搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

面向量子计算的拓扑超导体材料、物理和器件研究

姜达 余东洋 郑沾 曹晓超 林强 刘伍明

引用本文:
Citation:

面向量子计算的拓扑超导体材料、物理和器件研究

姜达, 余东洋, 郑沾, 曹晓超, 林强, 刘伍明

Research progress of material, physics, and device of topological superconductors for quantum computing

Jiang Da, Yu Dong-Yang, Zheng Zhan, Cao Xiao-Chao, Lin Qiang, Liu Wu-Ming
PDF
HTML
导出引用
  • 鉴于“摩尔定律”已经逼近极限, 众多替代传统计算的方法被提出, 其中量子计算是最受关注和研究最广泛的一种. 由于量子体系的不可封闭性, 外界大量不可控的因素会导致量子耗散和退相干, 为了尽可能避免量子叠加态的退相干, 制备具有鲁棒性的量子比特成为了关键环节之一. 马约拉纳零能模是拓扑和超导复合体系中涌现的准粒子, 具有非阿贝尔统计性质, 它的时空编织受到非局域的拓扑性质保护, 因此, 以马约拉纳零能模构造的拓扑量子比特对量子退相干具有天然的鲁棒性. 虽然经过全球范围内各个实验组艰苦卓绝的探求, 目前关于马约拉纳零能模的实验验证仍然扑朔迷离. 本文回顾了量子计算的发展历程和主要的技术手段, 重点介绍了拓扑超导态/体的理论、可观测的实验现象、以及最新的实验研究进展, 并对此做出了分析和评述. 最后对拓扑超导态/体在量子计算领域的应用前景进行了展望.
    Since the physical limit of Moore's law is being approached, many alternative computing methods have been proposed, among which quantum computing is the most concerned and widely studied. Owing to the non closeability of quantum system, the uncontrollable external factors will lead to quantum dissipation and decoherence. In order to avoid the decoherence of quantum superposition state, the fabrication of robust quantum bits has become one of the key factors. Majorana zero mode (MZM) is a quasi-particle emerging in the topological and superconducting hybrid system. It has non-Abelian statistical properties. Therefore, the topological qubit constructed by MZM has natural robustness to quantum decoherence. Despite the arduous exploration by various experimental groups, the experimental verification of MZM is still lacking. This paper reviews the history and main technical routes of quantum computing, focusing on the theory of topological superconductors, observable experimental phenomena, and the latest experimental progress. Furthermore we discuss and analyze the present status of the topological superconductor research. Finally, we prospect the future experiments and applications of topological superconductors in quantum computing.
      通信作者: 林强, qlin@zjut.edu.cn ; 刘伍明, wmliu@aphy.iphy.ac.cn
    • 基金项目: 国家自然科学基金 (批准号: 61727821, U20A20219, 61835013)和国家重点研发计划(批准号: 2021YFA1400900, 2021YFA0718300, 2021YFA1400243)资助的课题.
      Corresponding author: Lin Qiang, qlin@zjut.edu.cn ; Liu Wu-Ming, wmliu@aphy.iphy.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61727821, U20A20219, 61835013), and the National Key R&D Program of China (Grants Nos. 2021YFA1400900, 2021YFA0718300, 2021YFA1400243).
    [1]

    Park J 1970 Found. Phys. 1 23Google Scholar

    [2]

    Wootters W, Zurek W 1982 Nature 299 802Google Scholar

    [3]

    Bennett C 1973 IBM J. Res. Dev. 17 525Google Scholar

    [4]

    Benioff P 1980 J. Stat. Phys. 22 563Google Scholar

    [5]

    Manin Y I 1980 Sov. Radio 13

    [6]

    Deutsch D, Jozsa R 1992 Proc. R. Soc. London, Ser. A 439 553Google Scholar

    [7]

    Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895Google Scholar

    [8]

    Shor P W 1994 Proceedings 35th Annual Symposium on Foundations of Computer Science Santa Fe, NM, USA, November 20–22, 1994 pp124–134

    [9]

    Monroe C, Meekhof D M, King B E, Itano W M, Wineland D J 1995 Phys. Rev. Lett. 75 4714Google Scholar

    [10]

    Divincenzo D P 1997 Mesoscopic Electron Transport NATO ASI Series p345 (Dordrecht: Springer)

    [11]

    Grover L K 1996 In Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, Association for Computing Machinery New York, NY, USA, May 22–24, 1996 p212

