affiliation(s)
- Sutirtha Mukherjee
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Sudhansu S Mandal
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Ying-Hai Wu
- Department of Physics, 104 Davey Laboratory, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Arkadiusz Wójs
- Institute of Physics, Wroclaw University of Technology, 50-370 Wroclaw, Poland
| | - Jainendra K Jain
- Department of Physics, 104 Davey Laboratory, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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13
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Feldman BE, Levin AJ, Krauss B, Abanin DA, Halperin BI, Smet JH, Yacoby A. Fractional quantum Hall phase transitions and four-flux states in graphene. PHYSICAL REVIEW LETTERS 2013; 111:076802. [PMID: 23992076 DOI: 10.1103/physrevlett.111.076802] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2013] [Indexed: 06/02/2023]
Abstract
Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=-1/2 and -1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches -1/2, suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.
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Affiliation(s)
- Benjamin E Feldman
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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14
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Archer AC, Jain JK. Phase diagram of the two-component fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 2013; 110:246801. [PMID: 25165951 DOI: 10.1103/physrevlett.110.246801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2013] [Indexed: 06/03/2023]
Abstract
We calculate the phase diagram of the two component fractional quantum Hall effect as a function of the spin or valley Zeeman energy and the filling factor, which reveals new phase transitions and phase boundaries spanning many fractional plateaus. This phase diagram is relevant to the fractional quantum Hall effect in graphene and in GaAs and AlAs quantum wells, when either the spin or valley degree of freedom is active.
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Affiliation(s)
- Alexander C Archer
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Jainendra K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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15
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Liu Y, Pappas CG, Shayegan M, Pfeiffer LN, West KW, Baldwin KW. Observation of reentrant integer quantum Hall states in the lowest Landau level. PHYSICAL REVIEW LETTERS 2012; 109:036801. [PMID: 22861882 DOI: 10.1103/physrevlett.109.036801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2011] [Revised: 02/13/2012] [Indexed: 06/01/2023]
Abstract
Measurements on very low disorder two-dimensional electrons confined to relatively wide GaAs quantum well samples with tunable density reveal a close competition between the electron liquid and solid phases near the Landau level filling factor ν=1. As the density is raised, the fractional quantum Hall liquid at ν=4/5 suddenly disappears at a well-width dependent critical density, and then reappears at higher densities with insulating phases on its flanks. These insulating phases exhibit reentrant ν=1 integer quantum Hall effects and signal the formation of electron Wigner crystal states. Qualitatively similar phenomena are seen near ν=6/5.
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Affiliation(s)
- Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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16
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Pan W, Baldwin KW, West KW, Pfeiffer LN, Tsui DC. Spin transition in the ν=8/3 fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 2012; 108:216804. [PMID: 23003291 DOI: 10.1103/physrevlett.108.216804] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2011] [Indexed: 06/01/2023]
Abstract
We present here the results from a density dependent study of the activation energy gaps of the fractional quantum Hall effect states at Landau level fillings ν=8/3 and 7/3 in a series of high quality quantum wells. In the density range from 0.5×10(11) to 3×10(11) cm(-2), the 7/3 energy gap increases monotonically with increasing density, supporting its ground state being spin polarized. For the 8/3 state, however, its energy gap first decreases with increasing density, almost vanishes at n~0.8×10(11) cm(-2), and then turns around and increases with increasing density, clearly demonstrating a spin transition.
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Affiliation(s)
- W Pan
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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17
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Abergel DSL, Chakraborty T. Long-range Coulomb interaction in bilayer graphene. PHYSICAL REVIEW LETTERS 2009; 102:056807. [PMID: 19257539 DOI: 10.1103/physrevlett.102.056807] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2008] [Indexed: 05/27/2023]
Abstract
We report on our studies of interacting electrons in bilayer graphene in a magnetic field. We demonstrate that the long-range Coulomb interactions between electrons in this material are highly important and account for the band asymmetry in recent optical magneto-absorption experiments [E. A. Henriksen, Phys. Rev. Lett. 100, 087403 (2008)10.1103/PhysRevLett.100.087403]. We show that in the unbiased bilayer (where both layers are at the same electrostatic potential), the interactions can cause mixing of Landau levels in moderate magnetic fields. For the biased bilayer (when the two layers are at different potentials), we demonstrate that the interactions are responsible for a change in the total spin of the ground state for half-filled Landau levels in the valence band.
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Affiliation(s)
- D S L Abergel
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada.
