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Park H, Cai J, Anderson E, Zhang Y, Zhu J, Liu X, Wang C, Holtzmann W, Hu C, Liu Z, Taniguchi T, Watanabe K, Chu JH, Cao T, Fu L, Yao W, Chang CZ, Cobden D, Xiao D, Xu X. Observation of fractionally quantized anomalous Hall effect. Nature 2023; 622:74-79. [PMID: 37591304 DOI: 10.1038/s41586-023-06536-0] [Citation(s) in RCA: 34] [Impact Index Per Article: 34.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 08/11/2023] [Indexed: 09/29/2023]
Abstract
The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.
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Affiliation(s)
- Heonjoon Park
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Jiaqi Cai
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Eric Anderson
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Yinong Zhang
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Jiayi Zhu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Xiaoyu Liu
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Chong Wang
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | | | - Chaowei Hu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Zhaoyu Liu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Jiun-Haw Chu
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Ting Cao
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Wang Yao
- Department of Physics, University of Hong Kong, Hong Kong, China
- HKU-UCAS Joint Institute of Theoretical and Computational Physics, University of Hong Kong, Hong Kong, China
| | - Cui-Zu Chang
- Department of Physics, The Pennsylvania State University, University Park, PA, USA
| | - David Cobden
- Department of Physics, University of Washington, Seattle, WA, USA
| | - Di Xiao
- Department of Physics, University of Washington, Seattle, WA, USA
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA
| | - Xiaodong Xu
- Department of Physics, University of Washington, Seattle, WA, USA.
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA.
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Phuc HV, Kubakaddi SS, Dinh L, Bich TN, Hieu NN. Phonon-drag thermopower and thermoelectric performance of MoS 2monolayer in quantizing magnetic field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:315703. [PMID: 35636387 DOI: 10.1088/1361-648x/ac7496] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 05/30/2022] [Indexed: 06/15/2023]
Abstract
We present a theory of phonon-drag thermopower,Sxxg, in MoS2monolayer at a low-temperature regime in the presence of a quantizing magnetic fieldB. Our calculations forSxxgconsider the electron-acoustic phonon interaction via deformation potential (DP) and piezoelectric (PE) couplings for longitudinal (LA) and transverse (TA) phonon modes. The unscreened TA-DP is found to dominateSxxgover other mechanisms. TheSxxgis found to oscillate with the magnetic field where the lifting effect of the valley and spin degeneracies in MoS2monolayer has been clearly observed. An enhancedSxxgwith a peak value of∼1mV K-1at aboutT = 10 K is predicted, which is closer to the zero field experimental observation. In the Bloch-Grüneisen regime the temperature dependence ofSxxggives the power-lawSxxg∝Tδe, whereδevaries marginally around 3 and 5 for unscreened and screened couplings, respectively. In addition,Sxxgis smaller for larger electron densityne. The power factor PF is found to increase with temperatureT, decrease withne, and oscillate withB. The prediction of an increase of thermal conductivity with temperature and the magnetic field is responsible for the limit of the figure of merit (ZT). At a particular magnetic field and temperature,ZTcan be maximized by optimizing electron density. By fixingne=1012cm-2, the highestZTis found to be 0.57 atT = 5.8 K andB = 12.1 T. Our findings are compared with those in graphene and MoS2for the zero-magnetic field.
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Affiliation(s)
- Huynh V Phuc
- Division of Theoretical Physics, Dong Thap University, Cao Lanh 870000, Vietnam
| | - S S Kubakaddi
- Department of Physics, K. L. E. Technological University, Hubballi 580 031, Karnataka, India
| | - Le Dinh
- Center for Theoretical and Computational Physics, University of Education, Hue University, Hue 530000, Vietnam
| | - Tran N Bich
- Center for Theoretical and Computational Physics, University of Education, Hue University, Hue 530000, Vietnam
| | - Nguyen N Hieu
- Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
- Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam
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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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Schmidt TL, Rachel S, von Oppen F, Glazman LI. Inelastic electron backscattering in a generic helical edge channel. PHYSICAL REVIEW LETTERS 2012; 108:156402. [PMID: 22587268 DOI: 10.1103/physrevlett.108.156402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2011] [Indexed: 05/31/2023]
Abstract
We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperature-dependent deviation from the quantized conductance, δG ∝ T4. In addition, δG is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spin-orbit coupling.
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Affiliation(s)
- Thomas L Schmidt
- Department of Physics, Yale University, 217 Prospect Street, New Haven, Connecticut 06520, USA
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