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基于一维电子体系的超导复合器件和量子输运研究

邓小松 张志勇 康宁

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基于一维电子体系的超导复合器件和量子输运研究

邓小松, 张志勇, 康宁
cstr: 32037.14.aps.74.20241672

Research on hybrid superconducting devices and quantum transport based on one-dimensional electronic systems

DENG Xiaosong, ZHANG Zhiyong, KANG Ning
cstr: 32037.14.aps.74.20241672
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  • 低维电子材料与超导材料的复合体系一直是研究介观输运和低维超导特性的重要平台, 其中具有强自旋轨道耦合效应的低维结构与超导宏观量子态结合呈现出丰富的量子现象, 为探索新物性和研制新型拓扑量子器件提供了一个理想的平台. 采用高质量的一维电子材料构筑超导复合器件, 探索受限量子体系与超导界面的量子输运现象和器件调控机制迅速成为研究的前沿和热点. 其中的关键问题在于理解纳米尺度下低维体系与超导界面的特征散射机制和量子输运过程, 研究电荷态与拓扑局域态的耦合机制, 实现对拓扑态本征输运特性的探测, 在此基础上为研制新型超导纳电子器件和拓扑量子器件探索新原理和新方法. 由于多种能量尺度和束缚态的竞争, 介观尺度下的超导复合结构在器件物理、结构设计以及测量方案上都存在前所未有的挑战. 本文回顾了基于一维电子体系的超导复合器件的近期进展, 聚焦在以半导体纳米线和碳纳米管为代表的实验体系, 简要介绍了从材料和器件物理, 到输运测量的主要现象和实验挑战. 最后本文对一维体系拓扑量子器件的研制和输运研究进行了总结和展望.
    The hybrid system of low-dimensional electronic materials and superconducting materials has always been an attractive structure for studying mesoscopic transport and low-dimensional superconducting properties. Low-dimensional structures with strong spin-orbit coupling exhibit rich quantum phenomena combined with superconducting macroscopic quantum states. Therefore it has become an important platform for exploring novel physical properties and developing new topological quantum devices. The construction of hybrid superconducting devices based on high-quality one-dimensional electronic materials and the exploration of interfacial quantum transport phenomena have become the research frontiers. It is crucial to understand the characteristic scattering mechanisms and quantum transport processes in these hybrid systems on a nanoscale. The study of the coupling mechanism between the charge state and the topological localized state, and the experimental probe of the intrinsic transport properties of the topological states are the key issues, which enable the development of the new principles and methods for novel superconducting nano electronic devices and topological quantum devices. Due to the competition of multiple energy scales and complex bound states in these hybrid structures, the device physics and measurement schemes are facing unprecedented challenges. This paper reviews recent research progress of hybrid superconducting devices based on one-dimensional electronic systems, focusing on the material systems based on semiconducting nanowires and carbon nanotubes. Semiconducting nanowires with strong spin-orbit coupling and large Landau g-factor are expected to support Majorana bound states, and further improvements are needed in the material quality, interface between superconductors and nanowires, understanding of the transport mechanism, and detection scheme. The construction strategies of extending topological phase space, including broken symmetry, helical modes, semiconducting characteristics, and attenuation of the external magnetic field, are proposed and discussed in hybrid superconducting devices based on carbon nanotubes. The main phenomena and experimental challenges, ranging from material to device physics, are introduced briefly. Finally, this paper summarizes and prospects the development and transport studies of topological quantum devices based on one-dimensional systems.
      通信作者: 张志勇, zyzhang@pku.edu.cn ; 康宁, nkang@pku.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12374035, 62225101)和科技创新2030-“量子通信与量子计算机”重大项目(批准号: 2021ZD0302600) 资助的课题.
      Corresponding author: ZHANG Zhiyong, zyzhang@pku.edu.cn ; KANG Ning, nkang@pku.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12374035, 62225101) and the Science and Technology Innovation 2030-“Quantum Communication and Quantum Computer”, China (Grant No. 2021ZD0302600).
    [1]

    Winkelmann C B, Roch N, Wernsdorfer W, Bouchiat V, Balestro F 2009 Nat. Phys. 5 876Google Scholar

    [2]

    De Franceschi S, Kouwenhoven L, Schönenberger C, Wernsdorfer W 2010 Nat. Nanotechnol. 5 703Google Scholar

    [3]

    Doh Y J, van Dam J A, Roest A L, Bakkers E P A M, Kouwenhoven L P, De Franceschi S 2005 Science 309 272Google Scholar

    [4]

    Jarillo-Herrero P, van Dam J A, Kouwenhoven L P 2006 Nature 439 953Google Scholar

    [5]

    Heersche H B, Jarillo-Herrero P, Oostinga J B, Vandersypen L M K, Morpurgo A F 2007 Nature 446 56Google Scholar

    [6]

    Qu F M, Yang F, Shen J, Ding Y, Chen J, Ji Z Q, Liu G T, Fan J, Jing X N, Yang C L, Lu L 2012 Sci. Rep. 2 339Google Scholar

    [7]

    Veldhorst M, Snelder M, Hoek M, Gang T, Guduru V K, Wang X L, Zeitler U, van der Wiel W G, Golubov A A, Hilgenkamp H, Brinkman A 2012 Nat. Mater. 11 417Google Scholar

    [8]

    Bockrath M, Cobden D H, Lu J, Rinzler A G, Smalley R E, Balents L, McEuen P L 1999 Nature 397 598Google Scholar

    [9]

    Deshpande V V, Chandra B, Caldwell R, Novikov D S, Hone J, Bockrath M 2009 Science 323 106Google Scholar

    [10]

    Deshpande V V, Bockrath M 2008 Nat. Phys. 4 314Google Scholar

    [11]

    Li S, Kang N, Caroff P, Xu H Q 2017 Phys. Rev. B 95 014515Google Scholar

    [12]

    Hensgens T, Fujita T, Janssen L, Li X, Van Diepen C J, Reichl C, Wegscheider W, Das Sarma S, Vandersypen L M K 2017 Nature 548 70Google Scholar

    [13]

    Xiang J, Vidan A, Tinkham M, Westervelt R M, Lieber C M 2006 Nat. Nanotechnol. 1 208Google Scholar

    [14]

    He J J, Tanaka Y, Nagaosa N 2023 Nat. Commun. 14 3330Google Scholar

    [15]

    Herrmann L G, Portier F, Roche P, Yeyati A L, Kontos T, Strunk C 2010 Phys. Rev. Lett. 104 026801Google Scholar

    [16]

    Kitaev A Y 2001 Physics-Uspekhi 44 131Google Scholar

    [17]

    Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083Google Scholar

    [18]

    Maeno Y, Ikeda A, Mattoni G 2024 Nat. Phys. 20 1712Google Scholar

    [19]

    Dutta B, Umansky V, Banerjee M, Heiblum M 2022 Science 377 1198Google Scholar

    [20]

    Fu L,, Kane C L 2008 Phys. Rev. Lett. 100 096407Google Scholar

    [21]

    Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003Google Scholar

    [22]

    Yang F, Ding Y, Qu F M, Shen J, Chen J, Wei Z C, Ji Z Q, Liu G T, Fan J, Yang C L, Xiang T, Lu L 2012 Phys. Rev. B 85 104508Google Scholar

    [23]

    Wang D F, Kong L Y, Fan P, Chen H, Zhu S Y, Liu W Y, Cao L, Sun Y J, Du S X, Schneeloch J, Zhong R D, Gu G D, Fu L, Ding H, Gao H J 2018 Science 362 333Google Scholar

