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Feng G, Liu Y, Zhu Q, Feng Z, Luo S, Qin C, Chen L, Xu Y, Wang H, Zubair M, Qu K, Yang C, Hao S, Yue F, Duan C, Chu J, Tian B. Giant tunnel electroresistance through a Van der Waals junction by external ferroelectric polarization. Nat Commun 2024; 15:9701. [PMID: 39516220 PMCID: PMC11549478 DOI: 10.1038/s41467-024-54114-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2024] [Accepted: 11/02/2024] [Indexed: 11/16/2024] Open
Abstract
The burgeoning interest in two-dimensional semiconductors stems from their potential as ultrathin platforms for next-generation transistors. Nonetheless, there persist formidable challenges in fully obtaining high-performance complementary logic components and the underlying mechanisms for the polarity modulation of transistors are not yet fully understood. Here, we exploit both ferroelectric domain-based nonvolatile modulation of Fermi level in transitional metal dichalcogenides (MoS2) and quantum tunneling through nanoscale hexagonal boron nitride (h-BN). Our prototype devices, termed as vertical tunneling ferroelectric field-effect transistor, utilizes a Van der Waals MoS2/h-BN/metal tunnel junction as the channel. The Fermi level of MoS2 is bipolarly tuned by ferroelectric domains and sensitively detected by the direct quantum tunneling strength across the junction, demonstrating an impressive electroresistance ratio of up to 109 in the vertical tunneling ferroelectric field-effect transistor. It consumes only 0.16 fJ of energy to open a ratio window exceeding 104. This work not only validates the effectiveness of tailored tunnel barriers in manipulating electronic flow but also highlights a new avenue for the design flexibility and functional versatility of advanced ferroelectric memory technology.
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Affiliation(s)
- Guangdi Feng
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
- Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing, 401120, China
| | - Yifei Liu
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Qiuxiang Zhu
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China.
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China.
| | - Zhenyu Feng
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Shengwen Luo
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Cuijie Qin
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Luqiu Chen
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Yu Xu
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Haonan Wang
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Muhammad Zubair
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Ke Qu
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Chang Yang
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Shenglan Hao
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Fangyu Yue
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
| | - Chungang Duan
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Shanxi, 030006, China
| | - Junhao Chu
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China
- Institute of Optoelectronics, Fudan University, Shanghai, 200433, China
| | - Bobo Tian
- Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Electronics, East China Normal University, Shanghai, 200241, China.
- Shanghai Center of Brain-inspired Intelligent Materials and Devices, Shanghai, 200241, China.
- Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing, 401120, China.
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Yao C, Wu G, Huang M, Wang W, Zhang C, Wu J, Liu H, Zheng B, Yi J, Zhu C, Tang Z, Wang Y, Huang M, Huang L, Li Z, Xiang L, Li D, Li S, Pan A. Reconfigurable Artificial Synapse Based on Ambipolar Floating Gate Memory. ACS APPLIED MATERIALS & INTERFACES 2023; 15:23573-23582. [PMID: 37141554 DOI: 10.1021/acsami.3c00063] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
Artificial synapse networks capable of massively parallel computing and mimicking biological neural networks can potentially improve the processing efficiency of existing information technologies. Semiconductor devices functioning as excitatory and inhibitory synapses are crucial for developing intelligence systems, such as traffic control systems. However, achieving reconfigurability between two working modes (inhibitory and excitatory) and bilingual synaptic behavior in a single transistor remains challenging. This study successfully mimics a bilingual synaptic response using an artificial synapse based on an ambipolar floating gate memory comprising tungsten selenide (WSe2)/hexagonal boron nitride (h-BN)/ molybdenum telluride (MoTe2). In this WSe2/h-BN/MoTe2 structure, ambipolar semiconductors WSe2 and MoTe2 are inserted as channel and floating gates, respectively, and h-BN serves as the tunneling barrier layer. Using either positive or negative pulse amplitude modulations at the control gate, this device with bipolar channel conduction produced eight distinct resistance states. Based on this, we experimentally projected that we could achieve 490 memory states (210 hole-resistance states + 280 electron-resistance states). Using the bipolar charge transport and multistorage states of WSe2/h-BN/MoTe2 floating gate memory, we mimicked reconfigurable excitatory and inhibitory synaptic plasticity in a single device. Furthermore, the convolution neural network formed by these synaptic devices can recognize handwritten digits with an accuracy of >92%. This study identifies the unique properties of heterostructure devices based on two-dimensional materials as well as predicts their applicability in advanced recognition of neuromorphic computing.
