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从高质量半导体/超导体纳米线到马约拉纳零能模

文炼均 潘东 赵建华

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从高质量半导体/超导体纳米线到马约拉纳零能模

文炼均, 潘东, 赵建华

From high-quality semiconductor/superconductor nanowires to Majorana zero mode

Wen Lian-Jun, Pan Dong, Zhao Jian-Hua
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  • 作为马约拉纳费米子的“凝聚态版本”, 马约拉纳零能模是当前凝聚态物理领域的研究热点. 马约拉纳零能模满足非阿贝尔统计, 可以构建受拓扑保护的量子比特. 这种由空间上分离的马约拉纳零能模构建的拓扑量子比特不易受局域噪声的干扰, 具有长的退相干时间, 在容错量子计算中具有重要的应用前景. 半导体/超导体纳米线是研究马约拉纳零能模和拓扑量子计算的理想实验平台. 本文综述了高质量半导体纳米线外延生长、半导体/超导体异质结制备以及相应的马约拉纳零能模研究方面的进展, 并对半导体/超导体纳米线在量子计算中的应用前景进行了展望.
    As the version of Majorana fermions in condensed matter physics, the research of Majorana zero modes is one of the most interesting topics in physics currently. Majorana zero modes obey the non-Abelian statistics and can be used for constructing the topologically protected qubits. This kind of qubit constructed from spatially separated Majorana zero modes is immune to local noise, and has a long decoherence time, which makes it show important application prospects in fault-tolerant quantum computation. The semiconductor/superconductor nanowires are one of the most ideal experimental platforms for studying Majorana zero modes and topological quantum computation. This work reviews the research progress of the epitaxial growth of high-quality semiconductor nanowires, the fabrication of semiconductor/superconductor heterostructure nanowires, and Majorana zero modes in semiconductor/superconductor nanowires. The application prospects of semiconductor/ superconductor nanowires in quantum computation is also prospected finally.
      通信作者: 赵建华, jhzhao@semi.ac.cn
      作者简介:
      赵建华, 中国科学院半导体研究所研究员, 博士生导师, 中国科学院大学岗位教授. 1985年和1988年吉林大学学士、硕士, 1999年中国科学院物理研究所博士, 1999—2002年中国科学院半导体研究所、日本东北大学从事博士后, 2003年至今任半导体超晶格国家重点实验室研究员. 长期从事自旋电子学和半导体低维量子体系研究. 发表文章230余篇. 获黄昆物理奖、国家技术发明二等奖. 科技部重大研究计划项目首席科学家、国际纯粹与应用物理学联合会(IUPAP)磁学专业委员会委员、国际磁学与磁性材料顾问委员会(MMM Adcom)委员、中国科学院半导体研究所学术委员会副主任
    • 基金项目: 中国科学院战略性先导科技专项项目(B类)(批准号: XDB28000000)、国家自然科学基金(批准号: 61974138)、北京市自然科学基金(批准号: 1192017)和中国科学院青年创新促进会(批准号: 2017156)资助的课题
      Corresponding author: Zhao Jian-Hua, jhzhao@semi.ac.cn
    • Funds: Project supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), the National Natural Science Foundation of China (Grant No. 61974138), the Natural Science Foundation of Beijing, China (Grant No. 1192017), and the Youth Innovation Promotion Association of Chinese Academy of Sciences, China (Grant No. 2017156)
    [1]

    Wilczek F 2009 Nat. Phys. 5 614Google Scholar

    [2]

    何映萍, 洪健松, 刘雄军 2020 物理学报 69 110302Google Scholar

    He Y P, Hong J S, Liu X J 2020 Acta Phys. Sin. 69 110302Google Scholar

    [3]

    Kitaev A Y 2001 Phys. Usp. 44 131Google Scholar

    [4]

    Kitaev A Y 2003 Ann. Phys. 303 2Google Scholar

    [5]

    Chetan N, Simon S H, Stern A, Freedman M H, Sarma S D 2008 Rev. Mod. Phys. 80 1083Google Scholar

    [6]

    Sarma S D, Nayak C, Tewari S 2006 Phys. Rev. B 73 220502Google Scholar

    [7]

    Moore G W, Read N 1991 Nucl. Phys. B 360 362Google Scholar

    [8]

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

    [9]

    Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407Google Scholar

    [10]

    Sau J D, Lutchyn R M, Tewari S, Sarma S D 2010 Phys. Rev. Lett. 104 040502Google Scholar

    [11]

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

    [12]

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

    [13]

    Sato M, AndoY 2017 Rep. Prog. Phys. 80 076501Google Scholar

    [14]

    Stanescu T D, Tewari S 2013 J. Phys. Condens. Matter 25 233201Google Scholar

    [15]

    孔令元, 丁洪 2020 物理学报 69 110301Google Scholar

    Kong L Y, Ding H 2020 Acta Phys. Sin. 69 110301Google Scholar

    [16]

    李耀义, 贾金锋 2019 物理学报 68 137401Google Scholar

    Li Y Y, Jia J F 2019 Acta Phys. Sin. 68 137401Google Scholar

    [17]

    于春霖, 张浩 2020 物理学报 69 077303Google Scholar

    Yu C L, Zhang H 2020 Acta Phys. Sin. 69 077303Google Scholar

    [18]

    王靖 2020 物理学报 69 117302Google Scholar

    Wang J 2020 Acta Phys. Sin. 69 117302Google Scholar

    [19]

