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Wang C, Gupta A, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Winkler R, Shayegan M. Highly Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally Coupled Half-Filled Landau Level. PHYSICAL REVIEW LETTERS 2023; 131:056302. [PMID: 37595236 DOI: 10.1103/physrevlett.131.056302] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 07/06/2023] [Indexed: 08/20/2023]
Abstract
The even-denominator fractional quantum Hall states (FQHSs) in half-filled Landau levels are generally believed to host non-Abelian quasiparticles and be of potential use in topological quantum computing. Of particular interest is the competition and interplay between the even-denominator FQHSs and other ground states, such as anisotropic phases and composite fermion Fermi seas. Here, we report the observation of an even-denominator fractional quantum Hall state with highly anisotropic in-plane transport coefficients at Landau level filling factor ν=3/2. We observe this state in an ultra-high-quality GaAs two-dimensional hole system when a large in-plane magnetic field is applied. By increasing the in-plane field, we observe a sharp transition from an isotropic composite fermion Fermi sea to an anisotropic even-denominator FQHS. Our data and calculations suggest that a unique feature of two-dimensional holes, namely the coupling between heavy-hole and light-hole states, combines different orbital components in the wave function of one Landau level, and leads to the emergence of a highly anisotropic even-denominator fractional quantum Hall state. Our results demonstrate that the GaAs two-dimensional hole system is a unique platform for the exploration of exotic, many-body ground states.
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Affiliation(s)
- Chengyu Wang
- 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
| | - Y J Chung
- 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 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
| | - 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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2
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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}$$\nu = 8/5$$\end{document}ν=8/5, and a corresponding change in the \documentclass[12pt]{minimal}
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\begin{document}$$R_{xy}/R_{K} = (11/7)^{-1}$$\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}$$\nu = 4/3, 7/5$$\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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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] [Key Words] [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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Zhu Z, Sheng DN, Sodemann I. Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2020; 124:097604. [PMID: 32202902 DOI: 10.1103/physrevlett.124.097604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
We develop a proposal to realize a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings ν=±3+1/2 and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band structure of bilayer graphene and includes the fluctuations between the n=0 and n=1 cyclotron orbitals of its zeroth Landau level to delineate the most favorable region of parameters to experimentally access this unconventional critical point. We also find evidence for a new anisotropic gapless phase stabilized near the level crossing of n=0/1 orbits.
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Affiliation(s)
- Zheng Zhu
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Inti Sodemann
- Max-Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany
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5
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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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6
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Fu H, Wu Y, Zhang R, Sun J, Shan P, Wang P, Zhu Z, Pfeiffer LN, West KW, Liu H, Xie XC, Lin X. 3/2 fractional quantum Hall plateau in confined two-dimensional electron gas. Nat Commun 2019; 10:4351. [PMID: 31554799 PMCID: PMC6761136 DOI: 10.1038/s41467-019-12245-y] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2017] [Accepted: 08/27/2019] [Indexed: 11/09/2022] Open
Abstract
Even-denominator fractional quantum Hall (FQH) states, such as 5/2 and 7/2, have been well known in a two-dimensional electron gas (2DEG) for decades and are still investigated as candidates of non-Abelian statistics. In this paper, we present the observation of a 3/2 FQH plateau in a single-layer 2DEG with lateral confinement at a bulk filling factor of 5/3. The 3/2 FQH plateau is quantized at \documentclass[12pt]{minimal}
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\begin{document}$$\left( {\frac{h}{{e^2}}} \right)/\left( {\frac{3}{2}} \right)$$\end{document}he2∕32 within 0.02%, and can survive up to 300 mK. This even-denominator FQH plateau may imply intriguing edge structure and excitation in FQH system with lateral confinement. The observations in this work demonstrate that understanding the effect of the lateral confinement on the many-body system is critical in the pursuit of important theoretical proposals involving edge physics, such as the demonstration of non-Abelian statistics and the realization of braiding for fault-tolerant quantum computation. Fractional quantum Hall states in 2D electron gases arise due to strong electron-electron interactions, which makes a general theoretical understanding difficult. Fu et al. present data showing the ν = 5/3 quantum Hall state has a 3/2 plateau in the diagonal resistance that has not been captured by existing models.