    [12]

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

    [13]

    Chuang I L, Gershenfeld N, Kubinec M 1998 Phys. Rev. Lett. 80 3408Google Scholar

    [14]

    Pati A K, Braunstein S L 2000 Nature 404 164

    [15]

    Knill E, Laflamme R, Milburn G J 2001 Nature 409 46Google Scholar

    [16]

    Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188Google Scholar

    [17]

    Pittman T B, Fitch M J, Jacobs B C, Franson J D 2003 Phys. Rev. A 68 032316Google Scholar

    [18]

    O'Brien J L, Pryde G J, White A G, Ralph T C, Branning D 2003 Nature 426 264Google Scholar

    [19]

    Riebe M, Häffner H, Roos C F, Hänsel W, Benhelm J, Lancaster G P T, Körber T W, Becher C, Schmidt-Kaler F, James D F V, Blatt R 2004 Nature 429 734Google Scholar

    [20]

    Chanelière T, Matsukevich D N, Jenkins S D, Lan S Y, Kennedy T A B, Kuzmich A 2005 Nature 438 833Google Scholar

    [21]

    Hijlkema M, Weber B, Specht H P, Webster S C, Kuhn A, Rempe G 2007 Nat. Phys. 3 253Google Scholar

    [22]

    Menicucci N C, Flammia S T, Pfister O 2008 Phys. Rev. Lett. 101 130501Google Scholar

    [23]

    Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502Google Scholar

    [24]

    DiCarlo L, Chow J M, Gambetta J M, Bishop L S, Johnson B R, Schuster D I, Majer J, Blais A, Frunzio L, Girvin S M, Schoelkopf R J 2009 Nature 460 240Google Scholar

    [25]

    Politi A, Matthews J C F, O'Brien J L 2009 Science 325 1221Google Scholar

    [26]

    Devitt S J, Fowler A G, Stephens A M, Greentree A D, Hollenberg L C L, Munro W J, Nemoto K 2009 New J. Phys. 11 1221

    [27]

    Schneider C, Enderlein M, Huber T, Schaetz T 2010 Nat. Photonics 4 772Google Scholar

    [28]

    Monz T, Schindler P, Barreiro J T, Chwalla M, Nigg D, Coish W A, Harlander M, Hänsel W, Hennrich M, Blatt R 2011 Phys. Rev. Lett. 106 130506Google Scholar

    [29]

    Aaronson S, Arkhipov A 2011 The Computational Complexity of Linear Optics (New York: ACM Press) p333

    [30]

    Saeedi K, Simmons S, Salvail J Z, Dluhy P, Riemann H, Abrosimov N V, Becker P, Pohl H, Lorton J J L, Thewalt M W 2013 Science 342 830Google Scholar

    [31]

    Devitt S, Stephens A M, Munro W J, Nemoto K 2013 Nat. Commun. 4 2524Google Scholar

    [32]

    Nemoto K, Trupke M, Devitt S J, Stephens A M, Scharfenberger M, Buczak K, Nöbauer T, Everitt M S, Schmiedmayer J, Munro W J 2014 Phys. Rev. X 4 031022

    [33]

    Pfaff W, Jensen B H, Bernien H, Van Dam S B, Blok M S, Taminiau T H, Tiggelman M J, Schouten R N, Markham M, Twitchen D J, Hanson R 2014 Science 345 532Google Scholar

    [34]

    Monz T, Nigg D, Martinez E A, Brandl M F, Schindler P, Rines R, Wang S X, Chuang I L, Blatt R 2016 Science 351 1068Google Scholar

    [35]

    Devitt S J 2016 Phys. Rev. A 94 032329Google Scholar

    [36]

    O'Malley P J J 2016 Phys. Rev. X 6 031007

    [37]

    Kues M, Reimer C, Roztocki P, Cortés L R, Sciara S, Wetzel B, Zhang Y, Cino A, Chu S T, Little B E, Moss D J, Caspani L, Azaña J, Morandotti R 2017 Nature 546 622Google Scholar

    [38]

    Cao Y, Li Y, Cao Z, Yin J, Chen Y, Yin H, Chen T, Ma X, Peng C, Pan J 2017 Proc. Natl. Acad. Sci. U.S.A. 114 4920Google Scholar

    [39]