    [24]

    徐磊, 李沛岭, 吕昭征, 沈洁, 屈凡明, 刘广同, 吕力 2023 物理学报 72 177401Google Scholar

    Xu L, Li P L, Lü Z Z, Shen J, Qu F M, Liu G T, Lü L 2023 Acta Phys. Sin. 72 177401Google Scholar

    [25]

    初纯光, 王安琦, 廖志敏 2023 物理学报 72 087401Google Scholar

    Chu C G, Wang A Q, Liao Z M 2023 Acta Phys. Sin. 72 087401Google Scholar

    [26]

    Qi J J, Chen C Z, Song J T, Liu J, He K, Sun Q F, Xie X C 2025 Sci. China Phys. Mech. Astron. 68 227401Google Scholar

    [27]

    吕博赛, 娄硕, 沈沛约, 史志文 2024 物理 53 683Google Scholar

    Lü B S, Lou S, Shen P Y, Shi Z W 2024 Physics 53 683Google Scholar

    [28]

    Yazdani A, von Oppen F, Halperin B I, Yacoby A 2023 Science 380 eade0850Google Scholar

    [29]

    Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001Google Scholar

    [30]

    Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002Google Scholar

    [31]

    Lutchyn R M, Bakkers E P A M, Kouwenhoven L P, Krogstrup P, Marcus C M, Oreg Y 2018 Nat. Rev. Mater. 3 52Google Scholar

    [32]

    Dmytruk O, Klinovaja J 2018 Phys. Rev. B 97 155409Google Scholar

    [33]

    Nichele F, Chesi S, Hennel S, Wittmann A, Gerl C, Wegscheider W, Loss D, Ihn T, Ensslin K 2014 Phys. Rev. Lett. 113 046801Google Scholar

    [34]

    Miserev D S, Srinivasan A, Tkachenko O A, Tkachenko V A, Farrer I, Ritchie D A, Hamilton A R, Sushkov O P 2017 Phys. Rev. Lett. 119 116803Google Scholar

    [35]

    Nilsson H A, Caroff P, Thelander C, Larsson M, Wagner J B, Wernersson L E, Samuelson L, Xu H Q 2009 Nano Lett. 9 3151Google Scholar

    [36]

    Fasth C, Fuhrer A, Samuelson L, Golovach V N, Loss D 2007 Phys. Rev. Lett. 98 266801Google Scholar

    [37]

    Pribiag V S, Nadj-Perge S, Frolov S M, van den Berg J W G, van Weperen I, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2013 Nat. Nanotechnol. 8 170Google Scholar

    [38]

    Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887Google Scholar

    [39]

    Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414Google Scholar

    [40]

    Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A, Yazdani A 2014 Science 346 602Google Scholar

    [41]

    Sasaki S, Kriener M, Segawa K, Yada K, Tanaka Y, Sato M, Ando Y 2011 Phys. Rev. Lett. 107 217001Google Scholar

    [42]

    Fornieri A, Whiticar A M, Setiawan F, et al. 2019 Nature 569 89Google Scholar

    [43]

    Sun H H, Zhang K W, Hu L H, et al. 2016 Phys. Rev. Lett. 116 257003Google Scholar

    [44]

    Prada E, San-Jose P, de Moor M W A, Geresdi A, Lee E J H, Klinovaja J, Loss D, Nygård J, Aguado R, Kouwenhoven L P 2020 Nat. Rev. Phys. 2 575Google Scholar

    [45]

    Li S, Kang N, Fan D X, Wang L B, Huang Y Q, Caroff P, Xu H Q 2016 Sci. Rep. 6 24822Google Scholar

    [46]

    Plissard S R, van Weperen I, Car D, et al. 2013 Nat. Nanotechnol. 8 859Google Scholar

    [47]

    He J B, Pan D, Yang G, Liu M L, Ying J H, Lyu Z Z, Fan J, Jing X N, Liu G T, Lu B, Liu D E, Zhao J H, Lu L, Qu F M 2020 Phys. Rev. B 102 075121Google Scholar

    [48]

    Luthi F, Stavenga T, Enzing O W, Bruno A, Dickel C, Langford N K, Rol M A, Jespersen T S, Nygård J, Krogstrup P, DiCarlo L 2018 Phys. Rev. Lett. 120 100502Google Scholar

    [49]

    Hays M, Fatemi V, Bouman D, Cerrillo J, Diamond S, Serniak K, Connolly T, Krogstrup P, Nygård J, Levy Yeyati A, Geresdi A, Devoret M H 2021 Science 373 430Google Scholar

    [50]

    Thomas C, Hatke A T, Tuaz A, Kallaher R, Wu T, Wang T, Diaz R E, Gardner G C, Capano M A, Manfra M J 2018 Phys. Rev. Mater. 2 104602Google Scholar

    [51]

    Lee J S, Shojaei B, Pendharkar M, Feldman M, Mukherjee K, Palmstrøm C J 2019 Phys. Rev. Mater. 3 014603Google Scholar

    [52]

    Lei Z, Lehner C A, Cheah E, Karalic M, Mittag C, Alt L, Scharnetzky J, Wegscheider W, Ihn T, Ensslin K 2019 Appl. Phys. Lett. 115 012101Google Scholar

    [53]

    Mittag C, Karalic M, Lei Z, Thomas C, Tuaz A, Hatke A T, Gardner G C, Manfra M J, Ihn T, Ensslin K 2019 Phys. Rev. B 100 075422Google Scholar

    [54]

    Aghaee M, Akkala A, Alam Z, et al. (Microsoft Quantum) 2023 Phys. Rev. B 107 245423Google Scholar

    [55]

    Krogstrup P, Ziino N L B, Chang W, Albrecht S M, Madsen M H, Johnson E, Nygård J, Marcus C M, Jespersen T S 2015 Nat. Mater. 14 400Google Scholar

    [56]

    Vaitiekėnas S, Krogstrup P, Marcus C M 2020 Phys. Rev. B 101 060507Google Scholar

    [57]

    Deng M T, Vaitiekėnas S, Hansen E B, Danon J, Leijnse M, Flensberg K, Nygård J, Krogstrup P, Marcus C M 2016 Science 354 1557Google Scholar

    [58]

    Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Marcus C M 2016 Nature 531 206Google Scholar

    [59]

    Albrecht S M, Hansen E B, Higginbotham A P, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Danon J, Flensberg K, Marcus C M 2017 Phys. Rev. Lett. 118 137701Google Scholar

    [60]

    Bordin A, Wang G, Liu C X, ten Haaf S L D, van Loo N, Mazur G P, Xu D, van Driel D, Zatelli F, Gazibegovic S, Badawy G, Bakkers E P A M, Wimmer M, Kouwenhoven L P, Dvir T 2023 Phys. Rev. X 13 031031Google Scholar

    [61]

    Mazur G P, van Loo N, van Driel D, Wang J Y, Badawy G, Gazibegovic S, Bakkers E P A M, Kouwenhoven L P 2024 Phys. Rev. Appl. 22 054034Google Scholar

    [62]

    Pendharkar M, Zhang B, Wu H, et al. 2021 Science 372 508Google Scholar

    [63]

    Kanne T, Marnauza M, Olsteins D, Carrad D J, Sestoft J E, de Bruijckere J, Zeng L, Johnson E, Olsson E, Grove-Rasmussen K, Nygård J 2021 Nat. Nanotechnol. 16 776Google Scholar

    [64]

    Vaitiekėnas S, Liu Y, Krogstrup P, Marcus C M 2021 Nat. Phys. 17 43Google Scholar

    [65]