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18
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Shkolnikov YP, Misra S, Bishop NC, De Poortere EP, Shayegan M. Observation of quantum Hall "valley Skyrmions". PHYSICAL REVIEW LETTERS 2005; 95:066809. [PMID: 16090979 DOI: 10.1103/physrevlett.95.066809] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2005] [Indexed: 05/03/2023]
Abstract
We report measurements of the interaction-induced quantum Hall effect in a spin-polarized AlAs two-dimensional electron system where the electrons occupy two in-plane conduction band valleys. Via the application of in-plane strain, we tune the energies of these valleys and measure the energy gap of the quantum Hall state at filling factor nu = 1. The gap has a finite value even at zero strain and, with strain, rises much faster than expected from a single-particle picture, suggesting that the lowest energy charged excitations at nu = 1 are "valley Skyrmions."
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Affiliation(s)
- Y P Shkolnikov
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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19
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Csáthy GA, Xia JS, Vicente CL, Adams ED, Sullivan NS, Stormer HL, Tsui DC, Pfeiffer LN, West KW. Tilt-induced localization and delocalization in the second Landau level. PHYSICAL REVIEW LETTERS 2005; 94:146801. [PMID: 15904089 DOI: 10.1103/physrevlett.94.146801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2004] [Indexed: 05/02/2023]
Abstract
We have investigated the behavior of electronic phases of the second Landau level under tilted magnetic fields. The fractional quantum Hall liquids at nu=2+1/5 and 2+4/5 and the solid phases at nu=2.30, 2.44, 2.57, and 2.70 are quickly destroyed with tilt. This behavior can be interpreted as a tilt driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and a delocalization through the melting of solid phases in the top Landau level, respectively. The evolution towards the classical Hall gas of the solid phases is suggestive of antiferromagnetic ordering.
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Affiliation(s)
- G A Csáthy
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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20
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Schulze-Wischeler F, Mariani E, Hohls F, Haug RJ. Direct measurement of the g factor of composite fermions. PHYSICAL REVIEW LETTERS 2004; 92:156401. [PMID: 15169302 DOI: 10.1103/physrevlett.92.156401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2003] [Indexed: 05/24/2023]
Abstract
The activation gap Delta of the fractional quantum Hall states at constant fillings nu=2/3 and 2/5 has been measured as a function of the perpendicular magnetic field B. A linear dependence of Delta on B is observed while approaching the spin-polarization transition. This feature allows a direct measurement of the g factor of composite fermions which appears to be heavily renormalized by interactions and strongly sensitive to the electronic filling factor.
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21
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Schüller C, Broocks KB, Schröter P, Heyn C, Heitmann D, Bichler M, Wegscheider W, Chakraborty T, Apalkov VM. Optical probing of a fractionally charged quasihole in an incompressible liquid. PHYSICAL REVIEW LETTERS 2003; 91:116403. [PMID: 14525447 DOI: 10.1103/physrevlett.91.116403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2003] [Indexed: 05/24/2023]
Abstract
In photoluminescence spectroscopy of a low-mobility two-dimensional electron gas subjected to a quantizing magnetic field, we observe an anomaly around nu=1 / 3 at a very low temperature (0.1 K) and an intermediate electron density (0.9 x 10(11) cm(-2)). The anomaly is explained as due to perturbation of the incompressible liquid at the Laughlin state due to close proximity of a localized charged exciton which creates a fractionally charged quasihole in the liquid. The anomaly of approximately 2 meV can be destroyed by applying a small thermal energy of approximately 0.2 meV that is enough to close the quasihole energy gap.
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Affiliation(s)
- C Schüller
- Institut für Angewandte Physik und Zentrum für Mikrostrukturforschung, Universität Hamburg, D-20355 Hamburg, Germany
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22
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Desrat W, Maude DK, Potemski M, Portal JC, Wasilewski ZR, Hill G. Resistively detected nuclear magnetic resonance in the quantum hall regime: possible evidence for a Skyrme crystal. PHYSICAL REVIEW LETTERS 2002; 88:256807. [PMID: 12097116 DOI: 10.1103/physrevlett.88.256807] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2002] [Indexed: 05/23/2023]
Abstract
Resistively detected nuclear magnetic resonance measurements have been performed on a high mobility heterostructure in the quantum Hall regime. At millikelvin temperatures the nuclear resonances are observed in the vicinity of various integer and fractional filling factors without previous dynamic nuclear polarization. Near nu = 1, the observed large enhancement of the resonance amplitude accompanied by a reduction of T1 strongly suggests a greatly increased coupling between the electronic and nuclear spin systems. This is consistent with the proposed coupling of the nuclear spin system to the Goldstone mode of the Skyrme crystal.