    Liang Q Y, Venkatramani A V, Cantu S H, Nicholson T L, Hullans M J, Gorshkov A V, Thompson J D, Chin C, Lukin M D, Vuletic V 2018 Science 359 783Google Scholar

    [40]

    Watson T F, Philips S G J, Kawakami E, Ward D R, Scarlino P, Veldhorst M, Savage D E, Lagally M G, Friesen M, Coppersmith S N, Eriksson M A, Vandersypen L M K 2018 Nature 555 633Google Scholar

    [41]

    Lenzini F, Janousek J, Thearle O, Villa M, Haylock B, Kasture S, Cui L, Phan H P, Dao D V, Yonezawa H, Lam P K, Huntington E H, Lobino M 2018 Sci. Adv. 4 eaat9331Google Scholar

    [42]

    Kokail C, Maier C, van Bijnen R, Brydges T, Joshi M K, Jurcevic P, Muschik C A, Silvi P, Blatt R, Roos C F, Zoller P 2019 Nature 569 355Google Scholar

    [43]

    Wang H, Qin J, Ding X, Chen M, Chen S, You X, He Y, Jiang X, You L, Wang Z, Schneider C, Renema J J, Höfling S, Lu C, Pan J 2019 Phys. Rev. Lett. 123 250503Google Scholar

    [44]

    Mukai H, Sakata K, Devitt S J, Wang R, Zhou Y, Nakajima Y, Tsai J S 2020 New J. Phys. 22 043013Google Scholar

    [45]

    Bienfait A, Zhong Y P, Chang H S, Chou M H, Conner C R, Dumur E, Grebel J, Peairs G A, Povey R G, Satzinger K J, Cleland A N 2020 Phys. Rev. X 10 021055

    [46]

    Google AI Quantum Collaborators, Arute F, Arya K, Babbush R, Bacon D, Bardin J C, Barends R, Boixo S, Broughton M, Buckley B B, Buell D A, Burkett B, Bushnell N, Chen Y, Chen Z, Chiaro B, Collins R, Courtney W, Demura S, Dunsworth A, Eppens D, Farhi E, Fowler A, Foxen B, Gidney C, Giustina M, Graff R, Habegger S, Harrigan M P, Ho A, Hong S, Huang T, Huggins W J, Ioffe L, Isakov S V, Jeffrey E, Jiang Z, Jones C, Kafri D, Kechedzhi K, Kelly J, Kim S, Klimov P V, Korotkov A, Kostritsa F, Landhuis D, Laptev P, Lindmark M, Lucero E, Martin E, Martinis J M, McClean J R, McEwen M, Megrant A, Mi X, Mohseni M, Mruczkiewicz W, Mutus J, Naaman O, Neeley M, Neill C, Neven H, Niu M, O'Brien T E, Ostby E, Petukhov A, Putterman H, Quintana C, Roushan P, Rubin N C, Sank D, Satzinger K J, Smelyanskiy V, Strain D, Sung K J, Szalay M, Takeshita T Y, Vainsencher A, White T, Wiebe N, Yao Z, Yeh P, Zalcman A 2020 Science 369 1084Google Scholar

    [47]

    Joshi S K, Aktas D, Wengerowsky S, Loncaric M, Neumann S P, Liu B, Scheidl T, Lorenzo G C, Samec Z, Kling L, Qiu A, Razavi M, Stipcevic M, Rarity J, Ursin R 2020 Sci. Adv. 6 eaba0959Google Scholar

    [48]

    Zhong H, Wang H, Deng Y, Chen M, Peng L, Luo Y, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X, Zhang W, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N, Lu C, Pan J 2020 Science 370 1460Google Scholar

    [49]

    Chen Y, Zhang Q, Chen T, Cai W, Liao S, Zhang J, Chen K, Yin J, Ren J, Chen Z, Han S, Yu Q, Liang K, Zhou F, Yuan X, Zhao M, Wang T, Jiang X, Zhang L, Liu W, Li Y, Shen Q, Cao Y, Lu C, Shu R, Wang J, Li L, Liu N, Xu F, Wang X, Peng C, Pan J 2021 Nature 589 214Google Scholar

    [50]

    Liu H, Tian X, Gu C, Fan P, Ni X, Yang R, Zhang J, Hu M, Guo J, Cao X, Hu X, Zhao G, Lu Y, Gong Y, Xie Z, Zhu S 2021 Phys. Rev. Lett. 126 020503Google Scholar

    [51]

