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Sanchez-Manzano D, Orfila G, Sander A, Marcano L, Gallego F, Mawass MA, Grilli F, Arora A, Peralta A, Cuellar FA, Fernandez-Roldan JA, Reyren N, Kronast F, Leon C, Rivera-Calzada A, Villegas JE, Santamaria J, Valencia S. Size-Dependence and High Temperature Stability of Radial Vortex Magnetic Textures Imprinted by Superconductor Stray Fields. ACS APPLIED MATERIALS & INTERFACES 2024; 16:19681-19690. [PMID: 38564236 DOI: 10.1021/acsami.3c17671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
Swirling spin textures, including topologically nontrivial states, such as skyrmions, chiral domain walls, and magnetic vortices, have garnered significant attention within the scientific community due to their appeal from both fundamental and applied points of view. However, their creation, controlled manipulation, and stability are typically constrained to certain systems with specific crystallographic symmetries, bulk or interface interactions, and/or a precise stacking sequence of materials. Recently, a new approach has shown potential for the imprint of magnetic radial vortices in soft ferromagnetic compounds making use of the stray field of YBa2Cu3O7-δ superconducting microstructures in ferromagnet/superconductor (FM/SC) hybrids at temperatures below the superconducting transition temperature (TC). Here, we explore the lower size limit for the imprint of magnetic radial vortices in square and disc shaped structures as well as the persistence of these spin textures above TC, with magnetic domains retaining partial memory. Structures with circular geometry and with FM patterned to smaller radius than the superconductor island facilitate the imprinting of magnetic radial vortices and improve their stability above TC, in contrast to square structures where the presence of magnetic domains increases the dipolar energy. Micromagnetic modeling coupled with a SC field model reveals that the stabilization mechanism above TC is mediated by microstructural defects. Superconducting control of swirling spin textures, and their stabilization above the superconducting transition temperature by means of defect engineering holds promising prospects for shaping superconducting spintronics based on magnetic textures.
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Affiliation(s)
- David Sanchez-Manzano
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | - Gloria Orfila
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | - Anke Sander
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - Lourdes Marcano
- Helmholtz-Zentrum Berlin, Albert-Einstein Str. 15, 12489 Berlin, Germany
- Department of Physics, Faculty of Science, University of Oviedo, 33007 Oviedo, Spain
- Center for Cooperative Research in Biomaterials (CIC biomaGUNE), Basque Research and Technology Alliance (BRTA), Paseo de Miramón 194, 20014 Donostia-San Sebastián, Spain
| | - Fernando Gallego
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | | | - Francesco Grilli
- Institute for Technical Physics Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany
| | - Ashima Arora
- Helmholtz-Zentrum Berlin, Albert-Einstein Str. 15, 12489 Berlin, Germany
| | - Andrea Peralta
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | - Fabian A Cuellar
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | - Jose A Fernandez-Roldan
- Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, 01328 Dresden, Germany
| | - Nicolas Reyren
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - Florian Kronast
- Helmholtz-Zentrum Berlin, Albert-Einstein Str. 15, 12489 Berlin, Germany
| | - Carlos Leon
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | - Alberto Rivera-Calzada
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | - Javier E Villegas
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - Jacobo Santamaria
- GFMC. Department Física de Materiales. Facultad de Física. Universidad Complutense. 28040 Madrid, Spain
| | - Sergio Valencia
- Helmholtz-Zentrum Berlin, Albert-Einstein Str. 15, 12489 Berlin, Germany
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2
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Fermin R, van Dinter D, Hubert M, Woltjes B, Silaev M, Aarts J, Lahabi K. Superconducting Triplet Rim Currents in a Spin-Textured Ferromagnetic Disk. NANO LETTERS 2022; 22:2209-2216. [PMID: 35239357 PMCID: PMC8949790 DOI: 10.1021/acs.nanolett.1c04051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 02/23/2022] [Indexed: 06/14/2023]
Abstract
Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge in highly localized (sub-80 nm) channels at the rim of the ferromagnet, despite its trivial band structure. We show that these robust rim currents arise from the magnetization texture acting as an effective spin-orbit coupling, which results in spin accumulation at the bilayer-vacuum boundary. Lastly, we demonstrate that by altering the spin texture of a single ferromagnet, both 0 and π channels can be realized in the same device.