    Liu Y, Vaitiekėnas S, Martí-Sánchez S, et al. 2020 Nano Lett. 20 456Google Scholar

    [66]

    Vaitiekėnas S, Winkler G W, van Heck B, Karzig T, Deng M T, Flensberg K, Glazman L I, Nayak C, Krogstrup P, Lutchyn R M, Marcus C M 2020 Science 367 6485Google Scholar

    [67]

    Valentini M, Peñaranda F, Hofmann A, Brauns M, Hauschild R, Krogstrup P, San-Jose P, Prada E, Aguado R, Katsaros G 2021 Science 373 82Google Scholar

    [68]

    Woods B D, Das Sarma S, Stanescu T D 2019 Phys. Rev. B 99 161118Google Scholar

    [69]

    San-Jose P, Payá C, Marcus C M, Vaitiekėnas S, Prada E 2023 Phys. Rev. B 107 155423Google Scholar

    [70]

    San-Jose P, Prada E, Aguado R 2012 Phys. Rev. Lett. 108 257001Google Scholar

    [71]

    Legg H F, Laubscher K, Loss D, Klinovaja J 2023 Phys. Rev. B 108 214520Google Scholar

    [72]

    Wimmer M, Akhmerov A R, Dahlhaus J P, Beenakker C W J 2011 New J. Phys. 13 053016Google Scholar

    [73]

    Danon J, Hellenes A B, Hansen E B, Casparis L, Higginbotham A P, Flensberg K 2020 Phys. Rev. Lett. 124 036801Google Scholar

    [74]

    Pikulin D I, van Heck B, Karzig T, Martinez E A, Nijholt B, Laeven T, Winkler G W, Watson J D, Heedt S, Temurhan M, Svidenko V, Lutchyn R M, Thomas M, de Lange G, Casparis L, Nayak C 2021 arXiv: 2103. 12217 [cond-mat.mes-hall]

    [75]

    Hess R, Legg H F, Loss D, Klinovaja J 2023 Phys. Rev. Lett. 130 207001Google Scholar

    [76]

    Rosdahl T Ö, Vuik A, Kjaergaard M, Akhmerov A R 2018 Phys. Rev. B 97 045421Google Scholar

    [77]

    Banerjee A, Lesser O, Rahman M A, Thomas C, Wang T, Manfra M J, Berg E, Oreg Y, Stern A, Marcus C M 2023 Phys. Rev. Lett. 130 096202Google Scholar

    [78]

    Pan H, Sau J D, Das Sarma S 2021 Phys. Rev. B 103 014513Google Scholar

    [79]

    Tsintzis A, Souto R S, Flensberg K, Danon J, Leijnse M 2024 PRX Quantum 5 010323Google Scholar

    [80]

    Leijnse M, Flensberg K 2012 Phys. Rev. B 86 134528Google Scholar

    [81]

    Dvir T, Wang G, van Loo N, Liu C X, Mazur G P, Bordin A, ten Haaf S L D, Wang J Y, van Driel D, Zatelli F, Li X, Malinowski F K, Gazibegovic S, Badawy G, Bakkers E P A M, Wimmer M, Kouwenhoven L P 2023 Nature 614 445Google Scholar

    [82]

    Bordin A, Li X, van Driel D, Wolff J C, Wang Q, ten Haaf S L D, Wang G, van Loo N, Kouwenhoven L P, Dvir T 2024 Phys. Rev. Lett. 132 056602Google Scholar

    [83]

    Laird E A, Kuemmeth F, Steele G A, Grove-Rasmussen K, Nygård J, Flensberg K, Kouwenhoven L P 2015 Rev. Mod. Phys. 87 703Google Scholar

    [84]

    Minot E D, Yaish Y, Sazonova V, Park J Y, Brink M, McEuen P L 2003 Phys. Rev. Lett. 90 156401Google Scholar

    [85]

    Minot E D, Yaish Y, Sazonova V, McEuen P L 2004 Nature 428 536Google Scholar

    [86]

    Jhang S H, Marganska M, Skourski Y, Preusche D, Grifoni M, Wosnitza J, Strunk C 2011 Phys. Rev. Lett. 106 096802Google Scholar

    [87]

    Deng X S, Gong K, Wang Y, Liu Z, Jiang K L, Kang N, Zhang Z Y 2023 Phys. Rev. Lett. 130 207002Google Scholar

    [88]

    Jin Z, Chu H B, Wang J Y, Hong J X, Tan W C, Li Y 2007 Nano Lett. 7 2073Google Scholar

    [89]

    Wang X S, Li Q Q, Xie J, Jin Z, Wang J Y, Li Y, Jiang K L, Fan S S 2009 Nano Lett. 9 3137Google Scholar

    [90]

    Kong J, Yenilmez E, Tombler T W, Kim W, Dai H J, Laughlin R B, Liu L, Jayanthi C S, Wu S Y 2001 Phys. Rev. Lett. 87 106801Google Scholar

    [91]

    Liang W J, Bockrath M, Bozovic D, Hafner J H, Tinkham M, Park H 2001 Nature 411 665Google Scholar

    [92]

    Javey A, Guo J, Wang Q, Lundstrom M, Dai H J 2003 Nature 424 654Google Scholar

    [93]

    Zhang Z Y, Liang X L, Wang S, Yao K, Hu Y F, Zhu Y Z, Chen Q, Zhou W W, Li Y, Yao Y G, Zhang J, Peng L M 2007 Nano Lett. 7 3603Google Scholar

    [94]

    Urgell C, Yang W, De Bonis S L, Samanta C, Esplandiu M J, Dong Q, Jin Y, Bachtold A 2020 Nat. Phys. 16 32Google Scholar

    [95]

    Wen Y, Ares N, Schupp F J, Pei T, Briggs G A D, Laird E A 2020 Nat. Phys. 16 75Google Scholar

    [96]

    Wang S, Zhao S H, Shi Z W, Wu F Q, Zhao Z Y, Jiang L L, Watanabe K, Taniguchi T, Zettl A, Zhou C W, Wang F 2020 Nat. Mater. 19 986Google Scholar

    [97]

    Wu C C, Liu C H, Zhong Z H 2010 Nano Lett. 10 1032Google Scholar

    [98]

    Pei F, Laird E A, Steele G A, Kouwenhoven L P 2012 Nat. Nanotechnol. 7 630Google Scholar

    [99]

    Zhang R F, Ning Z Y, Zhang Y Y, Xie H H, Zhang Q, Qian W Z, Chen Q, Wei F 2013 Nanoscale 5 6584Google Scholar

    [100]

    Zhang R F, Ning Z Y, Zhang Y Y, Zheng Q S, Chen Q, Xie H H, Zhang Q, Qian W Z, Wei F 2013 Nat. Nanotechnol. 8 912Google Scholar

    [101]

    Zhang R F, Zhang Y Y, Zhang Q, Xie H H, Wang H D, Nie J Q, Wen Q, Wei F 2013 Nat. Commun. 4 1727Google Scholar

    [102]

    Shen B Y, Zhu Z X, Zhang J Y, Xie H H, Bai Y X, Wei F 2018 Adv. Mater. 30 1705844Google Scholar

    [103]

    Kasumov A Y, Deblock R, Kociak M, Reulet B, Bouchiat H, Khodos I I, Gorbatov Y B, Volkov V T, Journet C, Burghard M 1999 Science 284 1508Google Scholar

    [104]

    Mergenthaler M, Schupp F J, Nersisyan A, Ares N, Baumgartner A, Schönenberger C, Briggs G A D, Leek P J, Laird E A 2021 Mater. Quantum. Technol. 1 035003Google Scholar