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Affiliation(s)
- Hailong Fu
- International Center for Quantum Materials, Peking University, 100871, Beijing, China.,Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Yijia Wu
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Ruoxi Zhang
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Jian Sun
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Pujia Shan
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Pengjie Wang
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - Zheyi Zhu
- International Center for Quantum Materials, Peking University, 100871, Beijing, China
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - Haiwen Liu
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, 100875, Beijing, China
| | - X C Xie
- International Center for Quantum Materials, Peking University, 100871, Beijing, China.,Beijing Academy of Quantum Information Sciences, 100193, Beijing, China.,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, 100190, Beijing, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, 100871, Beijing, China. .,Beijing Academy of Quantum Information Sciences, 100193, Beijing, China. .,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, 100190, Beijing, China.
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Wang P, Huang K, Sun J, Hu J, Fu H, Lin X. Piezo-driven sample rotation system with ultra-low electron temperature. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:023905. [PMID: 30831686 DOI: 10.1063/1.5083994] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Accepted: 01/19/2019] [Indexed: 06/09/2023]
Abstract
Piezo-driven rotator is convenient for tilted magnetic field experiments due to its precise angle control. However, the rotator itself and the sample mounted on it are difficult to be cooled down because of extra heat leaks and presumably bad thermal contacts from the piezo. Here, we report a piezo-driven sample rotation system designed for ultra-low temperature environment. The sample, as well as the rotating sample holder, can be cooled to as low as 25 mK by customized thermal links and thermal contacts. More importantly, the electron temperature in the electrical transport measurements can also be cooled down to 25 mK with the help of home-made filters. To demonstrate the application of our rotation system at ultra-low electron temperature, a measurement revealing tilt-induced localization and delocalization in the second Landau level of two-dimensional electron gas is provided.
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Affiliation(s)
- Pengjie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ke Huang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jian Sun
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jingjin Hu
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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Falson J, Tabrea D, Zhang D, Sodemann I, Kozuka Y, Tsukazaki A, Kawasaki M, von Klitzing K, Smet JH. A cascade of phase transitions in an orbitally mixed half-filled Landau level. SCIENCE ADVANCES 2018; 4:eaat8742. [PMID: 30225370 PMCID: PMC6140610 DOI: 10.1126/sciadv.aat8742] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Accepted: 08/02/2018] [Indexed: 06/08/2023]
Abstract
Half-filled Landau levels host an emergent Fermi liquid that displays instability toward pairing, culminating in a gapped even-denominator fractional quantum Hall ground state. While this pairing may be probed by tuning the polarization of carriers in competing orbital and spin degrees of freedom, sufficiently high quality platforms offering such tunability remain few. We explore the ground states at filling factor ν = 5/2 in ZnO-based two-dimensional electron systems through a forced intersection of opposing spin branches of Landau levels taking quantum numbers N = 1 and 0. We reveal a cascade of phases with distinct magnetotransport features including a gapped phase polarized in the N = 1 level and a compressible phase in N = 0, along with an unexpected Fermi liquid, a second gapped, and a strongly anisotropic nematic-like phase at intermediate polarizations when the levels are near degeneracy. The phase diagram is produced by analyzing the proximity of the intersecting levels and highlights the excellent reproducibility and controllability that ZnO offers for exploring exotic fractionalized electronic phases.