    梁奇锋, 王志, 川上拓人, 胡晓 2020 物理学报 69 117102Google Scholar

    Liang Q F, Wang Z, Kawakami T, Hu X 2020 Acta Phys. Sin. 69 117102Google Scholar

    [20]

    Alicea J, Oreg Y, Refael G, Von Oppen F, Fisher M P A 2011 Nat. Phys. 7 412Google Scholar

    [21]

    Fu L 2010 Phys. Rev. Lett. 104 056402Google Scholar

    [22]

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

    [23]

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

    [24]

    Winkler G W, Wu Q S, Troyer M, Krogstrup P, Soluyanov A A 2016 Phys. Rev. Lett. 117 076403Google Scholar

    [25]

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

    [26]

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

    [27]

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

    [28]

    Pan D, Fu M Q, Yu X Z, Wang X L, Zhu L J, Nie S H, Wang S L, Chen Q, Xiong P, Von Molnar S, Zhao J H 2014 Nano Lett. 14 1214Google Scholar

    [29]

    Joyce H J, Wongleung J, Gao Q, Tan H H, Jagadish C 2010 Nano Lett. 10 908Google Scholar

    [30]

    Caroff P, Dick K A, Johansson J, Messing M E, Deppert K, Samuelson L 2009 Nat. Nanotechnol. 4 50Google Scholar

    [31]

    Zhang Z, Lu Z Y, Chen P P, Xu H Y, Guo Y N, Liao Z M, Shi S X, Lu W, Zou J 2013 Appl. Phys. Lett. 103 073109Google Scholar

    [32]

    Caroff P, Wagner J B, Dick K A, Nilsson H, Jeppsson M, Deppert K, Samuelson L, Wallenberg L R, Wernersson L 2008 Small 4 878Google Scholar

    [33]

    Ercolani D, Rossi F, Li A, Roddaro S, Grillo V, Salviati G, Beltram F, Sorba L 2009 Nanotechnology 20 505605Google Scholar

    [34]

    Plissard S, Slapak D R, Verheijen M A, Hocevar M, Immink G, Van Weperen I, Nadjperge S, Frolov S M, Kouwenhoven L P, Bakkers E P A M 2012 Nano Lett. 12 1794Google Scholar

    [35]

    So H, Pan D, Li L X, Zhao J H 2017 Nanotechnology 28 135704Google Scholar

    [36]

    Pan D, Fan D X, Kang N, Zhi J H, Yu X Z, Xu H Q, Zhao J H 2016 Nano Lett. 16 834Google Scholar

    [37]

    Badawy G, Gazibegovic S, Borsoi F, Heedt S, Wang C A, Koelling S, Verheijen M A, Kouwenhoven L P, Bakkers E P A M 2019 Nano Lett. 19 3575Google Scholar

    [38]

    Liu J, Potter A C, Law K T, Lee P A 2012 Phys. Rev. Lett. 109 267002Google Scholar

    [39]

    Aasen D, Hell M, Mishmash R V, Higginbotham A, Danon J, Leijnse M, Jespersen T S, Folk J A, Marcus C M, Flensberg K, Alicea J 2016 Phys. Rev. X 6 031016Google Scholar

    [40]

    Plissard S, Van Weperen I, Car D, Verheijen M A, Immink G, Kammhuber J, Cornelissen L J, Szombati D, Geresdi A, Frolov S M, Kouwenhoven L P, Bakkers E P A M 2013 Nat. Nanotechnol. 8 859Google Scholar

    [41]

    Krizek F, Kanne T, Razmadze D, Johnson E, Nygard J, Marcus C M, Krogstrup P 2017 Nano Lett. 17 6090Google Scholar

    [42]

    Yuan X, Caroff P, Wongleung J, Fu L, Tan H H, Jagadish C 2015 Adv. Mater. 27 6096Google Scholar

    [43]

    Tian B Z, Xie P, Kempa T J, Bell D C, Lieber C M 2009 Nat. Nanotechnol. 4 824Google Scholar

    [44]

    Kang J, Cohen Y, Ronen Y, Heiblum M, Buczko R, Kacman P, Popovitzbiro R, Shtrikman H 2013 Nano Lett. 13 5190Google Scholar

    [45]

    Dalacu D, Kam A, Austing D G, Poole P J 2013 Nano Lett. 13 2676Google Scholar

    [46]

    Car D, Wang J, Verheijen M A, Bakkers E E, Plissard S 2014 Adv. Mater. 26 4875Google Scholar

    [47]

    Rieger T, Rosenbach D, Vakulov D, Heedt S, Schapers T, Grutzmacher D, Lepsa M I 2016 Nano Lett. 16 1933Google Scholar

    [48]

    Kang J, Galicka M, Kacman P, Shtrikman H 2017 Nano Lett. 17 531Google Scholar

    [49]

    Gazibegovic S, Car D, Zhang H, Balk S C, Logan J A, De Moor M, Cassidy M, Schmits R, Xu D, Wang G, Krogstrup P, Op Het Veld R L M, Zuo K, Vos Y, Shen J, Bouman D, Shojaei B, Pennachio D J, Lee J S, Van Veldhoven P J, Koelling S, Verheijen M A, Kouwenhoven L P, Palmstrom C J, Bakkers E P A M 2017 Nature 548 434Google Scholar