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Affiliation(s)
- W Desrat
- Grenoble High Magnetic Field Laboratory, Max Planck Institut für Festkörperforschung and Centre National de la Recherche Scientifique, BP 166, 38042 Grenoble Cedex 9, France
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23
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De Poortere EP, Tutuc E, Papadakis SJ, Shayegan M. Resistance spikes at transitions between quantum hall ferromagnets. Science 2000; 290:1546-9. [PMID: 11090346 DOI: 10.1126/science.290.5496.1546] [Citation(s) in RCA: 143] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
We report a manifestation of first-order magnetic transitions in two-dimensional electron systems. This phenomenon occurs in aluminum arsenide quantum wells with sufficiently low carrier densities and appears as a set of hysteretic spikes in the resistance of a sample placed in crossed parallel and perpendicular magnetic fields, each spike occurring at the transition between states with different partial magnetizations. Our experiments thus indicate that the presence of magnetic domains at the transition starkly increases dissipation, an effect also suspected in other ferromagnetic materials. Analysis of the positions of the transition spikes allows us to deduce the change in exchange-correlation energy across the magnetic transition, which in turn will help improve our understanding of metallic ferromagnetism.
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Affiliation(s)
- E P De Poortere
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA.
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24
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Eom J, Cho H, Kang W, Campman KL, Gossard AC, Bichler M, Wegscheider W. Quantum hall ferromagnetism in a two-dimensional electron system. Science 2000; 289:2320-3. [PMID: 11009411 DOI: 10.1126/science.289.5488.2320] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Experiments on a nearly spin degenerate two-dimensional electron system reveals unusual hysteretic and relaxational transport in the fractional quantum Hall effect regime. The transition between the spin-polarized (with fill fraction nu = 1/3) and spin-unpolarized (nu = 2/5) states is accompanied by a complicated series of hysteresis loops reminiscent of a classical ferromagnet. In correlation with the hysteresis, magnetoresistance can either grow or decay logarithmically in time with remarkable persistence and does not saturate. In contrast to the established models of relaxation, the relaxation rate exhibits an anomalous divergence as temperature is reduced. These results indicate the presence of novel two-dimensional ferromagnetism with a complicated magnetic domain dynamic.
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Affiliation(s)
- J Eom
- James Franck Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA. Department of Electrical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA. Walter Schottky Instit
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25
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Melinte S, Freytag N, Horvatic M, Berthier C, Levy LP, Bayot V, Shayegan M. NMR determination of 2D electron spin polarization at nu = 1/2. PHYSICAL REVIEW LETTERS 2000; 84:354-357. [PMID: 11015909 DOI: 10.1103/physrevlett.84.354] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/1999] [Indexed: 05/23/2023]
Abstract
Using a "standard" NMR spin-echo technique we determined the spin polarization P of two-dimensional electrons, confined to GaAs quantum wells, from the hyperfine shift of Ga nuclei located in the wells. Concentrating on the temperature ( 0.05 less, similarT less, similar10 K) and magnetic field ( 7 less, similarB less, similar17 T) dependencies of P at Landau level filling factor nu = 1/2, we find that the results are described well by a simple model of noninteracting composite fermions, although some inconsistencies remain when the two-dimensional electron system is tilted in the magnetic field.
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Affiliation(s)
- S Melinte
- Unite PCPM, Universite Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
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26
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Murthy G. Composite fermion hofstadter problem: partially polarized density wave states in the nu = 2/5 fractional quantum hall effect. PHYSICAL REVIEW LETTERS 2000; 84:350-353. [PMID: 11015908 DOI: 10.1103/physrevlett.84.350] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/1999] [Indexed: 05/23/2023]
Abstract
It is well known that the nu = 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with a charge/spin density wave order for composite fermions is proposed to exist at intermediate values of the Zeeman coupling for nu = 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R. Shankar and the author is used to demonstrate the stability of this state to single-particle excitations and to compute gaps. A very recent experiment shows direct evidence for this state.