    [105]

    Bauml C, Bauriedl L, Marganska M, Grifoni M, Strunk C, Paradiso N 2021 Nano Lett. 21 8627Google Scholar

    [106]

    Sau J D, Tewari S 2013 Phys. Rev. B 88 054503Google Scholar

    [107]

    Huertas-Hernando D, Guinea F, Brataas A 2006 Phys. Rev. B 74 155426Google Scholar

    [108]

    Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H 2006 Phys. Rev. B 74 165310Google Scholar

    [109]

    Kuemmeth F, Ilani S, Ralph D C, McEuen P L 2008 Nature 452 448Google Scholar

    [110]

    Marganska M, Milz L, Izumida W, Strunk C, Grifoni M 2018 Phys. Rev. B 97 075141Google Scholar

    [111]

    Milz L, Izumida W, Grifoni M, Marganska M 2019 Phys. Rev. B 100 155417Google Scholar

    [112]

    Zhou B T, Yuan N F Q, Jiang H L, Law K T 2016 Phys. Rev. B 93 180501Google Scholar

    [113]

    Xi X X, Wang Z F, Zhao W W, Park J H, Law K T, Berger H, Forro L, Shan J, Mak K F 2016 Nat. Phys. 12 139Google Scholar

    [114]

    Saito Y, Nakamura Y, Bahramy M S, Kohama Y, Ye J T, Kasahara Y, Nakagawa Y, Onga M, Tokunaga M, Nojima T, Yanase Y, Iwasa Y 2016 Nat. Phys. 12 144Google Scholar

    [115]

    Lu J M, Zheliuk O, Leermakers I, Yuan N F Q, Zeitler U, Law K T, Ye J T 2015 Science 350 1353Google Scholar

    [116]

    Ye J T, Zhang Y J, Akashi R, Bahramy M S, Arita R, Iwasa Y 2012 Science 338 1193Google Scholar

    [117]

    de la Barrera S C, Sinko M R, Gopalan D P, Sivadas N, Seyler K L, Watanabe K, Taniguchi T, Tsen A W, Xu X D, Xiao D, Hunt B M 2018 Nat. Commun. 9 1427Google Scholar

    [118]

    Fatemi V, Wu S F, Cao Y, Bretheau L, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 362 926Google Scholar

    [119]

    Lesser O, Shavit G, Oreg Y 2020 Phys. Rev. Res. 2 023254Google Scholar

    [120]

    Han T Y, Shen J Y, Yuan N F Q, Lin J X Z, Wu Z F, Wu Y Y, Xu S G, An L H, Long G, Wang Y W, Lortz R, Wang N 2018 Phys. Rev. B 97 060505Google Scholar

    [121]

    Kim M, Park G H, Lee J, Lee J H, Park J, Lee H, Lee G H, Lee H J 2017 Nano Lett. 17 6125Google Scholar

    [122]

    Klinovaja J, Gangadharaiah S, Loss D 2012 Phys. Rev. Lett. 108 196804Google Scholar

    [123]

    Klinovaja J, Schmidt M J, Braunecker B, Loss D 2011 Phys. Rev. Lett. 106 156809Google Scholar

    [124]

    Klinovaja J, Schmidt M J, Braunecker B, Loss D 2011 Phys. Rev. B 84 085452Google Scholar

    [125]

    Egger R, Flensberg K 2012 Phys. Rev. B 85 235462Google Scholar

    [126]

    Murra P, Inotani D, Nitta M 2022 Phys. Rev. B 105 214525Google Scholar

    [127]

    Desjardins M M, Contamin L C, Delbecq M R, et al. 2019 Nat. Mater. 18 1060Google Scholar

    [128]

    Klinovaja J, Stano P, Loss D 2012 Phys. Rev. Lett. 109 236801Google Scholar

    [129]

    Klinovaja J, Stano P, Yazdani A, Loss D 2013 Phys. Rev. Lett. 111 186805Google Scholar

    [130]

    Kjaergaard M, Wolms K, Flensberg K 2012 Phys. Rev. B 85 020503Google Scholar

    [131]

    Klinovaja J, Loss D 2013 Phys. Rev. X 3 011008Google Scholar

    [132]

    Cottet A, Kontos T, Doucot B 2013 Phys. Rev. B 88 195415Google Scholar

    [133]

    van Woerkom D J, Proutski A, van Heck B, Bouman D, Vayrynen J I, Glazman L I, Krogstrup P, Nygard J, Kouwenhoven L P, Geresdi A 2017 Nat. Phys. 13 876Google Scholar

    [134]

    Vayrynen J I, Rastelli G, Belzig W, Glazman L I 2015 Phys. Rev. B 92 134508Google Scholar

    [135]

    Dartiailh M C, Kontos T, Doucot B, Cottet A 2017 Phys. Rev. Lett. 118 126803Google Scholar

    [136]

    Mergenthaler M, Nersisyan A, Patterson A, Esposito M, Baumgartner A, Schönenberger C, Briggs G A D, Laird E A, Leek P J 2021 Phys. Rev. Appl. 15 064050Google Scholar

    [137]

    Fatin G L, Matos-Abiague A, Scharf B, Zutic I 2016 Phys. Rev. Lett. 117 077002Google Scholar

    [138]

    Liu L J, Han J, Xu L, Zhou J S, Zhao C Y, Ding S J, Shi H W, Xiao M M, Ding L, Ma Z, Jin C H, Zhang Z Y, Peng L M 2020 Science 368 850Google Scholar

    [139]

    Mukhopadhyay R, Kane C L, Lubensky T C 2001 Phys. Rev. B 64 045120Google Scholar

  • 图 1  半导体纳米线与超导材料复合构筑拓扑量子器件 (a) 具有强自旋轨道耦合的一维体系在磁场下的色散关系, 体系中强自旋轨道耦合效应的存在使能带在k空间发生劈裂, 对应每个动量k都有确定的自旋方向[29]; (b) 复合体系中随化学势和磁场演化的电子相图, 在临界磁场之上, 磁场驱动体系发生拓扑超导相的相变[32]

    Fig. 1.  Topological devices based on the hybrid superconductor-semiconductor nanowire structures: (a) Electronic dispersion of an one-dimensional quantum wire with strong spin-orbit coupling under applied magnetic field[29], the presence of spin-orbit coupling results in the lifting of spin degeneracy; (b) the phase diagram for a proximitized semiconducting nanowire device as a function of the magnetic field and chemical potential, the interplay of spin-orbit coupling, Zeeman fields can drive a quantum phase transition into a topological superconductivity[32].

    图 2  构筑基于纳米线的量子点和超导干涉器件[11] (a) 基于单根InSb纳米线的器件SEM照片; (b) 纳米线复合器件中的安德列也夫束缚态能谱; (c)实现了复合器件中不同基态的栅极调控, 观察到0相与π相交替出现的安德列也夫束缚态

    Fig. 2.  The realization of the nanowire quantum dot-superconducting quantum interference device[11]: (a) SEM image of a typical device, showing that individual InSb nanowire is in contact with superconducting electrodes; (b) differential conductance ${\mathrm{d}}I/{\mathrm{d}}V$ map for the odd charge state as function of voltage bias $V_{{\mathrm{sd}}}$ and backgate voltage $V_{{\mathrm{g}}}$, indicating an Andreev bound state formed; (c) differential conductance ${\mathrm{d}}I/{\mathrm{d}}V$ plot as a function of $V_{{\mathrm{sd}}}$ and $V_{{\mathrm{g}}}$ at 10 mK and zero magnetic field, demonstrating a realization of continuous gate-tunable Andreev bound states with both 0-type levels and π-type levels.