    [50]

    Krizek F, Sestoft J E, Aseev P, Martisanchez S, Vaitiekenas S, Casparis L, Khan S A, Liu Y, Stankevic T, Whiticar A M, Fursina A, Boekhout F, Koops R, Uccelli E, Kouwenhoven L P, Marcus C M, Arbiol J, Krogstrup P 2018 Phys. Rev. Mater. 2 093401Google Scholar

    [51]

    Vaitiekenas S, Whiticar A M, Deng M T, Krizek F, Sestoft J E, Martisanchez S, Arbiol J, Krogstrup P, Casparis L, Marcus C M 2018 Phys. Rev. Lett. 121 147701Google Scholar

    [52]

    Friedl M, Cerveny K, Weigele P, Tutuncuoglu G, Martisanchez S, Huang C Y, Patlatiuk T, Potts H, Sun Z Y, Hill M O, Guniat L, Kim W, Zamani M, Dubrovskii V G, Arbiol J, Lauhon L J, Zumbuhl D M, Morral A F I 2018 Nano Lett. 18 2666Google Scholar

    [53]

    Aseev P, Wang G, Binci L, Singh A, Martisanchez S, Botifoll M, Stek L, Bordin A, Watson J D, Boekhout F, Abel D, Gamble J K, Van Hoogdalem K, Arbiol J, Kouwenhoven L P, Lange G D, Caroff P 2019 Nano Lett. 19 9102Google Scholar

    [54]

    Lee J S, Choi S, Pendharkar M, Pennachio D J, Markman B, Seas M, Kolling S, Verheijen M A, Casparis L, Petersson K D, Petkovic I, Schaller V, Rodwell M J W, Marcus C M, Krogstrup P, Kouwenhoven L P, Bakkers E P A M, Palmstrom C J 2019 Phys. Rev. Mater. 3 084606Google Scholar

    [55]

    Aseev P, Fursina A, Boekhout F, Krizek F, Sestoft J E, Borsoi F, Heedt S, Wang G, Binci L, Martisanchez S, Swoboda T, Koops R, Uccelli E, Arbiol J, Krogstrup P, Kouwenhoven L P, Caroff P 2019 Nano Lett. 19 218Google Scholar

    [56]

    Op het Veld R L M, Xu D, Schaller V, Verheijen M A, Peters S M E, Jung J, Tong C Y, Wang Q Z, de Moor M W A, Hesselmann B, Vermeulen K, Bommer J D S, Lee J S, Sarikov A, Pendharkar M, Marzegalli A, Koelling S, Kouwenhoven L P, Miglio L, Palmstrøm C J, Zhang H, Bakkers E P A M 2020 Commun. Phys. 3 59Google Scholar

    [57]

    Davies G J, Duncan W J, Skevington P J, French C L, Foord J S 1991 Mater. Sci. Eng., B 9 93Google Scholar

    [58]

    Kang J, Grivnin A, Bor E, Reiner J, Avraham N, Ronen Y, Cohen Y, Kacman P, Shtrikman H, Beidenkopf H 2017 Nano Lett. 17 7520Google Scholar

    [59]

    Wang J Y, Huang G Y, Huang S Y, Xue J H, Pan D, Zhao J H, Xu H Q 2018 Nano Lett. 18 4741Google Scholar

    [60]

    Wang J Y, Huang S Y, Huang G Y, Pan D, Zhao J H, Xu H Q 2017 Nano Lett. 17 4158Google Scholar

    [61]

    Fu M Q, Tang Z Q, Li X, Ning Z Y, Pan D, Zhao J H, Wei X L, Chen Q 2016 Nano Lett. 16 2478Google Scholar

    [62]

    Wang L B, Pan D, Huang G Y, Zhao J H, Kang N, Xu H Q 2019 Nanotechnology 30 124001Google Scholar

    [63]

    Wang J Y, Huang S Y, Lei Z J, Pan D, Zhao J H, Xu H Q 2016 Appl. Phys. Lett. 109 053106Google Scholar

    [64]

    Wang L B, Guo J K, Kang N, Pan D, Li S, Fan D X, Zhao J H, Xu H Q 2015 Appl. Phys. Lett. 106 173105Google Scholar

    [65]

    Fu M Q, Pan D, Yang Y J, Shi T W, Zhang Z Y, Zhao J H, Xu H Q, Chen Q 2014 Appl. Phys. Lett. 105 143101Google Scholar

    [66]

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

    [67]

    Hansen A E, Bjork M T, Fasth C, Thelander C, Samuelson L 2005 Phys. Rev. B 71 205328Google Scholar

    [68]

    Van Weperen I, Tarasinski B, Eeltink D, Pribiag V, Plissard S, Bakkers E E, Kouwenhoven L P, Wimmer M 2015 Phys. Rev. B 91 201413Google Scholar

    [69]

    Takei S, Fregoso B M, Hui H, Lobos A M, Sarma S D 2013 Phys. Rev. Lett. 110 186803Google Scholar

    [70]

    Chang W, Albrecht S M, Jespersen T S, Kuemmeth F, Krogstrup P, Nygard J, Marcus C M 2015 Nat. Nanotechnol. 10 232Google Scholar

    [71]

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

    [72]

    Gul O, Zhang H, Bommer J, De Moor M, Car D, Plissard S, Bakkers E E, Geresdi A, Watanabe K, Taniguchi T, Kouwenhoven L P 2018 Nat. Nanotechnol. 13 192Google Scholar