    Daiss S, Langenfeld S, Welte S, Distante E, Thomas P, Hartung L, Morin O, Rempe G 2021 Science 371 614Google Scholar

    [52]

    Pogorelov I, Feldker T, Marciniak C D, Postler L, Jacob G, Krieglsteiner O, Podlesnic V, Meth M, Negnevitsky V, Stadler M, Höfer B, Wächter C, Lakhmanskiy K, Blatt R, Schindler P, Monz T 2021 PRX Quantum 2 020343Google Scholar

    [53]

    Ebadi S, Wang T T, Levine H, Keesling A, Semeghini G, Omran A, Bluvstein D, Samajdar R, Pichler H, Ho W, Choi S, Sachdev S, Greiner M, Vuletić V, Lukin M D 2021 Nature 595 227Google Scholar

    [54]

    Scholl P, Schuler M, Williams H J, Eberharter A A, Barredo D, Schymik K, Lienhard V, Henry L, Lang T C, Lahaye T, Läuchli A M, Browaeys A 2021 Nature 595 233Google Scholar

    [55]

    Atas Y Y, Zhang J, Lewis R, Jahanpour A, Haase J F, Muschik C A 2021 Nat. Commun. 12 6499Google Scholar

    [56]

    Schrödinger E 1936 Proc. Cambridge Philos. Soc. 32 446Google Scholar

    [57]

    Kwiat P G, Mattle K, Weinfurter H, Zeilinger A, Sergienko A V, Shih Y 1995 Phys. Rev. Lett. 75 4337Google Scholar

    [58]

    Aharonovich I, Englund D, Toth M 2016 Nat. Photonics 10 631Google Scholar

    [59]

    Bouwmeester D, Pan J, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575Google Scholar

    [60]

    Takeda S, Mizuta T, Fuwa M, van Loock P, Furusawa A 2013 Nature 500 315Google Scholar

    [61]

    王吉林, 刘建设, 陈培毅 2009 微纳电子技术 46 321Google Scholar

    Wang J, Liu J, Chen P 2009 Micronanoelectron. Technol. 46 321Google Scholar

    [62]

    Nakamura Y, Pashkin Y A, Tsai J S 1999 Nature 398 786Google Scholar

    [63]

    Arute F, Arya K, Babbush R, Bacon D, Bardin J C, Barends R, Biswas R, Boixo S, Fernando G. S. L. Brandao F G S L, Buell D A, Burkett B, Chen Y, Chen Z, Chiaro B, Collins R, Courtney W, Dunsworth A, Farhi E, Foxen B, Fowler A, Gidney C, Giustina M, Graff R, Guerin K, Habegger S, Harrigan M P, Hartmann M J, Ho A, Hoffmann M, Huang T, Humble T S, Isakov S V, Jeffrey E, Jiang Z, Kafri D, Kechedzhi K, Kelly J, Klimov P V, Knysh S, Korotkov A, Kostritsa F, Landhuis D, Lindmark M, Lucero E, Lyakh D, Mandrà S, McClean J R, McEwen M, Megrant A, Mi X, Michielsen K, Mohseni M, Mutus J, Naaman O, Neeley M, Neill C, Niu M, Ostby E, Petukhov A, Platt J C, Quintana C, Rieffel E G, Roushan P, Rubin N C, Sank D, Satzinger K J, Smelyanskiy V, Sung K J, Trevithick M D, Vainsencher A, Villalonga B, White T, Yao Z, Yeh P, Zalcman A, Neven H, Martinis J M 2019 Nature 574 505Google Scholar

    [64]

    Gong M, Wang S, Zha C, Chen M C, Huang H L, Wu Y, Zhu Q, Zhao Y, Li S, Guo S, Qian H, Ye Y, Chen F, Ying C, Yu J, Fan D, Wu D, Su H, Deng H, Rong H, Zhang K, Cao S, Lin J, Xu Y, Sun L, Guo C, Li N, Liang F, Bastidas V M, Nemoto K, Munro W J, Huo Y H, Lu C Y, Peng C Z, Zhu X, Pan J W 2021 Science 372 948Google Scholar

    [65]

    Guo Q, Cheng C, Li H, Xu S, Zhang P, Wang Z, Song C, Liu W, Ren W, Dong H, Mondaini R, Wang H 2021 Phys. Rev. Lett. 127 240502Google Scholar

    [66]