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Affiliation(s)
- Joseph Falson
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Daniela Tabrea
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Ding Zhang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Inti Sodemann
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Yusuke Kozuka
- Department of Applied Physics and Quantum-Phase Electronics Center, University of Tokyo, Tokyo 113-8656, Japan
- Japan Science and Technology Agency, Precursory Research for Embryonic Science and Technology, Kawaguchi, Saitama 332-0012, Japan
| | - Atsushi Tsukazaki
- Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
| | - Masashi Kawasaki
- Department of Applied Physics and Quantum-Phase Electronics Center, University of Tokyo, Tokyo 113-8656, Japan
- RIKEN Center for Emergent Matter Science, Wako 351-0198, Japan
| | - Klaus von Klitzing
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Jurgen H. Smet
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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9
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Falson J, Kawasaki M. A review of the quantum Hall effects in MgZnO/ZnO heterostructures. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:056501. [PMID: 29353814 DOI: 10.1088/1361-6633/aaa978] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg x Zn[Formula: see text]O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility ([Formula: see text] cm2 Vs-1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic.
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Affiliation(s)
- Joseph Falson
- Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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10
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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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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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12
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Amet F, Bestwick AJ, Williams JR, Balicas L, Watanabe K, Taniguchi T, Goldhaber-Gordon D. Composite fermions and broken symmetries in graphene. Nat Commun 2015; 6:5838. [DOI: 10.1038/ncomms6838] [Citation(s) in RCA: 74] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 11/13/2014] [Indexed: 11/09/2022] Open
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13
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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: 7] [Impact Index Per Article: 0.7] [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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14
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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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15
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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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16
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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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17
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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: 34] [Impact Index Per Article: 3.1] [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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18
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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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19
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Tőke C, Jain JK. Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2). JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:235601. [PMID: 22569096 DOI: 10.1088/0953-8984/24/23/235601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effects in different parameter regions. We address the stability of various states in the SU(2) and SU(4) limits. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7, etc; SU(4) skyrmions are not found to be relevant for the low-energy physics. These results are discussed in light of experiments.
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Affiliation(s)
- C Tőke
- Institute of Physics, University of Pécs, Pécs, Budapest, Hungary
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20
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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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21
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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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22
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Wurstbauer U, Majumder D, Mandal SS, Dujovne I, Rhone TD, Dennis BS, Rigosi AF, Jain JK, Pinczuk A, West KW, Pfeiffer LN. Observation of nonconventional spin waves in composite-fermion ferromagnets. PHYSICAL REVIEW LETTERS 2011; 107:066804. [PMID: 21902358 DOI: 10.1103/physrevlett.107.066804] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2011] [Indexed: 05/31/2023]
Abstract
We find unexpected low energy excitations of fully spin-polarized composite-fermion ferromagnets in the fractional quantum Hall liquid, resulting from a complex interplay between a topological order manifesting through new energy levels and a magnetic order due to spin polarization. The lowest energy modes, which involve spin reversal, are remarkable in displaying unconventional negative dispersion at small momenta followed by a deep roton minimum at larger momenta. This behavior results from a nontrivial mixing of spin-wave and spin-flip modes creating a spin-flip excitonic state of composite-fermion particle-hole pairs. The striking properties of spin-flip excitons imply highly tunable mode couplings that enable fine control of topological states of itinerant two-dimensional ferromagnets.
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Affiliation(s)
- U Wurstbauer
- Department of Physics, Columbia University, New York, New York 10027, USA.
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23
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Shabani J, Liu Y, Shayegan M. Fractional quantum Hall effect at high fillings in a two-subband electron system. PHYSICAL REVIEW LETTERS 2010; 105:246805. [PMID: 21231548 DOI: 10.1103/physrevlett.105.246805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2010] [Indexed: 05/30/2023]
Abstract
Magnetotransport measurements in a clean two-dimensional electron system confined to a wide GaAs quantum well reveal that, when the electrons occupy two electric subbands, the sequences of fractional quantum Hall states observed at high fillings (ν>2) are distinctly different from those of a single-subband system. Notably, when the Fermi energy lies in the ground state Landau level of either of the subbands, no quantum Hall states are seen at the even-denominator ν=5/2 and 7/2 fillings; instead, the observed states are at ν=[i+p/(2p±1)], where i=2, 3, 4 and p=1, 2, 3, and include several new states at ν=13/5, 17/5, 18/5, 25/7, and 14/3.
