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Madathil PT, Villegas Rosales KA, Tai CT, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions. PHYSICAL REVIEW LETTERS 2023; 130:226503. [PMID: 37327438 DOI: 10.1103/physrevlett.130.226503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 05/12/2023] [Indexed: 06/18/2023]
Abstract
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent κ≃0.42. Here we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our Letter is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that κ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor ν=1/2 and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the nonuniversal κ observed in our experiments.
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Affiliation(s)
- P T Madathil
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - C T Tai
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Pu S, Sreejith GJ, Jain JK. Anderson Localization in the Fractional Quantum Hall Effect. PHYSICAL REVIEW LETTERS 2022; 128:116801. [PMID: 35363020 DOI: 10.1103/physrevlett.128.116801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor ν=n/(2n+1) has a striking quantitative correspondence to the localization of a single electron in the (n+1)th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation, these results can be extended to situations where a finite density of quasiparticles is present.
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Affiliation(s)
- Songyang Pu
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - G J Sreejith
- Indian Institute of Science Education and Research, Pune 411008, India
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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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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Huang TY, Liang CT, Chen YF, Simmons MY, Kim GH, Ritchie DA. Direct measurement of the spin gaps in a gated GaAs two-dimensional electron gas. NANOSCALE RESEARCH LETTERS 2013; 8:138. [PMID: 23522392 PMCID: PMC3626693 DOI: 10.1186/1556-276x-8-138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/12/2013] [Accepted: 03/09/2013] [Indexed: 06/02/2023]
Abstract
We have performed magnetotransport measurements on gated GaAs two-dimensional electron gases in which electrons are confined in a layer of the nanoscale. From the slopes of a pair of spin-split Landau levels (LLs) in the energy-magnetic field plane, we can perform direct measurements of the spin gap for different LLs. The measured g-factor g is greatly enhanced over its bulk value in GaAs (0.44) due to electron-electron (e-e) interactions. Our results suggest that both the spin gap and g determined from conventional activation energy studies can be very different from those obtained by direct measurements.
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Affiliation(s)
- Tsai-Yu Huang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Chi-Te Liang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Yang Fang Chen
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | - Michelle Y Simmons
- School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - Gil-Ho Kim
- School of Electronic and Electrical Engineering, Sungkyunkwan University, Suwon 440-746, South Korea
| | - David A Ritchie
- Cavendish Laboratory, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK
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Goldman VJ, Su B. Resonant tunneling in the quantum Hall regime: measurement of fractional charge. Science 2010; 267:1010-2. [PMID: 17811442 DOI: 10.1126/science.267.5200.1010] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
In experiments on resonant tunneling through a "quantum antidot" (a potential hill) in the quantum Hall (QH) regime, periodic conductance peaks were observed as a function of both magnetic field and back gate voltage. A combination of the two periods constitutes a measurement of the charge of the tunneling particles and implies that charge deficiency on the antidot is quantized in units of the charge of quasi-particles of the surrounding QH condensate. The experimentally determined value of the electron charge e is 1.57 x 10(-19) coulomb = (0.98 +/- 0.03) e for the states v = 1 and v = 2 of the integer QH effect, and the quasi-particle charge is 5.20 x 10(-20) coulomb = (0.325 +/- 0.01)e for the state v = (1/3) of the fractional QH effect.
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Glozman I, Johnson C, Jiang H. Fate of the Delocalized States in a Vanishing Magnetic Field. PHYSICAL REVIEW LETTERS 1995; 74:594-597. [PMID: 10058797 DOI: 10.1103/physrevlett.74.594] [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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Wu XG, Jain JK. Excitation spectrum and collective modes of composite fermions. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:1752-1761. [PMID: 9978896 DOI: 10.1103/physrevb.51.1752] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Abstract
Recent progress in the understanding of the two-dimensional electron system under the influence of a strong magnetic field is reviewed. This system is characterized by the existence of a particle called the composite fermion, which manifests itself in several dramatic experimental observations.
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Goldman VJ, Su B, Jain JK. Detection of composite fermions by magnetic focusing. PHYSICAL REVIEW LETTERS 1994; 72:2065-2068. [PMID: 10055779 DOI: 10.1103/physrevlett.72.2065] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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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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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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Chklovskii DB, Lee PA. Transport properties between quantum Hall plateaus. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:18060-18078. [PMID: 10008445 DOI: 10.1103/physrevb.48.18060] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zang J, Birman JL. Farey series, hierarchy structure, and scaling theory of the fractional quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:16305-16310. [PMID: 10006056 DOI: 10.1103/physrevb.47.16305] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Su B, Goldman VJ, Cunningham JE. Single-electron tunneling in nanometer-scale double-barrier heterostructure devices. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:7644-7655. [PMID: 10002505 DOI: 10.1103/physrevb.46.7644] [Citation(s) in RCA: 78] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Jain JK, Goldman VJ. Hierarchy of states in the fractional quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:1255-1258. [PMID: 10001602 DOI: 10.1103/physrevb.45.1255] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wang JK, Goldman VJ. Edge states in the fractional quantum Hall effect. PHYSICAL REVIEW LETTERS 1991; 67:749-752. [PMID: 10044979 DOI: 10.1103/physrevlett.67.749] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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