    图 3  拓扑态的固态量子器件构筑和探测 (a) 基于强自旋轨道耦合的二维电子气构筑超导界面和量子点接触的复合结构器件, 在磁场驱动下在拓扑相区域, 电导出现半整数的量子化平台[72]; (b) 三端非局域测量方案的器件构型, 用于区分安德列也夫和马约拉纳束缚态[73]; (c) 基于半导体纳米线与超导电极构筑耦合量子点的Kitaev链器件结构[82], 实验通过栅极实现对交叉安德列也夫反射和弹性共隧穿过程的精确调控[81]

    Fig. 3.  Construction and detection of topological solid-state quantum devices: (a) The conductance of a quantum point contact placed between superconductor and semiconducting wire with spin-orbit coupling[72]; (b) three-terminal setup for probing Andreev and Majorana bound states with nonlocal measurement of conductance[73]; (c) top panel: false color SEM microscopy of a fabricated nanowire device showing the realization of the Kitaev chain with coupled quantum dots through superconductor[82]. Illustration of the realization of the Kitaev chain with coupled quantum dots through superconductor, in which the coupling strength of crossed Andreev reflection and elastic co-tunnelling can be gate-tunable[81].

    图 4  单壁碳纳米管的能带结构与可调控性 (a) 碳纳米管卷曲矢量决定的金属型和半导体型碳纳米管能带结构[83]; (b) 基于碳纳米管的分离静电栅构筑的原位可控PN结结构[87]; (c) 碳纳米管中随内建电场增加而逐渐降低的磁导拐点, 表明电场和磁场对碳纳米管能带结构的控制; 插图为非单调磁导的温度依赖特性, 验证了磁导响应的机制[87]

    Fig. 4.  Tunability of electronic band structure in single-wall carbon nanotubes: (a) Band structures of metallic and semiconducting carbon nanotubes determined by the chiral vector[83]; (b) in situ controllable PN junction structure based on split gates of carbon nanotubes[87]; (c) the magnetoconductance peaks move towards lower magnetic fields with increasing built-in electric fields in a carbon nanotube, demonstrating the control of the band structure of carbon nanotubes by electric and magnetic fields; inset: temperature dependence of nonmonotonic magnetoconductance, suggesting the mechanism of the magnetic response[87].

    图 5  半导体型碳纳米管-超导薄膜异质结的拓扑态构建方案[110] (a) 半导体型碳纳米管-超导体异质结器件示意图, 在面内横向磁场下诱导出马约拉纳束缚态; (b) 马约拉纳束缚态能谱和局域波函数在磁场下的演化, 表明碳纳米管两端处磁场诱导的马约拉纳束缚态

    Fig. 5.  Topological state scheme based on semiconducting carbon nanotubes-superconducting films heterojunction[110]: (a) Schematic diagram of a semiconducting carbon nanotube-superconductor heterojunction device, where Majorana bound states can be induced by in-plane transverse magnetic field; (b) Majorana bound states spectrum and wave function as a function of magnetic field, demonstrating the Majorana bound states in the ends of carbon nanotube induced by magnetic field.

    图 6  碳纳米管-TMD超导体异质结的拓扑态构建方案 (a) 碳纳米管-TMD超导体异质结器件示意图, 在轴向磁场和横向电场下诱导出马约拉纳束缚态[119]; (b) 自旋轨道耦合、磁通效应、横向电场和伊辛近邻效应导致的半金属态碳纳米管; (c) 磁通和化学势的拓扑相图, –1表示拓扑相[119]; (d) 电子-电子相互作用诱导的无磁场拓扑相图[119]; (e) 碳纳米管-薄层NbSe2近邻下的超导电流和相滑移[105]

    Fig. 6.  Topological state scheme based on semiconducting carbon nanotubes-TMD superconductors heterojunction: (a) Schematic diagram of a carbon nanotube-TMD superconductor heterojunction device, where Majorana bound states can be arised by axial magnetic field and transverse electric field[119]; (b) semi-metallic carbon nanotubes induced by spin-orbit coupling, magnetic flux effect, transverse electric field and Ising proximity effect[119]; (c) topological phase diagram of magnetic flux and chemical potential, where –1 denotes topological phase[119]; (d) topological phase diagram induced by electron-electron interaction without magnetic field[119]; (e) supercurrent and phase slip in a carbon nanotube with thin NbSe2 proximity[105].

    图 7  碳纳米管-超导体异质结的拓扑态电场构建方案 (a) 碳纳米管-超导体异质结器件示意图, 在横向电场下诱导出马约拉纳束缚态; (b) 低电场下, 只有一个能带分支形成p波配对; (c) 高电场下, 两个能带分支都形成p波配对[122]

    Fig. 7.  Topological state scheme based on carbon nanotubes-superconductors heterojunction with electric field: (a) Schematic diagram of a carbon nanotube-superconductor heterojunction device, where Majorana bound states can be induced by strong transverse electric field; (b) one branch is in the p-wave phase at low electric field; (c) both branches are in the p-wave phase at high electric field[122].

    图 8  基于周期性空间分布的化学势和磁场的一维拓扑器件构建方案[126] (a) 通过静电栅极阵列在一维体系中实现周期性化学势的调控; (b)通过纳米尺度磁体阵列或本征磁畴结构诱导产生周期性磁场

    Fig. 8.  Topological device scheme based on periodically and spatially modulated chemical potential and magnetic fields[126]: (a) Periodically modulated chemical potentials induced by electrostatic gate arrays; (b) periodically modulated magnetic field induced by nanomagnetic arrays or intrinsic domain structure in magnetic substrates.

  • [1]

    Winkelmann C B, Roch N, Wernsdorfer W, Bouchiat V, Balestro F 2009 Nat. Phys. 5 876Google Scholar

    [2]

    De Franceschi S, Kouwenhoven L, Schönenberger C, Wernsdorfer W 2010 Nat. Nanotechnol. 5 703Google Scholar

    [3]

    Doh Y J, van Dam J A, Roest A L, Bakkers E P A M, Kouwenhoven L P, De Franceschi S 2005 Science 309 272Google Scholar

    [4]

    Jarillo-Herrero P, van Dam J A, Kouwenhoven L P 2006 Nature 439 953Google Scholar

    [5]

    Heersche H B, Jarillo-Herrero P, Oostinga J B, Vandersypen L M K, Morpurgo A F 2007 Nature 446 56Google Scholar

    [6]

    Qu F M, Yang F, Shen J, Ding Y, Chen J, Ji Z Q, Liu G T, Fan J, Jing X N, Yang C L, Lu L 2012 Sci. Rep. 2 339Google Scholar

    [7]

    Veldhorst M, Snelder M, Hoek M, Gang T, Guduru V K, Wang X L, Zeitler U, van der Wiel W G, Golubov A A, Hilgenkamp H, Brinkman A 2012 Nat. Mater. 11 417Google Scholar

    [8]

    Bockrath M, Cobden D H, Lu J, Rinzler A G, Smalley R E, Balents L, McEuen P L 1999 Nature 397 598Google Scholar

    [9]

    Deshpande V V, Chandra B, Caldwell R, Novikov D S, Hone J, Bockrath M 2009 Science 323 106Google Scholar

    [10]

    Deshpande V V, Bockrath M 2008 Nat. Phys. 4 314Google Scholar

    [11]

    Li S, Kang N, Caroff P, Xu H Q 2017 Phys. Rev. B 95 014515Google Scholar

    [12]