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Affiliation(s)
- J Shabani
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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24
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MacDonald AH. Theory of high-energy features in the tunneling spectra of quantum-Hall systems. PHYSICAL REVIEW LETTERS 2010; 105:206801. [PMID: 21231254 DOI: 10.1103/physrevlett.105.206801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2010] [Indexed: 05/30/2023]
Abstract
We show that the low-temperature sash features in lowest Landau-level (LLL) tunneling spectra recently discovered by Dial and Ashoori are intimately related to the discrete Haldane-pseudopotential interaction energy scales that govern fractional quantum-Hall physics. Our analysis is based on expressions for the tunneling density of states which become exact at filling factors close to ν=0 and ν=1, where the sash structure is most prominent. We comment on other aspects of LLL correlation physics that can be revealed by accurate temperature-dependent tunneling data.
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Affiliation(s)
- A H MacDonald
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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25
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Plochocka P, Schneider JM, Maude DK, Potemski M, Rappaport M, Umansky V, Bar-Joseph I, Groshaus JG, Gallais Y, Pinczuk A. Optical absorption to probe the quantum Hall ferromagnet at filling factor nu=1. PHYSICAL REVIEW LETTERS 2009; 102:126806. [PMID: 19392309 DOI: 10.1103/physrevlett.102.126806] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2009] [Indexed: 05/27/2023]
Abstract
Optical absorption measurements are used to probe the spin polarization in the integer and fractional quantum Hall effect regimes. The system is fully spin polarized only at filling factor nu=1 and at very low temperatures ( approximately 40 mK). A small change in filling factor (deltanu approximately +/-0.01) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at nu=1 is surprisingly fragile against increasing temperature, or against small changes in filling factor.
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Affiliation(s)
- P Plochocka
- Laboratoire National des Champs Magnétiques Intenses, Grenoble High Magnetic Field Laboratory, 38042 Grenoble, France.
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26
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Sinha J, Mohan S, Banerjee SS, Kahaly S, Kumar GR. Mapping giant magnetic fields around dense solid plasmas by high-resolution magneto-optical microscopy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:046118. [PMID: 18517701 DOI: 10.1103/physreve.77.046118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2007] [Indexed: 05/26/2023]
Abstract
We investigate the distribution of magnetic fields around dense solid plasmas generated by intense p-polarized laser approximately 10(16) W cm(-2), 100 fs) irradiation of magnetic tapes, using high sensitivity magneto-optical microscopy. By investigating the effect of irradiation on the magnetic tape, we present evidence for axial magnetic fields and map out the spatial distribution of these fields around the laser generated plasma. By using the axial magnetic field distribution as a diagnostic tool we uncover evidence for angular momentum associated with the plasma.
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Affiliation(s)
- Jaivardhan Sinha
- Department of Physics, Indian Institute of Technology, Kanpur-208016, U. P., India
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27
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Bishop NC, Padmanabhan M, Vakili K, Shkolnikov YP, De Poortere EP, Shayegan M. Valley polarization and susceptibility of composite fermions around a filling factor nu=3/2. PHYSICAL REVIEW LETTERS 2007; 98:266404. [PMID: 17678112 DOI: 10.1103/physrevlett.98.266404] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2007] [Indexed: 05/16/2023]
Abstract
We report magnetotransport measurements of fractional quantum Hall states in an AlAs quantum well around a Landau level filling factor nu=3/2, demonstrating that the quasiparticles are composite fermions (CFs) with a valley degree of freedom. By monitoring the valley level crossings for these states as a function of applied symmetry-breaking strain, we determine the CF valley susceptibility and polarization. The data can be explained well by a simple Landau level fan diagram for CFs, and are in nearly quantitative agreement with the results reported for CF spin polarization.