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Affiliation(s)
- Chengdong Yao
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Guangcheng Wu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Mingqiang Huang
- Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Wenqiang Wang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Cheng Zhang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Jiaxin Wu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Huawei Liu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Biyuan Zheng
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Jiali Yi
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Chenguang Zhu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Zilan Tang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Yizhe Wang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Ming Huang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Luying Huang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Ziwei Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Li Xiang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Dong Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Shengman Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
| | - Anlian Pan
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan Institute of Optoelectronic Integration, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China
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Zhang G, Lu G, Li X, Mei Z, Liang L, Fan S, Li Q, Wei Y. Reconfigurable Two-Dimensional Air-Gap Barristors. ACS NANO 2023; 17:4564-4573. [PMID: 36847653 DOI: 10.1021/acsnano.2c10593] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Reconfigurable logic circuits implemented by two-dimensional (2D) ambipolar semiconductors provide a prospective solution for the post-Moore era. It is still a challenge for ambipolar nanomaterials to realize reconfigurable polarity control and rectification with a simplified device structure. Here, an air-gap barristor based on an asymmetric stacking sequence of the electrode contacts was developed to resolve these issues. For the 2D ambipolar channel of WSe2, the barristor can not only be reconfigured as an n- or p-type unipolar transistor but also work as a switchable diode. The air gap around the bottom electrode dominates the reconfigurable behaviors by widening the Schottky barrier here, thus blocking the injection of both electrons and holes. The electrical performances can be improved by optimizing the electrode materials, which achieve an on/off ratio of 104 for the transistor and a rectifying ratio of 105 for the diode. A complementary inverter and a switchable AND/OR logic gate were constructed by using the air-gap barristors as building blocks. This work provides an efficient approach with great potential for low-dimensional reconfigurable electronics.
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Affiliation(s)
- Guangqi Zhang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
| | - Gaotian Lu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
| | - Xuanzhang Li
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
| | - Zhen Mei
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
| | - Liang Liang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
| | - Shoushan Fan
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
| | - Qunqing Li
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
| | - Yang Wei
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
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4
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Waltl M, Knobloch T, Tselios K, Filipovic L, Stampfer B, Hernandez Y, Waldhör D, Illarionov Y, Kaczer B, Grasser T. Perspective of 2D Integrated Electronic Circuits: Scientific Pipe Dream or Disruptive Technology? ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2201082. [PMID: 35318749 DOI: 10.1002/adma.202201082] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 03/14/2022] [Indexed: 06/14/2023]
Abstract
Within the last decade, considerable efforts have been devoted to fabricating transistors utilizing 2D semiconductors. Also, small circuits consisting of a few transistors have been demonstrated, including inverters, ring oscillators, and static random access memory cells. However, for industrial applications, both time-zero and time-dependent variability in the performance of the transistors appear critical. While time-zero variability is primarily related to immature processing, time-dependent drifts are dominated by charge trapping at defects located at the channel/insulator interface and in the insulator itself, which can substantially degrade the stability of circuits. At the current state of the art, 2D transistors typically exhibit a few orders of magnitude higher trap densities than silicon devices, which considerably increases their time-dependent variability, resulting in stability and yield issues. Here, the stability of currently available 2D electronics is carefully evaluated using circuit simulations to determine the impact of transistor-related issues on the overall circuit performance. The results suggest that while the performance parameters of transistors based on certain material combinations are already getting close to being competitive with Si technologies, a reduction in variability and defect densities is required. Overall, the criteria for parameter variability serve as guidance for evaluating the future development of 2D technologies.
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Affiliation(s)
- Michael Waltl
- Christian Doppler Laboratory for Single-Defect Spectroscopy at the Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
| | - Theresia Knobloch
- Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
| | - Konstantinos Tselios
- Christian Doppler Laboratory for Single-Defect Spectroscopy at the Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
| | - Lado Filipovic
- Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
| | - Bernhard Stampfer
- Christian Doppler Laboratory for Single-Defect Spectroscopy at the Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
| | - Yoanlys Hernandez
- Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
| | - Dominic Waldhör
- Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
| | - Yury Illarionov
- Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
- Ioffe Institute, Polytechnicheskaya 26, St-Petersburg, 194021, Russia
| | - Ben Kaczer
- imec, Kapeldreef 75, Leuven, 3001, Belgium
| | - Tibor Grasser
- Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, Vienna, 1040, Austria
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Yi J, Sun X, Zhu C, Li S, Liu Y, Zhu X, You W, Liang D, Shuai Q, Wu Y, Li D, Pan A. Double-Gate MoS 2 Field-Effect Transistors with Full-Range Tunable Threshold Voltage for Multifunctional Logic Circuits. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2101036. [PMID: 34057257 DOI: 10.1002/adma.202101036] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2021] [Revised: 04/07/2021] [Indexed: 05/07/2023]
Abstract
Multifunctional reconfigurable devices, with higher information capacity, smaller size, and more functions, are urgently needed and draw most attention in frontiers in information technology. 2D semiconductors, ascribing to ultrathin body and easy electrostatic control, show great potential in developing reconfigurable functional units. This work proposes a novel double-gate field-effect transistor architecture with equal top and bottom gate (TG and BG) and realizes flexible optimization of the subthreshold swing (SS) and threshold voltage (VTH ). While the TG and BG are used simultaneously, as a single gate to drive the transistor, ultralow average SS value of 65.5 mV dec-1 can be obtained in a large current range over 104 , enabling the application in high gain inverter. While one gate is used to initialize the channel doping, full logic swing inverter circuit with high noise margin (over 90%) is demonstrated. Such device prototype is further extended for designing reconfigurable logic applications and can be dynamically switched and well maintained between binary and ternary logics. This study provides important concept and device prototype for future multifunctional logic applications.
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Affiliation(s)
- Jiali Yi
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Xingxia Sun
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Chenguang Zhu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Shengman Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Yong Liu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Xiaoli Zhu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Wenxia You
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Delang Liang
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Qin Shuai
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Yanqing Wu
- Wuhan National High Magnetic Field Center and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China
| | - Dong Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Anlian Pan
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China
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