    [73]

    Zhang H, de Moor M W A, Bommer J D S, Xu D, Wang G Z, Van Loo N, Liu C X, Gazibegovic S, Logan J A, Car D, Veld R O H, Van Veldhoven P J, Koelling S, Verheijen M A, Pendharkar M, Pennachio D J, Shojaei B, Lee J S, Palmstrom C J, Bakkers E P A M, Sarma S D, Kouwenhoven L P 2021 arXiv 2101.11456

    [74]

    Law K T, Lee P A, Ng T K 2009 Phys. Rev. Lett. 103 237001Google Scholar

    [75]

    Fidkowski L, Alicea J, Lindner N H, Lutchyn R M, Fisher M P A 2012 Phys. Rev. B 85 245121Google Scholar

    [76]

    Lutchyn R M, Skrabacz J 2013 Phys. Rev. B 88 024511Google Scholar

    [77]

    VaitiekEnas S, Deng M T, Nygard J, Krogstrup P, Marcus C M 2018 Phys. Rev. Lett. 121 037703Google Scholar

    [78]

    Liu C X, Sau J D, Stanescu T D, Sarma S D 2017 Phys. Rev. B 96 075161Google Scholar

    [79]

    Laroche D, Bouman D, Van Woerkom D J, Proutski A, Murthy C, Pikulin D I, Nayak C, Van Gulik R, Nygard J, Krogstrup P, Kouwenhoven L P, Geresdi A 2019 Nat. Commun. 10 245Google Scholar

    [80]

    Van Heck B, Lutchyn R M, Glazman L I 2016 Phys. Rev. B 93 235431Google Scholar

    [81]

    Sticlet D, Bena C, Simon P 2012 Phys. Rev. Lett. 108 096802Google Scholar

    [82]

    Sagar V, Liang F 2016 Phys. Rev. B 94 235446Google Scholar

    [83]

    Yang Z C, Iadecola T, Chamon C, Mudry C 2019 Phys. Rev. B 99 155138Google Scholar

    [84]

    Karzig T, Knapp C, Lutchyn R M, Bonderson P, Hastings M B, Nayak C, Alicea J, Flensberg K, Plugge S, Oreg Y, Marcus C M, Freedman M H 2017 Phys. Rev. B 95 235305Google Scholar

    [85]

    Divincenzo D P 2000 Fortschr. Phys. 48 771

    [86]

    Bonderson P, Freedman M H, Nayak C 2008 Phys. Rev. Lett. 101 010501Google Scholar

    [87]

    Bonderson P, Freedman M, Nayak C 2009 Ann. Phys. 324 787Google Scholar

    [88]

    Pan D, Wang J Y, Zhang W, Zhu L J, Su X J, Fan F R, Fu Y H, Huang S Y, Wei D H, Zhang L J, Sui M L, Yartsev A, Xu H Q, Zhao J H 2019 Nano Lett. 19 1632Google Scholar

    [89]

    Gazibegovic S, Badawy G, Buckers T L J, Leubner P, Shen J, de Vries F K, Koelling S, KouwenhovenL P, VerheijenM A, Bakkers E P A M 2019 Adv. Mater. 31 1808181Google Scholar

    [90]

    de la Mata M, Leturcq R, Plissard S R, Rolland C, Magen C, Arbiol J, Caroff P 2016 Nano Lett. 16 825Google Scholar

    [91]

    Sun Q, Gao H, Zhang X, Yao X, Xu S, Zheng K, Chen P P, Lu W Zou J 2020 Nanoscale 12 271Google Scholar

    [92]

    Zhang S K, Jiao H X, Wang X D, Chen Y, Wang H, Zhu L Q, Jiang W, Liu J J, Sun L X, Lin T, Shen H, Hu W D, Meng X J, Pan D, Wang J L, Zhao J H, Chu J H 2020 Adv. Funct. Mater. 30 2006156Google Scholar

    [93]

    Kang N, Fan D X, Zhi J H, Pan D, Li S, Wang C, Guo J K, Zhao J H, Xu H Q 2019 Nano Lett. 19 561Google Scholar

    [94]

    Zhi J H, Kang N, Li S, Fan D X, Su F, Pan D, Zhao S, Zhao J H, Xu H Q 2019 Phys. Status Solidi B 256 1800538Google Scholar

    [95]

    Zhi J H, Kang N, Su F, Fan D X, Li S, Pan D, Zhao S, Zhao J H, Xu H Q 2019 Phys. Rev. B 99 245302Google Scholar

    [96]

    Wen L J, Liu L, Liao D Y, Zhuo R, Pan D, Zhao J H 2020 Nanotechnology 31 465602Google Scholar

    [97]

    Fan F R, Chen Y J, Pan D, Zhao J H, Xu H Q 2020 Appl. Phys. Lett. 117 132101Google Scholar

  • 图 1  (a) 纳米线的气-液-固生长过程示意图; (b), (c) Si衬底上Ag辅助生长的纯纤锌矿InAs纳米线[28]; (d), (e) Si衬底上Ag辅助生长的InAs/InSb轴向异质结纳米线[36]; (f) 利用电子束曝光技术, 对InP衬底进行图形化处理, 定义纳米线的生长位置[45]; (g) InP衬底上Au辅助生长的InAs纳米线阵列[45]

    Fig. 1.  (a) The schematic diagram of the nanowires grown with a vapor-liquid-solid manner; (b), (c) Ag-assisted growth of pure wurzite InAs nanowires on Si substrates[28]; (d), (e) Ag-assisted growth of InAs/InSb axial heterojunction nanowires on Si substrates[36]; (f) nanowire growth position is defined by electron beam lithography on InP substrates[45]; (g) Au-assisted growth of InAs nanowire arrays on InP substrates[45].