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Affiliation(s)
- N C Bishop
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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28
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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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29
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Gervais G, Engel LW, Stormer HL, Tsui DC, Baldwin KW, West KW, Pfeiffer LN. Competition between a fractional quantum hall liquid and bubble and Wigner crystal phases in the third Landau level. PHYSICAL REVIEW LETTERS 2004; 93:266804. [PMID: 15698005 DOI: 10.1103/physrevlett.93.266804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2004] [Indexed: 05/24/2023]
Abstract
Magnetotransport measurements were performed in an ultrahigh mobility GaAs/AlGaAs quantum well of density approximately 3.0 x 10(11) cm(-2). The temperature dependence of the magnetoresistance Rxx was studied in detail in the vicinity of nu=9/2. In particular, we discovered new minima in Rxx at a filling factor nu approximately 41/5 and 44/5, but only at intermediate temperatures 80 approximately less than T approximately less than 120 mK. We interpret these as evidence for a fractional quantum Hall liquid forming in the N=2 Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at T=0.
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Affiliation(s)
- G Gervais
- Department of Physics and Department of Applied Physics, Columbia University, New York, New York 10027, USA
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30
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Lai K, Pan W, Tsui DC, Lyon S, Mühlberger M, Schäffler F. Two-flux composite fermion series of the fractional quantum Hall states in strained Si. PHYSICAL REVIEW LETTERS 2004; 93:156805. [PMID: 15524923 DOI: 10.1103/physrevlett.93.156805] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2004] [Indexed: 05/24/2023]
Abstract
Magnetotransport properties are investigated in a high-mobility two-dimensional electron system in the strained Si quantum well of a (100) Si(0.75)Ge(0.25)/Si/Si(0.75)Ge0.25 heterostructure, at temperatures down to 30 mK and in magnetic fields up to 45 T. We observe around nu=1/2 the two-flux composite fermion (CF) series of the fractional quantum Hall effect (FQHE) at nu=2/3, 3/5, 4/7, and at nu=4/9, 2/5, 1/3. Among these FQHE states, the nu=1/3, 4/7, and 4/9 states are seen for the first time in the Si/SiGe system. Interestingly, of the CF series, the 3/5 state is weaker than the nearby 4/7 state and the 3/7 state is conspicuously missing, resembling the observation in the IQHE regime that the nu=3 is weaker than the nearby nu=4 state. Our results can be quantitatively understood in the picture of CF's with the valley degree of freedom.
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Affiliation(s)
- K Lai
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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31
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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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32
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Smet JH, Deutschmann RA, Ertl F, Wegschei der W, Abstreiter G, von Klitzing K. Anomalous-filling-factor-dependent nuclear-spin polarization in a 2D electron system. PHYSICAL REVIEW LETTERS 2004; 92:086802. [PMID: 14995804 DOI: 10.1103/physrevlett.92.086802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2003] [Indexed: 05/24/2023]
Abstract
Spin-related electronic phase transitions in the fractional quantum Hall regime are accompanied by a large change in resistance. Combined with their sensitivity to spin orientation of nuclei residing in the same plane as the 2D electrons, they offer a convenient electrical probe to carry out nuclear magnetometry. Despite conditions which should allow both electronic and nuclear-spin subsystems to approach thermodynamic equilibrium, we uncover for the nuclei a remarkable and strongly electronic filling-factor-dependent deviation from the anticipated thermal nuclear-spin polarization.
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Affiliation(s)
- J H Smet
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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33
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Dujovne I, Pinczuk A, Kang M, Dennis BS, Pfeiffer LN, West KW. Evidence of Landau levels and interactions in low-lying excitations of composite fermions at 1/3<or= nu <or=2/5. PHYSICAL REVIEW LETTERS 2003; 90:036803. [PMID: 12570516 DOI: 10.1103/physrevlett.90.036803] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2002] [Indexed: 05/24/2023]
Abstract
Excitation modes in the range 2/5>or=nu>or=1/3 of the fractional quantum Hall regime are observed by resonant inelastic light scattering. Spectra of spin-reversed excitations suggest a structure of lowest spin-split Landau levels of composite fermions that is similar to that of electrons. Spin-flip energies determined from spectra reveal significant composite fermion interactions. The filling factor dependence of mode energies displays an abrupt change in the middle of the range when there is partial population of a composite fermion level.