    Hensgens T, Fujita T, Janssen L, Li X, Van Diepen C J, Reichl C, Wegscheider W, Das Sarma S, Vandersypen L M K 2017 Nature 548 70Google Scholar

    [13]

    Xiang J, Vidan A, Tinkham M, Westervelt R M, Lieber C M 2006 Nat. Nanotechnol. 1 208Google Scholar

    [14]

    He J J, Tanaka Y, Nagaosa N 2023 Nat. Commun. 14 3330Google Scholar

    [15]

    Herrmann L G, Portier F, Roche P, Yeyati A L, Kontos T, Strunk C 2010 Phys. Rev. Lett. 104 026801Google Scholar

    [16]

    Kitaev A Y 2001 Physics-Uspekhi 44 131Google Scholar

    [17]

    Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083Google Scholar

    [18]

    Maeno Y, Ikeda A, Mattoni G 2024 Nat. Phys. 20 1712Google Scholar

    [19]

    Dutta B, Umansky V, Banerjee M, Heiblum M 2022 Science 377 1198Google Scholar

    [20]

    Fu L,, Kane C L 2008 Phys. Rev. Lett. 100 096407Google Scholar

    [21]

    Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003Google Scholar

    [22]

    Yang F, Ding Y, Qu F M, Shen J, Chen J, Wei Z C, Ji Z Q, Liu G T, Fan J, Yang C L, Xiang T, Lu L 2012 Phys. Rev. B 85 104508Google Scholar

    [23]

    Wang D F, Kong L Y, Fan P, Chen H, Zhu S Y, Liu W Y, Cao L, Sun Y J, Du S X, Schneeloch J, Zhong R D, Gu G D, Fu L, Ding H, Gao H J 2018 Science 362 333Google Scholar

    [24]

    徐磊, 李沛岭, 吕昭征, 沈洁, 屈凡明, 刘广同, 吕力 2023 物理学报 72 177401Google Scholar

    Xu L, Li P L, Lü Z Z, Shen J, Qu F M, Liu G T, Lü L 2023 Acta Phys. Sin. 72 177401Google Scholar

    [25]

    初纯光, 王安琦, 廖志敏 2023 物理学报 72 087401Google Scholar

    Chu C G, Wang A Q, Liao Z M 2023 Acta Phys. Sin. 72 087401Google Scholar

    [26]

    Qi J J, Chen C Z, Song J T, Liu J, He K, Sun Q F, Xie X C 2025 Sci. China Phys. Mech. Astron. 68 227401Google Scholar

    [27]

    吕博赛, 娄硕, 沈沛约, 史志文 2024 物理 53 683Google Scholar

    Lü B S, Lou S, Shen P Y, Shi Z W 2024 Physics 53 683Google Scholar

    [28]

    Yazdani A, von Oppen F, Halperin B I, Yacoby A 2023 Science 380 eade0850Google Scholar

    [29]

    Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001Google Scholar

    [30]

    Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002Google Scholar

    [31]

    Lutchyn R M, Bakkers E P A M, Kouwenhoven L P, Krogstrup P, Marcus C M, Oreg Y 2018 Nat. Rev. Mater. 3 52Google Scholar

    [32]

    Dmytruk O, Klinovaja J 2018 Phys. Rev. B 97 155409Google Scholar

    [33]

    Nichele F, Chesi S, Hennel S, Wittmann A, Gerl C, Wegscheider W, Loss D, Ihn T, Ensslin K 2014 Phys. Rev. Lett. 113 046801Google Scholar

    [34]

    Miserev D S, Srinivasan A, Tkachenko O A, Tkachenko V A, Farrer I, Ritchie D A, Hamilton A R, Sushkov O P 2017 Phys. Rev. Lett. 119 116803Google Scholar

    [35]

    Nilsson H A, Caroff P, Thelander C, Larsson M, Wagner J B, Wernersson L E, Samuelson L, Xu H Q 2009 Nano Lett. 9 3151Google Scholar

    [36]

    Fasth C, Fuhrer A, Samuelson L, Golovach V N, Loss D 2007 Phys. Rev. Lett. 98 266801Google Scholar

    [37]

    Pribiag V S, Nadj-Perge S, Frolov S M, van den Berg J W G, van Weperen I, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2013 Nat. Nanotechnol. 8 170Google Scholar

    [38]

    Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887Google Scholar

    [39]

    Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414Google Scholar

    [40]

    Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A, Yazdani A 2014 Science 346 602Google Scholar

    [41]

    Sasaki S, Kriener M, Segawa K, Yada K, Tanaka Y, Sato M, Ando Y 2011 Phys. Rev. Lett. 107 217001Google Scholar

    [42]

    Fornieri A, Whiticar A M, Setiawan F, et al. 2019 Nature 569 89Google Scholar

    [43]

    Sun H H, Zhang K W, Hu L H, et al. 2016 Phys. Rev. Lett. 116 257003Google Scholar

    [44]

    Prada E, San-Jose P, de Moor M W A, Geresdi A, Lee E J H, Klinovaja J, Loss D, Nygård J, Aguado R, Kouwenhoven L P 2020 Nat. Rev. Phys. 2 575Google Scholar

    [45]

    Li S, Kang N, Fan D X, Wang L B, Huang Y Q, Caroff P, Xu H Q 2016 Sci. Rep. 6 24822Google Scholar

    [46]

    Plissard S R, van Weperen I, Car D, et al. 2013 Nat. Nanotechnol. 8 859Google Scholar

    [47]

    He J B, Pan D, Yang G, Liu M L, Ying J H, Lyu Z Z, Fan J, Jing X N, Liu G T, Lu B, Liu D E, Zhao J H, Lu L, Qu F M 2020 Phys. Rev. B 102 075121Google Scholar

    [48]

    Luthi F, Stavenga T, Enzing O W, Bruno A, Dickel C, Langford N K, Rol M A, Jespersen T S, Nygård J, Krogstrup P, DiCarlo L 2018 Phys. Rev. Lett. 120 100502Google Scholar

    [49]

    Hays M, Fatemi V, Bouman D, Cerrillo J, Diamond S, Serniak K, Connolly T, Krogstrup P, Nygård J, Levy Yeyati A, Geresdi A, Devoret M H 2021 Science 373 430Google Scholar

    [50]

    Thomas C, Hatke A T, Tuaz A, Kallaher R, Wu T, Wang T, Diaz R E, Gardner G C, Capano M A, Manfra M J 2018 Phys. Rev. Mater. 2 104602Google Scholar

    [51]

    Lee J S, Shojaei B, Pendharkar M, Feldman M, Mukherjee K, Palmstrøm C J 2019 Phys. Rev. Mater. 3 014603Google Scholar

    [52]

    Lei Z, Lehner C A, Cheah E, Karalic M, Mittag C, Alt L, Scharnetzky J, Wegscheider W, Ihn T, Ensslin K 2019 Appl. Phys. Lett. 115 012101Google Scholar

    [53]

    Mittag C, Karalic M, Lei Z, Thomas C, Tuaz A, Hatke A T, Gardner G C, Manfra M J, Ihn T, Ensslin K 2019 Phys. Rev. B 100 075422Google Scholar

    [54]

    Aghaee M, Akkala A, Alam Z, et al. (Microsoft Quantum) 2023 Phys. Rev. B 107 245423Google Scholar

    [55]

    Krogstrup P, Ziino N L B, Chang W, Albrecht S M, Madsen M H, Johnson E, Nygård J, Marcus C M, Jespersen T S 2015 Nat. Mater. 14 400Google Scholar

    [56]