    图 2  (a) InP (111)B衬底上InAs纳米线网络的选区生长[55]; (b)基于金属播种方法制备的InSb纳米线网络[53]; (c)立式InAs/Al纳米线的高分辨透射电子显微图像[58]; (d)面内InAs/Al纳米线网络的截面高分辨透射电子显微图像[55]

    Fig. 2.  (a) The selective area growth of InAs nanowire networks on InP (111)B substates[55]; (b) the fabrication of InSb nanowire networks via a metal-sown selective area growth technique[53]; (c) the high-resolution transmission electron microscope image of the free-standing InAs/Al nanowire[58]; (d) the cross-sectional high-resolution transmission electron microscope image of the in-plane InAs/Al nanowire network[55].

    图 3  (a)半导体/超导体纳米线隧穿电导测量的器件示意图, 其中底栅控制整个半导体纳米线的化学势, 超导栅调控半导体/超导体异质结区域的化学势, 隧穿栅控制异质结与电极之间的耦合; (b)半导体/超导体纳米线器件的微分电导G随塞曼能EZ和偏压V变化的示意图[78]; (c)约瑟夫森电流I(φ)随超导相位差φ变化的示意图[12]; (d)仅考虑Rashba自旋轨道耦合时, 半导体/超导体纳米线中x方向上的自旋极化分布[81]

    Fig. 3.  (a) The schematic diagram of semiconductor/superconductor nanowire device for detecting zero-energy conductance peaks: The super-gate and global back-gate are respectively used for controlling the chemical potential of the semiconductor/superconductor heterojunction and the semiconductor nanowire, and the tunnel-gate is used for tuning the coupling between the semiconductor/superconductor heterojunction nanowire and the lead; (b) the schematic diagram of the differential conductance G varing with Zeeman energy EZ and bias voltage V[78]; (c) the schematic plot of Josephoson current I(φ) as a function of the superconducting phase difference φ[12]; (d) the spin polarization distribution along the x direction in semiconductor/superconductor nanowire with Rashba spin-orbit coupling[81].

    图 4  (a)−(d) T型结中马约拉纳零能模的编织过程[39]; (e)马约拉纳干涉仪[82]; (f)基于投影测量的马约拉纳零能模编织过程[82]; (g)马约拉纳零能模网络, 其中紫色区域R(t)代表Kekule涡旋[83]

    Fig. 4.  (a)−(d) The braiding of Majorana zero modes in a T-junction[39]; (e) Majorana interferometer[82]; (f) the measurement-based braiding of Majorana zero modes[82]; (g) the network of Majorana zero modes: the Kekule vortex represented by R(t)[83].

    图 5  (a)−(c) InSb纳米片的扫描电子显微图[36]; (d) InSb纳米片的高分辨透射电子显微图[36]; (e) InAs纳米片的扫描电子显微图[88]; (f) InAs纳米片的高分辨透射电子显微图[88]

    Fig. 5.  (a)−(c) Scanning electron microscope images of InSb nanosheets[36]; (d) the high-resolution transmission electron microscope image of the InSb nanosheet[36]; (e) the scanning electron microscope image of InAs nanosheets[88]; (f) the high-resolution transmission electron microscope image of the InAs nanosheet[88].

  • [1]

    Wilczek F 2009 Nat. Phys. 5 614Google Scholar

    [2]

    何映萍, 洪健松, 刘雄军 2020 物理学报 69 110302Google Scholar

    He Y P, Hong J S, Liu X J 2020 Acta Phys. Sin. 69 110302Google Scholar

    [3]

    Kitaev A Y 2001 Phys. Usp. 44 131Google Scholar

    [4]

    Kitaev A Y 2003 Ann. Phys. 303 2Google Scholar

    [5]

    Chetan N, Simon S H, Stern A, Freedman M H, Sarma S D 2008 Rev. Mod. Phys. 80 1083Google Scholar

    [6]

    Sarma S D, Nayak C, Tewari S 2006 Phys. Rev. B 73 220502Google Scholar

    [7]

    Moore G W, Read N 1991 Nucl. Phys. B 360 362Google Scholar

    [8]

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

    [9]

    Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407Google Scholar

    [10]

    Sau J D, Lutchyn R M, Tewari S, Sarma S D 2010 Phys. Rev. Lett. 104 040502Google Scholar

    [11]

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

    [12]

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

    [13]

    Sato M, AndoY 2017 Rep. Prog. Phys. 80 076501Google Scholar

    [14]

    Stanescu T D, Tewari S 2013 J. Phys. Condens. Matter 25 233201Google Scholar

    [15]

    孔令元, 丁洪 2020 物理学报 69 110301Google Scholar

    Kong L Y, Ding H 2020 Acta Phys. Sin. 69 110301Google Scholar

    [16]