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Affiliation(s)
- G Murthy
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
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27
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Michels JG, Daly MS, Gee P, Hill S, Nicholas RJ, Singleton J, Summers GM, Warburton RJ, Foxon CT, Harris JJ. Cyclotron resonance and spin states in GaAs/Ga1-xAlxAs heterojunctions: Experiment and theory. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:13807-13815. [PMID: 9985297 DOI: 10.1103/physrevb.54.13807] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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28
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Mandal SS, Ravishankar V. Theory of arbitrarily polarized quantum Hall states: Filling fractions and wave functions. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8688-8698. [PMID: 9984546 DOI: 10.1103/physrevb.54.8688] [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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29
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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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30
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Chakraborty T, Pietiläinen P. Thermodynamics and spin polarizations of the fractional quantum Hall states. PHYSICAL REVIEW LETTERS 1996; 76:4018-4021. [PMID: 10061171 DOI: 10.1103/physrevlett.76.4018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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31
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Chakraborty T, Pietiläinen P. Electron correlations in antidot arrays in a magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:4664-4667. [PMID: 9984024 DOI: 10.1103/physrevb.53.4664] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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32
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Xie XC, He S. Skyrmion excitations in quantum Hall systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:1046-1049. [PMID: 9983551 DOI: 10.1103/physrevb.53.1046] [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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33
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Du RR, Yeh AS, Stormer HL, Tsui DC, Pfeiffer LN, West KW. Fractional quantum Hall effect around nu =3/2: Composite fermions with a spin. PHYSICAL REVIEW LETTERS 1995; 75:3926-3929. [PMID: 10059766 DOI: 10.1103/physrevlett.75.3926] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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34
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Bayer M, Dremin AA, Kulakovskii VD, Forchel A, Faller F, Knipp PA, Reinecke TL. Coupling of geometric confinement and magnetic confinement in In0.09Ga0.91As/GaAs quantum wells in magnetic fields with varying orientations. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:14728-14738. [PMID: 9980810 DOI: 10.1103/physrevb.52.14728] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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35
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Kamilla RK, Jain JK. Composite-fermion description of correlated electrons in quantum dots: Low-Zeeman-energy limit. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:2798-2804. [PMID: 9981350 DOI: 10.1103/physrevb.52.2798] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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36
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Moon K, Mori H, Yang K, Girvin SM, MacDonald AH, Zheng L, Yoshioka D, Zhang SC. Spontaneous interlayer coherence in double-layer quantum Hall systems: Charged vortices and Kosterlitz-Thouless phase transitions. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:5138-5170. [PMID: 9979391 DOI: 10.1103/physrevb.51.5138] [Citation(s) in RCA: 234] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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37
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Leadley DR, Nicholas RJ, Foxon CT, Harris JJ. Measurements of the effective mass and scattering times of composite fermions from magnetotransport analysis. PHYSICAL REVIEW LETTERS 1994; 72:1906-1909. [PMID: 10055734 DOI: 10.1103/physrevlett.72.1906] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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38
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Wu XG, Jain JK. Fractional quantum Hall states in the low-Zeeman-energy limit. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:7515-7519. [PMID: 10009491 DOI: 10.1103/physrevb.49.7515] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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39
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Jain JK, Wu XG. Hund's rule for composite fermions. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:5085-5088. [PMID: 10011454 DOI: 10.1103/physrevb.49.5085] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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40
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Wu XG, Dev G, Jain JK. Mixed-spin incompressible states in the fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 1993; 71:153-156. [PMID: 10054396 DOI: 10.1103/physrevlett.71.153] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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41
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Halperin BI, Lee PA, Read N. Theory of the half-filled Landau level. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:7312-7343. [PMID: 10004728 DOI: 10.1103/physrevb.47.7312] [Citation(s) in RCA: 829] [Impact Index Per Article: 26.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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42
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He S, Xie XC. Quantized Hall effect and quantum phase transitions in coupled two-layer electron systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:4394-4412. [PMID: 10006587 DOI: 10.1103/physrevb.47.4394] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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43
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Halonen V. Fractional quantum Hall effect in a parabolic quantum well in tilted magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:4003-4006. [PMID: 10006517 DOI: 10.1103/physrevb.47.4003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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44
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Belkhir L, Jain JK. Theory of spin-singlet fractional quantum Hall effect at nu =1/2. PHYSICAL REVIEW LETTERS 1993; 70:643-646. [PMID: 10054166 DOI: 10.1103/physrevlett.70.643] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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45
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Gasser W. Fractional quantum numbers and electron correlations. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:1324-1328. [PMID: 10006142 DOI: 10.1103/physrevb.47.1324] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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46
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Herbut IF. Spin-singlet states and the nu =2/3 fractional quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:15582-15585. [PMID: 10003695 DOI: 10.1103/physrevb.46.15582] [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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47
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Engel LW, Hwang SW, Sajoto T, Tsui DC, Shayegan M. Fractional quantum Hall effect at nu =2/3 and 3/5 in tilted magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:3418-3425. [PMID: 10001916 DOI: 10.1103/physrevb.45.3418] [Citation(s) in RCA: 75] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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48
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Davies AG, Newbury R, Pepper M, Frost JE, Ritchie DA, Jones GA. Fractional quantum Hall effect in high-mobility two-dimensional hole gases in tilted magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:13128-13131. [PMID: 9999507 DOI: 10.1103/physrevb.44.13128] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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49
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Chakraborty T, Pietiläinen P. Recombination radiation from a two-dimensional electron system in a strong magnetic field: Spin dependence. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:13078-13081. [PMID: 9999494 DOI: 10.1103/physrevb.44.13078] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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50
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Goldberg BB, Heiman D, Dahl M, Pinczuk A, Pfeiffer L, West K. Localization and many-body interactions in the quantum Hall effect determined by polarized optical emission. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:4006-4009. [PMID: 10000035 DOI: 10.1103/physrevb.44.4006] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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