    Vaitiekėnas S, Krogstrup P, Marcus C M 2020 Phys. Rev. B 101 060507Google Scholar

    [57]

    Deng M T, Vaitiekėnas S, Hansen E B, Danon J, Leijnse M, Flensberg K, Nygård J, Krogstrup P, Marcus C M 2016 Science 354 1557Google Scholar

    [58]

    Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Marcus C M 2016 Nature 531 206Google Scholar

    [59]

    Albrecht S M, Hansen E B, Higginbotham A P, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Danon J, Flensberg K, Marcus C M 2017 Phys. Rev. Lett. 118 137701Google Scholar

    [60]

    Bordin A, Wang G, Liu C X, ten Haaf S L D, van Loo N, Mazur G P, Xu D, van Driel D, Zatelli F, Gazibegovic S, Badawy G, Bakkers E P A M, Wimmer M, Kouwenhoven L P, Dvir T 2023 Phys. Rev. X 13 031031Google Scholar

    [61]

    Mazur G P, van Loo N, van Driel D, Wang J Y, Badawy G, Gazibegovic S, Bakkers E P A M, Kouwenhoven L P 2024 Phys. Rev. Appl. 22 054034Google Scholar

    [62]

    Pendharkar M, Zhang B, Wu H, et al. 2021 Science 372 508Google Scholar

    [63]

    Kanne T, Marnauza M, Olsteins D, Carrad D J, Sestoft J E, de Bruijckere J, Zeng L, Johnson E, Olsson E, Grove-Rasmussen K, Nygård J 2021 Nat. Nanotechnol. 16 776Google Scholar

    [64]

    Vaitiekėnas S, Liu Y, Krogstrup P, Marcus C M 2021 Nat. Phys. 17 43Google Scholar

    [65]

    Liu Y, Vaitiekėnas S, Martí-Sánchez S, et al. 2020 Nano Lett. 20 456Google Scholar

    [66]

    Vaitiekėnas S, Winkler G W, van Heck B, Karzig T, Deng M T, Flensberg K, Glazman L I, Nayak C, Krogstrup P, Lutchyn R M, Marcus C M 2020 Science 367 6485Google Scholar

    [67]

    Valentini M, Peñaranda F, Hofmann A, Brauns M, Hauschild R, Krogstrup P, San-Jose P, Prada E, Aguado R, Katsaros G 2021 Science 373 82Google Scholar

    [68]

    Woods B D, Das Sarma S, Stanescu T D 2019 Phys. Rev. B 99 161118Google Scholar

    [69]

    San-Jose P, Payá C, Marcus C M, Vaitiekėnas S, Prada E 2023 Phys. Rev. B 107 155423Google Scholar

    [70]

    San-Jose P, Prada E, Aguado R 2012 Phys. Rev. Lett. 108 257001Google Scholar

    [71]

    Legg H F, Laubscher K, Loss D, Klinovaja J 2023 Phys. Rev. B 108 214520Google Scholar

    [72]

    Wimmer M, Akhmerov A R, Dahlhaus J P, Beenakker C W J 2011 New J. Phys. 13 053016Google Scholar

    [73]

    Danon J, Hellenes A B, Hansen E B, Casparis L, Higginbotham A P, Flensberg K 2020 Phys. Rev. Lett. 124 036801Google Scholar

    [74]

    Pikulin D I, van Heck B, Karzig T, Martinez E A, Nijholt B, Laeven T, Winkler G W, Watson J D, Heedt S, Temurhan M, Svidenko V, Lutchyn R M, Thomas M, de Lange G, Casparis L, Nayak C 2021 arXiv: 2103. 12217 [cond-mat.mes-hall]

    [75]

    Hess R, Legg H F, Loss D, Klinovaja J 2023 Phys. Rev. Lett. 130 207001Google Scholar

    [76]

    Rosdahl T Ö, Vuik A, Kjaergaard M, Akhmerov A R 2018 Phys. Rev. B 97 045421Google Scholar

    [77]

    Banerjee A, Lesser O, Rahman M A, Thomas C, Wang T, Manfra M J, Berg E, Oreg Y, Stern A, Marcus C M 2023 Phys. Rev. Lett. 130 096202Google Scholar

    [78]

    Pan H, Sau J D, Das Sarma S 2021 Phys. Rev. B 103 014513Google Scholar

    [79]

    Tsintzis A, Souto R S, Flensberg K, Danon J, Leijnse M 2024 PRX Quantum 5 010323Google Scholar

    [80]

    Leijnse M, Flensberg K 2012 Phys. Rev. B 86 134528Google Scholar

    [81]

    Dvir T, Wang G, van Loo N, Liu C X, Mazur G P, Bordin A, ten Haaf S L D, Wang J Y, van Driel D, Zatelli F, Li X, Malinowski F K, Gazibegovic S, Badawy G, Bakkers E P A M, Wimmer M, Kouwenhoven L P 2023 Nature 614 445Google Scholar

    [82]

    Bordin A, Li X, van Driel D, Wolff J C, Wang Q, ten Haaf S L D, Wang G, van Loo N, Kouwenhoven L P, Dvir T 2024 Phys. Rev. Lett. 132 056602Google Scholar

    [83]

    Laird E A, Kuemmeth F, Steele G A, Grove-Rasmussen K, Nygård J, Flensberg K, Kouwenhoven L P 2015 Rev. Mod. Phys. 87 703Google Scholar

    [84]

    Minot E D, Yaish Y, Sazonova V, Park J Y, Brink M, McEuen P L 2003 Phys. Rev. Lett. 90 156401Google Scholar

    [85]

    Minot E D, Yaish Y, Sazonova V, McEuen P L 2004 Nature 428 536Google Scholar

    [86]

    Jhang S H, Marganska M, Skourski Y, Preusche D, Grifoni M, Wosnitza J, Strunk C 2011 Phys. Rev. Lett. 106 096802Google Scholar

    [87]

    Deng X S, Gong K, Wang Y, Liu Z, Jiang K L, Kang N, Zhang Z Y 2023 Phys. Rev. Lett. 130 207002Google Scholar

    [88]

    Jin Z, Chu H B, Wang J Y, Hong J X, Tan W C, Li Y 2007 Nano Lett. 7 2073Google Scholar

    [89]

    Wang X S, Li Q Q, Xie J, Jin Z, Wang J Y, Li Y, Jiang K L, Fan S S 2009 Nano Lett. 9 3137Google Scholar

    [90]

    Kong J, Yenilmez E, Tombler T W, Kim W, Dai H J, Laughlin R B, Liu L, Jayanthi C S, Wu S Y 2001 Phys. Rev. Lett. 87 106801Google Scholar

    [91]

    Liang W J, Bockrath M, Bozovic D, Hafner J H, Tinkham M, Park H 2001 Nature 411 665Google Scholar

    [92]

    Javey A, Guo J, Wang Q, Lundstrom M, Dai H J 2003 Nature 424 654Google Scholar

    [93]

    Zhang Z Y, Liang X L, Wang S, Yao K, Hu Y F, Zhu Y Z, Chen Q, Zhou W W, Li Y, Yao Y G, Zhang J, Peng L M 2007 Nano Lett. 7 3603Google Scholar

    [94]

    Urgell C, Yang W, De Bonis S L, Samanta C, Esplandiu M J, Dong Q, Jin Y, Bachtold A 2020 Nat. Phys. 16 32Google Scholar

    [95]

    Wen Y, Ares N, Schupp F J, Pei T, Briggs G A D, Laird E A 2020 Nat. Phys. 16 75Google Scholar

    [96]