    李耀义, 贾金锋 2019 物理学报 68 137401Google Scholar

    Li Y Y, Jia J F 2019 Acta Phys. Sin. 68 137401Google Scholar

    [17]

    于春霖, 张浩 2020 物理学报 69 077303Google Scholar

    Yu C L, Zhang H 2020 Acta Phys. Sin. 69 077303Google Scholar

    [18]

    王靖 2020 物理学报 69 117302Google Scholar

    Wang J 2020 Acta Phys. Sin. 69 117302Google Scholar

    [19]

    梁奇锋, 王志, 川上拓人, 胡晓 2020 物理学报 69 117102Google Scholar

    Liang Q F, Wang Z, Kawakami T, Hu X 2020 Acta Phys. Sin. 69 117102Google Scholar

    [20]

    Alicea J, Oreg Y, Refael G, Von Oppen F, Fisher M P A 2011 Nat. Phys. 7 412Google Scholar

    [21]

    Fu L 2010 Phys. Rev. Lett. 104 056402Google Scholar

    [22]

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

    [23]

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

    [24]

    Winkler G W, Wu Q S, Troyer M, Krogstrup P, Soluyanov A A 2016 Phys. Rev. Lett. 117 076403Google Scholar

    [25]

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

    [26]

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

    [27]

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

    [28]

    Pan D, Fu M Q, Yu X Z, Wang X L, Zhu L J, Nie S H, Wang S L, Chen Q, Xiong P, Von Molnar S, Zhao J H 2014 Nano Lett. 14 1214Google Scholar

    [29]

    Joyce H J, Wongleung J, Gao Q, Tan H H, Jagadish C 2010 Nano Lett. 10 908Google Scholar

    [30]

    Caroff P, Dick K A, Johansson J, Messing M E, Deppert K, Samuelson L 2009 Nat. Nanotechnol. 4 50Google Scholar

    [31]

    Zhang Z, Lu Z Y, Chen P P, Xu H Y, Guo Y N, Liao Z M, Shi S X, Lu W, Zou J 2013 Appl. Phys. Lett. 103 073109Google Scholar

    [32]

    Caroff P, Wagner J B, Dick K A, Nilsson H, Jeppsson M, Deppert K, Samuelson L, Wallenberg L R, Wernersson L 2008 Small 4 878Google Scholar

    [33]

    Ercolani D, Rossi F, Li A, Roddaro S, Grillo V, Salviati G, Beltram F, Sorba L 2009 Nanotechnology 20 505605Google Scholar

    [34]

    Plissard S, Slapak D R, Verheijen M A, Hocevar M, Immink G, Van Weperen I, Nadjperge S, Frolov S M, Kouwenhoven L P, Bakkers E P A M 2012 Nano Lett. 12 1794Google Scholar

    [35]

    So H, Pan D, Li L X, Zhao J H 2017 Nanotechnology 28 135704Google Scholar

    [36]

    Pan D, Fan D X, Kang N, Zhi J H, Yu X Z, Xu H Q, Zhao J H 2016 Nano Lett. 16 834Google Scholar

    [37]

    Badawy G, Gazibegovic S, Borsoi F, Heedt S, Wang C A, Koelling S, Verheijen M A, Kouwenhoven L P, Bakkers E P A M 2019 Nano Lett. 19 3575Google Scholar

    [38]

    Liu J, Potter A C, Law K T, Lee P A 2012 Phys. Rev. Lett. 109 267002Google Scholar

    [39]

    Aasen D, Hell M, Mishmash R V, Higginbotham A, Danon J, Leijnse M, Jespersen T S, Folk J A, Marcus C M, Flensberg K, Alicea J 2016 Phys. Rev. X 6 031016Google Scholar

    [40]

    Plissard S, Van Weperen I, Car D, Verheijen M A, Immink G, Kammhuber J, Cornelissen L J, Szombati D, Geresdi A, Frolov S M, Kouwenhoven L P, Bakkers E P A M 2013 Nat. Nanotechnol. 8 859Google Scholar

    [41]

    Krizek F, Kanne T, Razmadze D, Johnson E, Nygard J, Marcus C M, Krogstrup P 2017 Nano Lett. 17 6090Google Scholar

    [42]

    Yuan X, Caroff P, Wongleung J, Fu L, Tan H H, Jagadish C 2015 Adv. Mater. 27 6096Google Scholar

    [43]

    Tian B Z, Xie P, Kempa T J, Bell D C, Lieber C M 2009 Nat. Nanotechnol. 4 824Google Scholar

    [44]

    Kang J, Cohen Y, Ronen Y, Heiblum M, Buczko R, Kacman P, Popovitzbiro R, Shtrikman H 2013 Nano Lett. 13 5190Google Scholar

    [45]

    Dalacu D, Kam A, Austing D G, Poole P J 2013 Nano Lett. 13 2676Google Scholar

    [46]

    Car D, Wang J, Verheijen M A, Bakkers E E, Plissard S 2014 Adv. Mater. 26 4875Google Scholar

    [47]

    Rieger T, Rosenbach D, Vakulov D, Heedt S, Schapers T, Grutzmacher D, Lepsa M I 2016 Nano Lett. 16 1933Google Scholar

    [48]

    Kang J, Galicka M, Kacman P, Shtrikman H 2017 Nano Lett. 17 531Google Scholar

    [49]