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Affiliation(s)
- Remko Fermin
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Dyon van Dinter
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Michel Hubert
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Bart Woltjes
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Mikhail Silaev
- Department
of Physics and Nanoscience Center, University
of Jyväskylä, P.O. Box 35 (YFL), FI-40014 Jyväskylä, Finland
- Computational
Physics Laboratory, Physics Unit, Faculty of Engineering and Natural
Sciences, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Jan Aarts
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Kaveh Lahabi
- Huygens-Kamerlingh
Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
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3
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Sanchez-Manzano D, Mesoraca S, Cuellar FA, Cabero M, Rouco V, Orfila G, Palermo X, Balan A, Marcano L, Sander A, Rocci M, Garcia-Barriocanal J, Gallego F, Tornos J, Rivera A, Mompean F, Garcia-Hernandez M, Gonzalez-Calbet JM, Leon C, Valencia S, Feuillet-Palma C, Bergeal N, Buzdin AI, Lesueur J, Villegas JE, Santamaria J. Extremely long-range, high-temperature Josephson coupling across a half-metallic ferromagnet. NATURE MATERIALS 2022; 21:188-194. [PMID: 34857910 DOI: 10.1038/s41563-021-01162-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 10/21/2021] [Indexed: 06/13/2023]
Abstract
The Josephson effect results from the coupling of two superconductors across a spacer such as an insulator, a normal metal or a ferromagnet to yield a phase coherent quantum state. However, in junctions with ferromagnetic spacers, very long-range Josephson effects have remained elusive. Here we demonstrate extremely long-range (micrometric) high-temperature (tens of kelvins) Josephson coupling across the half-metallic manganite La0.7Sr0.3MnO3 combined with the superconducting cuprate YBa2Cu3O7. These planar junctions, in addition to large critical currents, display the hallmarks of Josephson physics, such as critical current oscillations driven by magnetic flux quantization and quantum phase locking effects under microwave excitation (Shapiro steps). The latter display an anomalous doubling of the Josephson frequency predicted by several theories. In addition to its fundamental interest, the marriage between high-temperature, dissipationless quantum coherent transport and full spin polarization brings opportunities for the practical realization of superconducting spintronics, and opens new perspectives for quantum computing.
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Affiliation(s)
- D Sanchez-Manzano
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - S Mesoraca
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - F A Cuellar
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - M Cabero
- IMDEA Nanoscience Institute, Universidad Autonoma, Cantoblanco, Spain
- Centro Nacional de Microscopia Electronica, Universidad Complutense, Madrid, Spain
| | - V Rouco
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - G Orfila
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - X Palermo
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - A Balan
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - L Marcano
- Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany
| | - A Sander
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
| | - M Rocci
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
- Instituto Nanoscienze, Consiglio Thales Alenia Space Italia, L'Aquila, Italy
| | | | - F Gallego
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - J Tornos
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - A Rivera
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - F Mompean
- Instituto de Ciencia de Materiales de Madrid (ICMM, CSIC), Cantoblanco, Spain
- Laboratorio de Heteroestructuras con Aplicación en Spintrónica, Unidad Asociada (UCM-CSIC), Madrid, Spain
| | - M Garcia-Hernandez
- Instituto de Ciencia de Materiales de Madrid (ICMM, CSIC), Cantoblanco, Spain
- Laboratorio de Heteroestructuras con Aplicación en Spintrónica, Unidad Asociada (UCM-CSIC), Madrid, Spain
| | - J M Gonzalez-Calbet
- Centro Nacional de Microscopia Electronica, Universidad Complutense, Madrid, Spain
- Departamento Química Inorgánica, Facultad de Química, Universidad Complutense, Madrid, Spain
| | - C Leon
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain
| | - S Valencia
- Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany
| | - C Feuillet-Palma
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, CNRS, PSL Research University, Sorbonne University, Paris, France
| | - N Bergeal
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, CNRS, PSL Research University, Sorbonne University, Paris, France
| | - A I Buzdin
- LOMA, CNRS, Université Bordeaux, Talence, France
- Digital Biodesign and Personalized Healthcare, Sechenov First Moscow State Medical University, Moscow, Russia
| | - J Lesueur
- Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, CNRS, PSL Research University, Sorbonne University, Paris, France
| | - Javier E Villegas
- Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau, France.
| | - J Santamaria
- GFMC, Departamento Fisica de Materiales, Facultad de Fisica, Universidad Complutense, Madrid, Spain.
- Laboratorio de Heteroestructuras con Aplicación en Spintrónica, Unidad Asociada (UCM-CSIC), Madrid, Spain.
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4
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Kapran OM, Morari R, Golod T, Borodianskyi EA, Boian V, Prepelita A, Klenov N, Sidorenko AS, Krasnov VM. In situ transport characterization of magnetic states in Nb/Co superconductor/ferromagnet heterostructures. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2021; 12:913-923. [PMID: 34497739 PMCID: PMC8381831 DOI: 10.3762/bjnano.12.68] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 07/25/2021] [Indexed: 06/13/2023]
Abstract
Employment of the non-trivial proximity effect in superconductor/ferromagnet (S/F) heterostructures for the creation of novel superconducting devices requires accurate control of magnetic states in complex thin-film multilayers. In this work, we study experimentally in-plane transport properties of microstructured Nb/Co multilayers. We apply various transport characterization techniques, including magnetoresistance, Hall effect, and the first-order-reversal-curves (FORC) analysis. We demonstrate how FORC can be used for detailed in situ characterization of magnetic states. It reveals that upon reduction of the external field, the magnetization in ferromagnetic layers first rotates in a coherent scissor-like manner, then switches abruptly into the antiparallel state and after that splits into the polydomain state, which gradually turns into the opposite parallel state. The polydomain state is manifested by a profound enhancement of resistance caused by a flux-flow phenomenon, triggered by domain stray fields. The scissor state represents the noncollinear magnetic state in which the unconventional odd-frequency spin-triplet order parameter should appear. The non-hysteretic nature of this state allows for reversible tuning of the magnetic orientation. Thus, we identify the range of parameters and the procedure for in situ control of devices based on S/F heterostructures.