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Affiliation(s)
- Irene Dujovne
- Department of Applied Physics and Applied Math, Columbia University, New York, New York 10027, USA
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34
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Freytag N, Horvatić M, Berthier C, Shayegan M, Lévy LP. NMR investigation of how free composite fermions are at nu=1 / 2. PHYSICAL REVIEW LETTERS 2002; 89:246804. [PMID: 12484971 DOI: 10.1103/physrevlett.89.246804] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2002] [Indexed: 05/24/2023]
Abstract
NMR measurements of the electron spin polarization (P) have been performed on a 2D electron system at and around half-filled lowest Landau level. Comparing the magnetic field and the temperature dependence of P to models of free and interacting composite fermions (CF), the imbalance of spin-up and spin-down CF Fermi seas is mapped as a function of Zeeman energy. Independent measurements of the CF effective mass, g factor, and Fermi energy are obtained from the thermal activation of P in tilted fields. The filling factor dependence of the P for 2 / 5<nu<2 / 3 reveals a broken particle-hole symmetry for the partially polarized CF Fermi sea.
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Affiliation(s)
- N Freytag
- Grenoble High Magnetic Field Laboratory, MPI-FKF and CNRS, B.P. 166, France.
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35
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Kumada N, Terasawa D, Shimoda Y, Azuhata H, Sawada A, Ezawa ZF, Muraki K, Saku T, Hirayama Y. Phase diagram of interacting composite fermions in the bilayer nu=2/3 quantum hall effect. PHYSICAL REVIEW LETTERS 2002; 89:116802. [PMID: 12225161 DOI: 10.1103/physrevlett.89.116802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2001] [Indexed: 05/23/2023]
Abstract
We study the phase diagram of composite fermions (CFs) in the presence of spin and pseudospin degrees of freedom in the bilayer nu=2/3 quantum Hall (QH) state. Activation studies elucidate the existence of three different QH states with two different types of hysteresis in the magnetotransport. While a noninteracting CF model provides a qualitative account of the phase diagram, the observed renormalization of tunneling gap and a non-QH state at high densities are not explained in the noninteracting CF model, and are suggested to be manifestations of interactions between CFs.
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Affiliation(s)
- N Kumada
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
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36
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Avishai Y, Meir Y. New spin-orbit-induced universality class in the integer quantum Hall regime. PHYSICAL REVIEW LETTERS 2002; 89:076602. [PMID: 12190544 DOI: 10.1103/physrevlett.89.076602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2001] [Indexed: 05/23/2023]
Abstract
Using heuristic arguments and numerical simulations it is argued that the critical exponent nu describing the localization length divergence at the integer quantum-Hall transition is modified in the presence of spin-orbit scattering with short-range correlations. The exponent is very close to nu=4/3, the percolation correlation length exponent, consistent with the prediction of a semiclassical argument. In addition, a band of weakly localized states is conjectured.
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Affiliation(s)
- Yshai Avishai
- Department of Physics and Ilse Katz Center for Meso- and Nanoscale Science and Technology, Ben Gurion University, Beer Sheva, Israel
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37
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Willett RL, West KW, Pfeiffer LN. Experimental demonstration of Fermi surface effects at filling factor 5/2. PHYSICAL REVIEW LETTERS 2002; 88:066801. [PMID: 11863836 DOI: 10.1103/physrevlett.88.066801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2001] [Indexed: 05/23/2023]
Abstract
Using small wavelength surface acoustic waves (SAW) on ultrahigh mobility heterostructures, Fermi surface properties are detected at 5/2 filling factor at temperatures higher than those at which the quantum Hall state forms. An enhanced conductivity is observed at 5/2 by employing sub-0.5-microm SAW, indicating a quasiparticle mean-free path substantially smaller than that in the lowest Landau level. These findings are consistent with the presence of a filled Fermi sea of composite fermions, which may pair at lower temperatures to form the 5/2 ground state.