    Gazibegovic S, Car D, Zhang H, Balk S C, Logan J A, De Moor M, Cassidy M, Schmits R, Xu D, Wang G, Krogstrup P, Op Het Veld R L M, Zuo K, Vos Y, Shen J, Bouman D, Shojaei B, Pennachio D J, Lee J S, Van Veldhoven P J, Koelling S, Verheijen M A, Kouwenhoven L P, Palmstrom C J, Bakkers E P A M 2017 Nature 548 434Google Scholar

    [50]

    Krizek F, Sestoft J E, Aseev P, Martisanchez S, Vaitiekenas S, Casparis L, Khan S A, Liu Y, Stankevic T, Whiticar A M, Fursina A, Boekhout F, Koops R, Uccelli E, Kouwenhoven L P, Marcus C M, Arbiol J, Krogstrup P 2018 Phys. Rev. Mater. 2 093401Google Scholar

    [51]

    Vaitiekenas S, Whiticar A M, Deng M T, Krizek F, Sestoft J E, Martisanchez S, Arbiol J, Krogstrup P, Casparis L, Marcus C M 2018 Phys. Rev. Lett. 121 147701Google Scholar

    [52]

    Friedl M, Cerveny K, Weigele P, Tutuncuoglu G, Martisanchez S, Huang C Y, Patlatiuk T, Potts H, Sun Z Y, Hill M O, Guniat L, Kim W, Zamani M, Dubrovskii V G, Arbiol J, Lauhon L J, Zumbuhl D M, Morral A F I 2018 Nano Lett. 18 2666Google Scholar

    [53]

    Aseev P, Wang G, Binci L, Singh A, Martisanchez S, Botifoll M, Stek L, Bordin A, Watson J D, Boekhout F, Abel D, Gamble J K, Van Hoogdalem K, Arbiol J, Kouwenhoven L P, Lange G D, Caroff P 2019 Nano Lett. 19 9102Google Scholar

    [54]

    Lee J S, Choi S, Pendharkar M, Pennachio D J, Markman B, Seas M, Kolling S, Verheijen M A, Casparis L, Petersson K D, Petkovic I, Schaller V, Rodwell M J W, Marcus C M, Krogstrup P, Kouwenhoven L P, Bakkers E P A M, Palmstrom C J 2019 Phys. Rev. Mater. 3 084606Google Scholar

    [55]

    Aseev P, Fursina A, Boekhout F, Krizek F, Sestoft J E, Borsoi F, Heedt S, Wang G, Binci L, Martisanchez S, Swoboda T, Koops R, Uccelli E, Arbiol J, Krogstrup P, Kouwenhoven L P, Caroff P 2019 Nano Lett. 19 218Google Scholar

    [56]

    Op het Veld R L M, Xu D, Schaller V, Verheijen M A, Peters S M E, Jung J, Tong C Y, Wang Q Z, de Moor M W A, Hesselmann B, Vermeulen K, Bommer J D S, Lee J S, Sarikov A, Pendharkar M, Marzegalli A, Koelling S, Kouwenhoven L P, Miglio L, Palmstrøm C J, Zhang H, Bakkers E P A M 2020 Commun. Phys. 3 59Google Scholar

    [57]

    Davies G J, Duncan W J, Skevington P J, French C L, Foord J S 1991 Mater. Sci. Eng., B 9 93Google Scholar

    [58]

    Kang J, Grivnin A, Bor E, Reiner J, Avraham N, Ronen Y, Cohen Y, Kacman P, Shtrikman H, Beidenkopf H 2017 Nano Lett. 17 7520Google Scholar

    [59]

    Wang J Y, Huang G Y, Huang S Y, Xue J H, Pan D, Zhao J H, Xu H Q 2018 Nano Lett. 18 4741Google Scholar

    [60]

    Wang J Y, Huang S Y, Huang G Y, Pan D, Zhao J H, Xu H Q 2017 Nano Lett. 17 4158Google Scholar

    [61]

    Fu M Q, Tang Z Q, Li X, Ning Z Y, Pan D, Zhao J H, Wei X L, Chen Q 2016 Nano Lett. 16 2478Google Scholar

    [62]

    Wang L B, Pan D, Huang G Y, Zhao J H, Kang N, Xu H Q 2019 Nanotechnology 30 124001Google Scholar

    [63]

    Wang J Y, Huang S Y, Lei Z J, Pan D, Zhao J H, Xu H Q 2016 Appl. Phys. Lett. 109 053106Google Scholar

    [64]

    Wang L B, Guo J K, Kang N, Pan D, Li S, Fan D X, Zhao J H, Xu H Q 2015 Appl. Phys. Lett. 106 173105Google Scholar

    [65]

    Fu M Q, Pan D, Yang Y J, Shi T W, Zhang Z Y, Zhao J H, Xu H Q, Chen Q 2014 Appl. Phys. Lett. 105 143101Google Scholar

    [66]

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

    [67]

    Hansen A E, Bjork M T, Fasth C, Thelander C, Samuelson L 2005 Phys. Rev. B 71 205328Google Scholar

    [68]

    Van Weperen I, Tarasinski B, Eeltink D, Pribiag V, Plissard S, Bakkers E E, Kouwenhoven L P, Wimmer M 2015 Phys. Rev. B 91 201413Google Scholar

    [69]

    Takei S, Fregoso B M, Hui H, Lobos A M, Sarma S D 2013 Phys. Rev. Lett. 110 186803Google Scholar

