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Yeh CC, Liao PC, Yang Y, Lin WC, Panna AR, Rigosi AF, Elmquist RE, Liang CT. Conformity Experiment on Inelastic Scattering Exponent of Electrons in Two Dimensions. PHYSICAL REVIEW LETTERS 2024; 133:096302. [PMID: 39270171 DOI: 10.1103/physrevlett.133.096302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2024] [Revised: 04/22/2024] [Accepted: 07/15/2024] [Indexed: 09/15/2024]
Abstract
The quantum Hall (QH) effect is one of the most widely studied physical phenomenon in two dimensions. The plateau-plateau transition within this effect can be comprehensively described by the scaling theory, which encompasses three pivotal exponents: the critical exponent κ, the inelastic scattering exponent p, and the universal exponent γ. Prior studies have focused on measuring κ and estimating γ, assuming a constant p value of 2 across magnetic fields. Here, our work marks a significant advancement by measuring all three exponents within a single graphene device and a conventional two-dimensional electron system. This study uniquely determines p at low magnetic fields (weak localization region and well outside the QH regime) and high magnetic fields (in the vicinity of the QH regime). Employing a comprehensive analytical approach that includes weak localization, plateau-plateau transitions, and variable range hopping, we have directly determined κ, p, and γ. Our findings reveal a distinct variation in p, shifting from 1 in the low magnetic field regime to 2 in the QH regime in graphene.
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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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Yamada S, Fujimoto A, Hidaka S, Akabori M, Imanaka Y, Takehana K. Fractional quantum Hall effects in In 0.75Ga 0.25As bilayer electron systems observed as "Finger print". Sci Rep 2019; 9:7446. [PMID: 31092854 PMCID: PMC6520355 DOI: 10.1038/s41598-019-43290-8] [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: 07/16/2018] [Accepted: 04/03/2019] [Indexed: 11/10/2022] Open
Abstract
Observations of fractional quantum Hall (FQH) plateaus are reported in bilayer electron gas system in wide (>80 nm) In0.75Ga0.25As wells. Several q/p (p = 5, 3, and 2, q > 5) QH states are confirmed at high temperatures (~1.6 K) when the critical conditions including an electron density imbalance as well as a dynamical resistance behavior at the bilayer-monolayer transition are properly satisfied. The former leads to a quantum limit in either of the layers and the latter might bring a meta-stable nature into FQH phenomena. Such a behavior occurs as a probability process associating with impurities or defects in the wells, they inevitably reflect the local structural landscapes of each sample. This is verified by the new finding that the kinds of fractional plateaus (what set of fractional filling factors) appeared are different depending on the samples, that is, they are the "finger print" in each sample.
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Affiliation(s)
- Syoji Yamada
- Osaka Institute of Technology, 5-16-1, Omiya, Asahi-ku Osaka, 535-8585, Japan.
| | - Akira Fujimoto
- Osaka Institute of Technology, 5-16-1, Omiya, Asahi-ku Osaka, 535-8585, Japan
| | - Siro Hidaka
- LT Center, Osaka University, 1-1, Machikaneyama, Toyonaka, Osaka, 560-0043, Japan
| | - Masashi Akabori
- Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292, Japan
| | - Yasutaka Imanaka
- National Institute for Materials Science, 3-13, Sakura, Tsukuba, Ibaraki, 305-0003, Japan
| | - Kanji Takehana
- National Institute for Materials Science, 3-13, Sakura, Tsukuba, Ibaraki, 305-0003, Japan
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Dodoo-Amoo NA, Saeed K, Mistry D, Khanna SP, Li L, Linfield EH, Davies AG, Cunningham JE. Non-universality of scaling exponents in quantum Hall transitions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:475801. [PMID: 25351842 DOI: 10.1088/0953-8984/26/47/475801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We have investigated experimentally the scaling behaviour of quantum Hall transitions in GaAs/AlGaAs heterostructures of a range of mobility, carrier concentration, and spacer layer width. All three critical scaling exponents γ, κ and p were determined independently for each sample. We measure the localization length exponent to be γ ≈ 2.3, in good agreement with expected predictions from scaling theory, but κ and p are found to possess non-universal values. Results obtained for κ range from κ = 0.16 ± 0.02 to κ = 0.67 ± 0.02, and are found to be Landau level (LL) dependent, whereas p is found to decrease with increasing sample mobility. Our results demonstrate the existence of two transport regimes in the LL conductivity peak; universality is found within the quantum coherent transport regime present in the tails of the conductivity peak, but is absent within the classical transport regime found close to the critical point at the centre of the conductivity peak. We explain these results using a percolation model and show that the critical scaling exponent depends on certain important length scales that correspond to the microscopic description of electron transport in the bulk of a two-dimensional electron system.
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Affiliation(s)
- N A Dodoo-Amoo
- School of Electronic and Electrical Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT,UK
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Visser AD, Ponomarenko LA, Galistu G, Lang DTND, Pruisken AMM, Zeitler U, Maude D. Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/1742-6596/51/1/088] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Li W, Csáthy GA, Tsui DC, Pfeiffer LN, West KW. Scaling and universality of integer quantum Hall plateau-to-plateau transitions. PHYSICAL REVIEW LETTERS 2005; 94:206807. [PMID: 16090272 DOI: 10.1103/physrevlett.94.206807] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2004] [Indexed: 05/03/2023]
Abstract
We have investigated the integer quantum Hall plateau-to-plateau transition in two-dimensional electrons confined to AlxGa(1-x)As-Al0.33Ga0.67As heterostructures over a broad range of Al concentration x. For x between 0.65% and 1.6%, where the dominant contribution to disorder is from the short-range alloy potential fluctuations, we observe a perfect power-law scaling in the temperature range from 30 mK to 1 K with a critical exponent kappa = 0.42 +/- 0.01.
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Affiliation(s)
- Wanli Li
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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Sorensen ES, MacDonald AH. Integer quantum Hall effect in double-layer systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:10675-10687. [PMID: 9984864 DOI: 10.1103/physrevb.54.10675] [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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Polyakov DG. Spin-flip scattering in the quantum Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:15777-15788. [PMID: 9983414 DOI: 10.1103/physrevb.53.15777] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hanna CB, Arovas DP, Mullen K, Girvin SM. Effect of spin degeneracy on scaling in the quantum Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:5221-5232. [PMID: 9981707 DOI: 10.1103/physrevb.52.5221] [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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Wei HP, Engel LW, Tsui DC. Current scaling in the integer quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:14609-14612. [PMID: 9975690 DOI: 10.1103/physrevb.50.14609] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lee DK. Degenerate Landau bands with interband disorder: A semiclassical picture. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:7743-7746. [PMID: 9974759 DOI: 10.1103/physrevb.50.7743] [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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Lee DK, Chalker JT, Ko DY. Localization in a random magnetic field: The semiclassical limit. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:5272-5285. [PMID: 9976868 DOI: 10.1103/physrevb.50.5272] [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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Wang T, Clark KP, Spencer GF, Mack AM, Kirk WP. Magnetic-field-induced metal-insulator transition in two dimensions. PHYSICAL REVIEW LETTERS 1994; 72:709-712. [PMID: 10056503 DOI: 10.1103/physrevlett.72.709] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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