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Coraiola M, Svetogorov AE, Haxell DZ, Sabonis D, Hinderling M, Ten Kate SC, Cheah E, Krizek F, Schott R, Wegscheider W, Cuevas JC, Belzig W, Nichele F. Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction. ACS Nano 2024; 18:9221-9231. [PMID: 38488287 DOI: 10.1021/acsnano.4c01642] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/27/2024]
Abstract
We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of |η| ≈ 34%, is widely tunable─both in amplitude and sign─as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with nonsinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes generated on the chip break both time-reversal and spatial symmetries. Our work presents an approach for developing Josephson diodes with wide-range tunability that do not rely on exotic materials.
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Affiliation(s)
- Marco Coraiola
- IBM Research Europe─Zurich, 8803 Rüschlikon, Switzerland
| | | | | | | | | | | | - Erik Cheah
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Filip Krizek
- IBM Research Europe─Zurich, 8803 Rüschlikon, Switzerland
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
- Institute of Physics, Czech Academy of Sciences, 162 00 Prague, Czech Republic
| | - Rüdiger Schott
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Werner Wegscheider
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Juan Carlos Cuevas
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Wolfgang Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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2
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Li L, Wu Y, Liu X, Liu J, Ruan H, Zhi Z, Zhang Y, Huang P, Ji Y, Tang C, Yang Y, Che R, Kou X. Room-Temperature Gate-Tunable Nonreciprocal Charge Transport in Lattice-Matched InSb/CdTe Heterostructures. Adv Mater 2023; 35:e2207322. [PMID: 36526594 DOI: 10.1002/adma.202207322] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Revised: 10/30/2022] [Indexed: 06/17/2023]
Abstract
Symmetry manipulation can be used to effectively tailor the physical order in solid-state systems. With the breaking of both the inversion and time-reversal symmetries, nonreciprocal magneto-transport may arise in nonmagnetic systems to enrich spin-orbit effects. Here, the observation of unidirectional magnetoresistance (UMR) in lattice-matched InSb/CdTe films is investigated up to room temperature. Benefiting from the strong built-in electric field of 0.13 V nm-1 in the heterojunction region, the resulting Rashba-type spin-orbit coupling and quantum confinement result in a distinct sinusoidal UMR signal with a nonreciprocal coefficient that is 1-2 orders of magnitude larger than most non-centrosymmetric materials at 298 K. Moreover, this heterostructure configuration enables highly efficient gate tuning of the rectification response, wherein the UMR amplitude is enhanced by 40%. The results of this study advocate the use of narrow-bandgap semiconductor-based hybrid systems with robust spin textures as suitable platforms for the pursuit of controllable chiral spin-orbit applications.
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Affiliation(s)
- Lun Li
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Yuyang Wu
- Laboratory of Advanced Materials, Shanghai Key Lab of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai, 200438, China
- Department of Materials Science, Fudan University, Shanghai, 200438, China
| | - Xiaoyang Liu
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
- Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, 200050, China
- University of Chinese Academy of Science, Beijing, 101408, China
| | - Jiuming Liu
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Hanzhi Ruan
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Zhenghang Zhi
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
- Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, 200050, China
- University of Chinese Academy of Science, Beijing, 101408, China
| | - Yong Zhang
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
- Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, 200050, China
- University of Chinese Academy of Science, Beijing, 101408, China
| | - Puyang Huang
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Yuchen Ji
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Chenjia Tang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, 201210, China
| | - Yumeng Yang
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Renchao Che
- Laboratory of Advanced Materials, Shanghai Key Lab of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai, 200438, China
- Department of Materials Science, Fudan University, Shanghai, 200438, China
| | - Xufeng Kou
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, 201210, China
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3
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Song C, Zhao L, Liu J, Jiang W. Experimental Realization of a Skyrmion Circulator. Nano Lett 2022; 22:9638-9644. [PMID: 36411254 DOI: 10.1021/acs.nanolett.2c03789] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Magnetic skyrmions are mobile topological spin textures that can be manipulated by different means. Their applications have been frequently discussed in the context of information carriers for racetrack memory devices, which on the other hand, exhibit a skyrmion Hall effect as a result of the nontrivial real-space topology. While the skyrmion Hall effect is believed to be detrimental for constructing racetrack devices, we show here that it can be implemented for realizing a three-terminal skyrmion circulator. In analogy to the microwave circulator, nonreciprocal transportation and circulation of skyrmions are studied both numerically and experimentally. In particular, successful control of the circulating direction of being either clockwise or counterclockwise is demonstrated, simply by changing the sign of the topological charge. Our studies suggest that the topological property of skyrmions can be incorporated for enabling novel spintronic functionalities; the skyrmion circulator is just one example.