    [70]

    Chang W, Albrecht S M, Jespersen T S, Kuemmeth F, Krogstrup P, Nygard J, Marcus C M 2015 Nat. Nanotechnol. 10 232Google Scholar

    [71]

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

    [72]

    Gul O, Zhang H, Bommer J, De Moor M, Car D, Plissard S, Bakkers E E, Geresdi A, Watanabe K, Taniguchi T, Kouwenhoven L P 2018 Nat. Nanotechnol. 13 192Google Scholar

    [73]

    Zhang H, de Moor M W A, Bommer J D S, Xu D, Wang G Z, Van Loo N, Liu C X, Gazibegovic S, Logan J A, Car D, Veld R O H, Van Veldhoven P J, Koelling S, Verheijen M A, Pendharkar M, Pennachio D J, Shojaei B, Lee J S, Palmstrom C J, Bakkers E P A M, Sarma S D, Kouwenhoven L P 2021 arXiv 2101.11456

    [74]

    Law K T, Lee P A, Ng T K 2009 Phys. Rev. Lett. 103 237001Google Scholar

    [75]

    Fidkowski L, Alicea J, Lindner N H, Lutchyn R M, Fisher M P A 2012 Phys. Rev. B 85 245121Google Scholar

    [76]

    Lutchyn R M, Skrabacz J 2013 Phys. Rev. B 88 024511Google Scholar

    [77]

    VaitiekEnas S, Deng M T, Nygard J, Krogstrup P, Marcus C M 2018 Phys. Rev. Lett. 121 037703Google Scholar

    [78]

    Liu C X, Sau J D, Stanescu T D, Sarma S D 2017 Phys. Rev. B 96 075161Google Scholar

    [79]

    Laroche D, Bouman D, Van Woerkom D J, Proutski A, Murthy C, Pikulin D I, Nayak C, Van Gulik R, Nygard J, Krogstrup P, Kouwenhoven L P, Geresdi A 2019 Nat. Commun. 10 245Google Scholar

    [80]

    Van Heck B, Lutchyn R M, Glazman L I 2016 Phys. Rev. B 93 235431Google Scholar

    [81]

    Sticlet D, Bena C, Simon P 2012 Phys. Rev. Lett. 108 096802Google Scholar

    [82]

    Sagar V, Liang F 2016 Phys. Rev. B 94 235446Google Scholar

    [83]

    Yang Z C, Iadecola T, Chamon C, Mudry C 2019 Phys. Rev. B 99 155138Google Scholar

    [84]

    Karzig T, Knapp C, Lutchyn R M, Bonderson P, Hastings M B, Nayak C, Alicea J, Flensberg K, Plugge S, Oreg Y, Marcus C M, Freedman M H 2017 Phys. Rev. B 95 235305Google Scholar

    [85]

    Divincenzo D P 2000 Fortschr. Phys. 48 771

    [86]

    Bonderson P, Freedman M H, Nayak C 2008 Phys. Rev. Lett. 101 010501Google Scholar

    [87]

    Bonderson P, Freedman M, Nayak C 2009 Ann. Phys. 324 787Google Scholar

    [88]

    Pan D, Wang J Y, Zhang W, Zhu L J, Su X J, Fan F R, Fu Y H, Huang S Y, Wei D H, Zhang L J, Sui M L, Yartsev A, Xu H Q, Zhao J H 2019 Nano Lett. 19 1632Google Scholar

    [89]

    Gazibegovic S, Badawy G, Buckers T L J, Leubner P, Shen J, de Vries F K, Koelling S, KouwenhovenL P, VerheijenM A, Bakkers E P A M 2019 Adv. Mater. 31 1808181Google Scholar

    [90]

    de la Mata M, Leturcq R, Plissard S R, Rolland C, Magen C, Arbiol J, Caroff P 2016 Nano Lett. 16 825Google Scholar

    [91]

    Sun Q, Gao H, Zhang X, Yao X, Xu S, Zheng K, Chen P P, Lu W Zou J 2020 Nanoscale 12 271Google Scholar

    [92]

    Zhang S K, Jiao H X, Wang X D, Chen Y, Wang H, Zhu L Q, Jiang W, Liu J J, Sun L X, Lin T, Shen H, Hu W D, Meng X J, Pan D, Wang J L, Zhao J H, Chu J H 2020 Adv. Funct. Mater. 30 2006156Google Scholar

    [93]

    Kang N, Fan D X, Zhi J H, Pan D, Li S, Wang C, Guo J K, Zhao J H, Xu H Q 2019 Nano Lett. 19 561Google Scholar

    [94]

    Zhi J H, Kang N, Li S, Fan D X, Su F, Pan D, Zhao S, Zhao J H, Xu H Q 2019 Phys. Status Solidi B 256 1800538Google Scholar

    [95]

    Zhi J H, Kang N, Su F, Fan D X, Li S, Pan D, Zhao S, Zhao J H, Xu H Q 2019 Phys. Rev. B 99 245302Google Scholar

    [96]

    Wen L J, Liu L, Liao D Y, Zhuo R, Pan D, Zhao J H 2020 Nanotechnology 31 465602Google Scholar

    [97]

    Fan F R, Chen Y J, Pan D, Zhao J H, Xu H Q 2020 Appl. Phys. Lett. 117 132101Google Scholar

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  • 收稿日期:  2020-10-21
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