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Affiliation(s)
- R L Willett
- Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, USA
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38
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Kukushkin IV, Smet JH, von Klitzing K, Wegscheider W. Cyclotron resonance of composite fermions. Nature 2002; 415:409-12. [PMID: 11807549 DOI: 10.1038/415409a] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
It is occasionally possible to interpret strongly interacting many-body systems within a single-particle framework by introducing suitable fictitious entities, or 'quasi-particles'. A notable recent example of the successful application of such an approach is for a two-dimensional electron system that is exposed to a strong perpendicular magnetic field. The conduction properties of the system are governed by electron-electron interactions, which cause the fractional quantum Hall effect. Composite fermions, electrons that are dressed with magnetic flux quanta pointing opposite to the applied magnetic field, were identified as apposite quasi-particles that simplify our understanding of the fractional quantum Hall effect. They precess, like electrons, along circular cyclotron orbits, but with a diameter determined by a reduced effective magnetic field. The frequency of their cyclotron motion has hitherto remained enigmatic, as the effective mass is no longer related to the band mass of the original electrons and is entirely generated from electron-electron interactions. Here we demonstrate enhanced absorption of a microwave field in the composite fermion regime, and interpret it as a resonance with the frequency of their circular motion. From this inferred cyclotron resonance, we derive a composite fermion effective mass that varies from 0.7 to 1.2 times that of the electron mass in vacuum as their density is tuned from 0.6 x 10(11) cm(-2) to 1.2 x 10(11) cm(-2).
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Affiliation(s)
- I V Kukushkin
- Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
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Kukushkin IV, Smet JH, Eberl K. Optical investigation of spin-wave excitations in fractional quantum hall states and of interaction between composite fermions. PHYSICAL REVIEW LETTERS 2000; 85:3688-3691. [PMID: 11030982 DOI: 10.1103/physrevlett.85.3688] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2000] [Indexed: 05/23/2023]
Abstract
We demonstrate that the temperature dependence of the electron spin polarization for the fractional states nu = 1/3 and nu = 2/3 displays activated behavior. This study enables the first measurement of the fractional quantum Hall spin-flip gaps. They are found to be systematically larger in comparison with the gaps simultaneously measured in transport. For nu = 1/3 and nu = 1/2, these spin-flip gaps allow the determination of the composite fermion interaction energy. This energy is investigated as a function of the finite width of the 2D channel.
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Affiliation(s)
- IV Kukushkin
- Max-Planck-Institut fur Festkorperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany and Institute of Solid State Physics, RAS, Chernogolovka, 142432 Russia
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40
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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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41
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Shankar R. Magnetic phenomena at and near nu = 1 / 2 and 1 / 4: theory, experiment, and interpretation. PHYSICAL REVIEW LETTERS 2000; 84:3946-3949. [PMID: 11019246 DOI: 10.1103/physrevlett.84.3946] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/1999] [Indexed: 05/23/2023]
Abstract
I show that the Hamiltonian theory of composite fermions is capable of yielding a unified description in fair agreement with recent experiments on polarization P and relaxation rate 1/T1 in quantum Hall states at filling nu = p/(2ps+1), at and near nu = 1 / 2 and 1 / 4 ( s = 1,2) at zero and nonzero temperatures. I show how rotational invariance and two dimensionality can make the underlying interacting theory behave like a free one in a limited context.
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Affiliation(s)
- R Shankar
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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42
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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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Gee PJ, Peeters FM, Singleton J, Uji S, Aoki H, Foxon CT, Harris JJ. Composite fermions in tilted magnetic fields and the effect of the confining potential width on the composite-fermion effective mass. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:R14313-R14316. [PMID: 9985515 DOI: 10.1103/physrevb.54.r14313] [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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44
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Tieke B, Zeitler U, Fletcher R, Wiegers SA, Geim AK, Maan JC, Henini M. Even denominator filling factors in the thermoelectric power of a two-dimensional electron gas. PHYSICAL REVIEW LETTERS 1996; 76:3630-3633. [PMID: 10061016 DOI: 10.1103/physrevlett.76.3630] [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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