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Affiliation(s)
- Chengkun Song
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
| | - Le Zhao
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
| | - Jiahao Liu
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
- Institute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha410073, China
| | - Wanjun Jiang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing100084, China
- Frontier Science Center for Quantum Information, Tsinghua University, Beijing100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing100084, China
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4
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Abstract
Our work shows a fascinating application of finite-momentum superconductivity, the supercurrent diode effect, which is being reported in a growing number of experiments. We show that, under external magnetic field, Cooper pairs can acquire finite momentum so that critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal. When both inversion and time-reversal symmetries are broken, the critical current of a superconductor can be nonreciprocal. In this work, we show that, in certain classes of two-dimensional superconductors with antisymmetric spin–orbit coupling, Cooper pairs acquire a finite momentum upon the application of an in-plane magnetic field, and, as a result, critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal. This supercurrent diode effect is also manifested in the polarity dependence of in-plane critical fields induced by a supercurrent. These nonreciprocal effects may be found in polar SrTiO3 film, few-layer MoTe2 in the Td phase, and twisted bilayer graphene in which the valley degree of freedom plays a role analogous to spin.
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5
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Baumgartner C, Fuchs L, Costa A, Picó-Cortés J, Reinhardt S, Gronin S, Gardner GC, Lindemann T, Manfra MJ, Faria Junior PE, Kochan D, Fabian J, Paradiso N, Strunk C. Effect of Rashba and Dresselhaus spin-orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions. J Phys Condens Matter 2022; 34:154005. [PMID: 35051919 DOI: 10.1088/1361-648x/ac4d5e] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
Simultaneous breaking of inversion- and time-reversal symmetry in Josephson junction (JJ) leads to a possible violation of theI(φ) = -I(-φ) equality for the current-phase relation. This is known as anomalous Josephson effect and it produces a phase shiftφ0in sinusoidal current-phase relations. In ballistic JJs with non-sinusoidal current phase relation the observed phenomenology is much richer, including the supercurrent diode effect and the magnetochiral anisotropy (MCA) of Josephson inductance. In this work, we present measurements of both effects on arrays of JJs defined on epitaxial Al/InAs heterostructures. We show that the orientation of the current with respect to the lattice affects the MCA, possibly as the result of a finite Dresselhaus component. In addition, we show that the two-fold symmetry of the Josephson inductance reflects in the activation energy for phase slips.
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Affiliation(s)
- C Baumgartner
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - L Fuchs
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - A Costa
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - Jordi Picó-Cortés
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - S Reinhardt
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - S Gronin
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907 United States of America
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - G C Gardner
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907 United States of America
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - T Lindemann
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - M J Manfra
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907 United States of America
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907 United States of America
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907 United States of America
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - P E Faria Junior
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - D Kochan
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - J Fabian
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - N Paradiso
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - C Strunk
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
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Ye C, Xie X, Lv W, Huang K, Yang AJ, Jiang S, Liu X, Zhu D, Qiu X, Tong M, Zhou T, Hsu CH, Chang G, Lin H, Li P, Yang K, Wang Z, Jiang T, Renshaw Wang X. Nonreciprocal Transport in a Bilayer of MnBi 2Te 4 and Pt. Nano Lett 2022; 22:1366-1373. [PMID: 35073094 DOI: 10.1021/acs.nanolett.1c04756] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
MnBi2Te4 (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi2Te3 phase at the surface due to inevitable structural defects. Here, we report an observation of nonreciprocal transport, that is, current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the Néel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.