    Wang S, Zhao S H, Shi Z W, Wu F Q, Zhao Z Y, Jiang L L, Watanabe K, Taniguchi T, Zettl A, Zhou C W, Wang F 2020 Nat. Mater. 19 986Google Scholar

    [97]

    Wu C C, Liu C H, Zhong Z H 2010 Nano Lett. 10 1032Google Scholar

    [98]

    Pei F, Laird E A, Steele G A, Kouwenhoven L P 2012 Nat. Nanotechnol. 7 630Google Scholar

    [99]

    Zhang R F, Ning Z Y, Zhang Y Y, Xie H H, Zhang Q, Qian W Z, Chen Q, Wei F 2013 Nanoscale 5 6584Google Scholar

    [100]

    Zhang R F, Ning Z Y, Zhang Y Y, Zheng Q S, Chen Q, Xie H H, Zhang Q, Qian W Z, Wei F 2013 Nat. Nanotechnol. 8 912Google Scholar

    [101]

    Zhang R F, Zhang Y Y, Zhang Q, Xie H H, Wang H D, Nie J Q, Wen Q, Wei F 2013 Nat. Commun. 4 1727Google Scholar

    [102]

    Shen B Y, Zhu Z X, Zhang J Y, Xie H H, Bai Y X, Wei F 2018 Adv. Mater. 30 1705844Google Scholar

    [103]

    Kasumov A Y, Deblock R, Kociak M, Reulet B, Bouchiat H, Khodos I I, Gorbatov Y B, Volkov V T, Journet C, Burghard M 1999 Science 284 1508Google Scholar

    [104]

    Mergenthaler M, Schupp F J, Nersisyan A, Ares N, Baumgartner A, Schönenberger C, Briggs G A D, Leek P J, Laird E A 2021 Mater. Quantum. Technol. 1 035003Google Scholar

    [105]

    Bauml C, Bauriedl L, Marganska M, Grifoni M, Strunk C, Paradiso N 2021 Nano Lett. 21 8627Google Scholar

    [106]

    Sau J D, Tewari S 2013 Phys. Rev. B 88 054503Google Scholar

    [107]

    Huertas-Hernando D, Guinea F, Brataas A 2006 Phys. Rev. B 74 155426Google Scholar

    [108]

    Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H 2006 Phys. Rev. B 74 165310Google Scholar

    [109]

    Kuemmeth F, Ilani S, Ralph D C, McEuen P L 2008 Nature 452 448Google Scholar

    [110]

    Marganska M, Milz L, Izumida W, Strunk C, Grifoni M 2018 Phys. Rev. B 97 075141Google Scholar

    [111]

    Milz L, Izumida W, Grifoni M, Marganska M 2019 Phys. Rev. B 100 155417Google Scholar

    [112]

    Zhou B T, Yuan N F Q, Jiang H L, Law K T 2016 Phys. Rev. B 93 180501Google Scholar

    [113]

    Xi X X, Wang Z F, Zhao W W, Park J H, Law K T, Berger H, Forro L, Shan J, Mak K F 2016 Nat. Phys. 12 139Google Scholar

    [114]

    Saito Y, Nakamura Y, Bahramy M S, Kohama Y, Ye J T, Kasahara Y, Nakagawa Y, Onga M, Tokunaga M, Nojima T, Yanase Y, Iwasa Y 2016 Nat. Phys. 12 144Google Scholar

    [115]

    Lu J M, Zheliuk O, Leermakers I, Yuan N F Q, Zeitler U, Law K T, Ye J T 2015 Science 350 1353Google Scholar

    [116]

    Ye J T, Zhang Y J, Akashi R, Bahramy M S, Arita R, Iwasa Y 2012 Science 338 1193Google Scholar

    [117]

    de la Barrera S C, Sinko M R, Gopalan D P, Sivadas N, Seyler K L, Watanabe K, Taniguchi T, Tsen A W, Xu X D, Xiao D, Hunt B M 2018 Nat. Commun. 9 1427Google Scholar

    [118]

    Fatemi V, Wu S F, Cao Y, Bretheau L, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 362 926Google Scholar

    [119]

    Lesser O, Shavit G, Oreg Y 2020 Phys. Rev. Res. 2 023254Google Scholar

    [120]

    Han T Y, Shen J Y, Yuan N F Q, Lin J X Z, Wu Z F, Wu Y Y, Xu S G, An L H, Long G, Wang Y W, Lortz R, Wang N 2018 Phys. Rev. B 97 060505Google Scholar

    [121]

    Kim M, Park G H, Lee J, Lee J H, Park J, Lee H, Lee G H, Lee H J 2017 Nano Lett. 17 6125Google Scholar

    [122]

    Klinovaja J, Gangadharaiah S, Loss D 2012 Phys. Rev. Lett. 108 196804Google Scholar

    [123]

    Klinovaja J, Schmidt M J, Braunecker B, Loss D 2011 Phys. Rev. Lett. 106 156809Google Scholar

    [124]

    Klinovaja J, Schmidt M J, Braunecker B, Loss D 2011 Phys. Rev. B 84 085452Google Scholar

    [125]

    Egger R, Flensberg K 2012 Phys. Rev. B 85 235462Google Scholar

    [126]

    Murra P, Inotani D, Nitta M 2022 Phys. Rev. B 105 214525Google Scholar

    [127]

    Desjardins M M, Contamin L C, Delbecq M R, et al. 2019 Nat. Mater. 18 1060Google Scholar

    [128]

    Klinovaja J, Stano P, Loss D 2012 Phys. Rev. Lett. 109 236801Google Scholar

    [129]

    Klinovaja J, Stano P, Yazdani A, Loss D 2013 Phys. Rev. Lett. 111 186805Google Scholar

    [130]

    Kjaergaard M, Wolms K, Flensberg K 2012 Phys. Rev. B 85 020503Google Scholar

    [131]

    Klinovaja J, Loss D 2013 Phys. Rev. X 3 011008Google Scholar

    [132]

    Cottet A, Kontos T, Doucot B 2013 Phys. Rev. B 88 195415Google Scholar

    [133]

    van Woerkom D J, Proutski A, van Heck B, Bouman D, Vayrynen J I, Glazman L I, Krogstrup P, Nygard J, Kouwenhoven L P, Geresdi A 2017 Nat. Phys. 13 876Google Scholar

    [134]

    Vayrynen J I, Rastelli G, Belzig W, Glazman L I 2015 Phys. Rev. B 92 134508Google Scholar

    [135]

    Dartiailh M C, Kontos T, Doucot B, Cottet A 2017 Phys. Rev. Lett. 118 126803Google Scholar

    [136]

    Mergenthaler M, Nersisyan A, Patterson A, Esposito M, Baumgartner A, Schönenberger C, Briggs G A D, Laird E A, Leek P J 2021 Phys. Rev. Appl. 15 064050Google Scholar

    [137]

    Fatin G L, Matos-Abiague A, Scharf B, Zutic I 2016 Phys. Rev. Lett. 117 077002Google Scholar

    [138]

    Liu L J, Han J, Xu L, Zhou J S, Zhao C Y, Ding S J, Shi H W, Xiao M M, Ding L, Ma Z, Jin C H, Zhang Z Y, Peng L M 2020 Science 368 850Google Scholar

    [139]

    Mukhopadhyay R, Kane C L, Lubensky T C 2001 Phys. Rev. B 64 045120Google Scholar

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出版历程
  • 收稿日期:  2024-12-02
  • 修回日期:  2024-12-24
  • 上网日期:  2025-01-24
  • 刊出日期:  2025-04-05

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