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Affiliation(s)
- Olena M Kapran
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | - Roman Morari
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
- Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny, Russia
| | - Taras Golod
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | - Evgenii A Borodianskyi
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | - Vladimir Boian
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
| | - Andrei Prepelita
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
| | - Nikolay Klenov
- Lomonosov Moscow State University, Faculty of Physics, Moscow, 119991, Russia
- Moscow Technical University of Communication and Informatics, 111024 Moscow, Russia
| | - Anatoli S Sidorenko
- Institute of Electronic Engineering and Nanotechnologies, MD2028 Chisinau, Moldova
- Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny, Russia
- Laboratory of Functional Nanostructures, Orel State University named after I.S. Turgenev, 302026, Russia
| | - Vladimir M Krasnov
- Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
- Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny, Russia
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5
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Bhatia E, Srivastava A, Devine-Stoneman J, Stelmashenko NA, Barber ZH, Robinson JWA, Senapati K. Nanoscale Domain Wall Engineered Spin-Triplet Josephson Junctions and SQUID. NANO LETTERS 2021; 21:3092-3097. [PMID: 33724857 DOI: 10.1021/acs.nanolett.1c00273] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Spin-singlet Cooper pairs convert to spin-triplet Cooper pairs on passing through a magnetically noncollinear structure at a superconductor(S)/ferromagnet(F) interface. In this context, the generation of triplet supercurrents through intrinsic ferromagnetic domain walls, which are naturally occurring noncollinear magnetic features, was proposed theoretically in the past decade. However, an experimental demonstration has been lacking in the literature, particularly because of the difficulty in accessing a single domain wall, which is typically buried between two domains in a ferromagnetic material. By patterning a ferromagnetic nanoconstriction, we have been able to realize a nanoscale S/F/S planar junction, where a single domain wall (pinned at the nanoconstriction) acts as a Josephson barrier. In this geometry, we are able to show the predicted long-range triplet supercurrent across a ferromagnetic barrier exceeding 70 nm. Using this technique, we have demonstrated a ferromagnetic planar nano-SQUID device consisting of two Nb/Ni/Nb spin-triplet Josephson junctions.
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Affiliation(s)
- Ekta Bhatia
- School of Physical Sciences, National Institute of Science Education and Research (NISER), HBNI, Bhubaneswar, Odisha 752050, India
| | - Anand Srivastava
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - James Devine-Stoneman
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Nadia A Stelmashenko
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Zoe H Barber
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Jason W A Robinson
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Kartik Senapati
- School of Physical Sciences, National Institute of Science Education and Research (NISER), HBNI, Bhubaneswar, Odisha 752050, India
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6
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Ying J, He J, Yang G, Liu M, Lyu Z, Zhang X, Liu H, Zhao K, Jiang R, Ji Z, Fan J, Yang C, Jing X, Liu G, Cao X, Wang X, Lu L, Qu F. Magnitude and Spatial Distribution Control of the Supercurrent in Bi 2O 2Se-Based Josephson Junction. NANO LETTERS 2020; 20:2569-2575. [PMID: 32203670 DOI: 10.1021/acs.nanolett.0c00025] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Many proposals for exploring topological quantum computation are based on superconducting quantum devices constructed on materials with strong spin-orbit coupling (SOC). For these devices, full control of both the magnitude and the spatial distribution of the supercurrent is highly demanded, but has been elusive up to now. We constructed a proximity-type Josephson junction on nanoplates of Bi2O2Se, a new emerging semiconductor with strong SOC. Through electrical gating, we show that the supercurrent can be fully turned ON and OFF, and its real-space pathways can be configured either through the bulk or along the edges. Our work demonstrates Bi2O2Se as a promising platform for constructing multifunctional hybrid superconducting devices as well as for searching for topological superconductivity.
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Affiliation(s)
- Jianghua Ying
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jiangbo He
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Guang Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Mingli Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhaozheng Lyu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xiang Zhang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Huaiyuan Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physics, Nankai University, Tianjin 300071, China
| | - Kui Zhao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Ruiyang Jiang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhongqing Ji
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Jie Fan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Changli Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiunian Jing
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Guangtong Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Xuewei Cao
- School of Physics, Nankai University, Tianjin 300071, China
| | - Xuefeng Wang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
| | - Li Lu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Fanming Qu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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