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Affiliation(s)
- Chen Ye
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
| | - Xiangnan Xie
- State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, P.R. China
| | - Wenxing Lv
- Physics Laboratory, Industrial Training Center, Shenzhen Polytechnic, Shenzhen, Guangdong 518055, P.R. China
| | - Ke Huang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
| | - Allen Jian Yang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
| | - Sicong Jiang
- Department of NanoEngineering and Program of Chemical Engineering, University of California San Diego, La Jolla, California 92093-0448, United States
- Program of Materials Science and Engineering, University of California San Diego, La Jolla, California 92093-0418, United States
| | - Xue Liu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
- Institutes of Physical Science and Information Technology, Anhui University, Hefei 230601, P.R. China
| | - Dapeng Zhu
- Fert Beijing Institute, MIIT Key Laboratory of Spintronics, School of Integrated Circuit Science and Engineering, Beihang University, Beijing 100191, P.R. China
- Beihang-Goertek Joint Microelectronics Institute, Qingdao Research Institute, Beihang University, Qingdao 266000, P.R. China
| | - Xuepeng Qiu
- Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology and School of Physics Science and Engineering, Tongji University, Shanghai 200092, P.R. China
| | - Mingyu Tong
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, P.R. China
| | - Tong Zhou
- State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, P.R. China
| | - Chuang-Han Hsu
- Insitute of Physics, Academia Sinica, Taipei 11529, Taiwan
| | - Guoqing Chang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
| | - Hsin Lin
- Insitute of Physics, Academia Sinica, Taipei 11529, Taiwan
| | - Peisen Li
- College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, P.R. China
| | - Kesong Yang
- Department of NanoEngineering and Program of Chemical Engineering, University of California San Diego, La Jolla, California 92093-0448, United States
- Program of Materials Science and Engineering, University of California San Diego, La Jolla, California 92093-0418, United States
| | - Zhenyu Wang
- State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, P.R. China
- National Innovation Institute of Defense Technology, Academy of Military Sciences PLA China, Beijing 100010, P.R. China
- Beijing Academy of Quantum Information Sciences, Beijing 100084, P.R. China
| | - Tian Jiang
- State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, P.R. China
- Beijing Institute for Advanced Study, National University of Defense Technology, Changsha 410073, P.R. China
| | - Xiao Renshaw Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link 637371, Singapore
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore
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7
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Lee JH, Harada T, Trier F, Marcano L, Godel F, Valencia S, Tsukazaki A, Bibes M. Nonreciprocal Transport in a Rashba Ferromagnet, Delafossite PdCoO 2. Nano Lett 2021; 21:8687-8692. [PMID: 34613718 DOI: 10.1021/acs.nanolett.1c02756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Rashba interfaces yield efficient spin-charge interconversion and give rise to nonreciprocal transport phenomena. Here, we report magnetotransport experiments in few-nanometer-thick films of PdCoO2, a delafossite oxide known to display a large Rashba splitting and surface ferromagnetism. By analyzing the angle dependence of the first- and second-harmonic longitudinal and transverse resistivities, we identify a Rashba-driven unidirectional magnetoresistance that competes with the anomalous Nernst effect below the Curie point. We estimate a Rashba coefficient of 0.75 ± 0.3 eV Å and argue that our results qualify delafossites as a new family of oxides for nanospintronics and spin-orbitronics, beyond perovskite materials.
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Affiliation(s)
- Jin Hong Lee
- Unité Mixte de Physique, CNRS, Thales, Université Paris Sud, Université Paris-Saclay, F-91767 Palaiseau, France
| | - Takayuki Harada
- MANA, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Felix Trier
- Department of Energy Conservation and Storage, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Lourdes Marcano
- Departamento Electricidad y Electrónica, Universidad del Paıs Vasco-UPV/EHU, 48940 Leioa, Spain
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Straße 15, 12489 Berlin, Germany
| | - Florian Godel
- Unité Mixte de Physique, CNRS, Thales, Université Paris Sud, Université Paris-Saclay, F-91767 Palaiseau, France
| | - Sergio Valencia
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Straße 15, 12489 Berlin, Germany
| | - Atsushi Tsukazaki
- Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
- Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan
| | - Manuel Bibes
- Unité Mixte de Physique, CNRS, Thales, Université Paris Sud, Université Paris-Saclay, F-91767 Palaiseau, France
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Liu Y, Holder T, Yan B. Chirality-Induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene. Innovation (N Y) 2021; 2:100085. [PMID: 33738460 PMCID: PMC7938422 DOI: 10.1016/j.xinn.2021.100085] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 01/18/2021] [Indexed: 11/27/2022] Open
Abstract
Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum-transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle, and reaches about 20% for an angle of 1.5° in a 10 T in-plane magnetic field. We propose the band structure topology (asymmetry), which leads to a direction-sensitive mean free path, as a useful way to anticipate the UMR effect. The UMR provides a probe for chirality and band flatness in the twisted bilayers. Twisted bilayer graphene (TBG) was recently discovered to exhibit fascinating phenomena like the superconductivity and Mott insulating state TBG's chirality leads to a unidirectional magnetoresistance (UMR), where magnetoresistance is lower in a chirality-dependent direction. The flat bands of TBG enhance the UMR dramatically The giant UMR represents diode-like current rectification and can convert radiation (e.g., terahertz) into currents for energy-harvesting and photodetection
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Affiliation(s)
- Yizhou Liu
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Tobias Holder
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Binghai Yan
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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