    Zhang X, Li H, Cao G, Xiao M, Guo G C, Guo G P National Sci. Rev. 6 32

    [67]

    Petta J R, Johnson A C, Taylor J M, Laird E A, Yacoby A, Lukin M D, Marcus C M, Hanson M P, Gossard A C 2005 Science 309 2180Google Scholar

    [68]

    Wang Z 2010 Topological Quantum Computation (Rhode Island: American Mathematical Soc) p112

    [69]

    Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324Google Scholar

    [70]

    Hile S J, Fricke L, House M G, Peretz E, Chen C Y, Wang Y, Broome M, Gorman S K, Keizer J G, Rahman R, Simmons M Y 2018 Sci. adv. 4 1459

    [71]

    Morello A, Pla J J, Zwanenburg F A, Chan K W, Tan K Y, Huebl H, Möttönen M, Nugroho C D, Yang C, van Donkelaar J A, Alves A D C, Jamieson D N, Escott C C, Hollenberg L C L, Clark R G, Dzurak A S 2010 Nature 467 687Google Scholar

    [72]

    Harvey-Collard P, D’Anjou B, Rudolph M, Jacobson N T, Dominguez J, Eyck G A T, Wendt J R, Pluym T, Lilly M P, Coish W A, Pioro-Ladrière M, Carroll M S 2018 Phys. Rev. X 8 021046

    [73]

    Yoneda J, Takeda K, Otsuka T, Nakajima T, Delbecq M R, Allison G, Honda T, Kodera T, Oda S, Hoshi Y, Usami N, Itoh K M, Tarucha S 2018 Nat. Nanotechnol. 13 102Google Scholar

    [74]

    Muhonen J T, Dehollain J P, Laucht A, Hudson F E, Kalra R, Sekiguchi T, Itoh K M, Jamieson D N, McCallum J C, Dzurak A S, Morello A 2014 Nat. Nanotechnol. 9 986Google Scholar

    [75]

    Huang W, Yang C H, Chan K W, Tanttu T, Hensen B, Leon R C C, Fogarty M A, Hwang J C C, Hudson F E, Itoh K M, Morello A, Laucht A, Dzurak A S 2019 Nature 569 532Google Scholar

    [76]

    Blume-Kohout R, Gamble J K, Nielsen E, Rudinger K, Mizrahi J, Fortier K, Maunz P 2017 Nat. Commun. 8 1Google Scholar

    [77]

    Mądzik M T, Asaad S, Youssry A, Joecker B, Rudinger K M, Nielsen E, Young K C, Proctor T J, Baczewski A D, Laucht A, Schmitt V, Hudson F E, Itoh K M, Jakob A M, Johnson B C, Jamieson D N, Dzurak A S, Ferrie C, Blume-Kohout R, Morello A 2022 Nature 601 348Google Scholar

    [78]

    Noiri A, Takeda K, Nakajima T, Kobayashi T, Sammak A, Scappucci G, Tarucha S 2022 Nature 601 338Google Scholar

    [79]

    Xue X, Russ M, Samkharadze N, Undseth B, Sammak A, Scappucci G, Vandersypen L M K 2022 Nature 601 343Google Scholar

    [80]

    Monz T, Kim K, Villar A S, Schindler P, Chwalla M, Riebe M. Roos C F, Haffner H, Hansel W, Hennrich M, Blatt R 2009 Phys. Rev. Lett. 103 200503Google Scholar

    [81]

    Wilk T, Webster S C, Kuhn A, Rempe G 2007 Science 317 488Google Scholar

    [82]

    DeMille D 2002 Phys. Rev. Lett. 88 067901Google Scholar

    [83]

    Jaksch D, Bruder C, Cirac J I, Gardiner C W, Zoller P 1998 Phys. Rev. Lett. 81 3108Google Scholar

    [84]

    Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 415 39Google Scholar

    [85]

    Cirac J I, Zoller P 2004 Phys. Today 57 38

    [86]

    Pu Y F, Zhang S, Wu Y K, Jiang N, Chang W, Li C, Duan L M 2021 Nat. Photonics 15 374Google Scholar

    [87]

    Hartke T, Oreg B, Jia N, Zwierlein M 2022 Nature 601 537Google Scholar

    [88]

    Singh K, Anand S, Pocklington A, Kemp J T, Bernien H 2022 Phys. Rev. X 12 011040

    [89]

    Gao W B, Lu C Y, Yao X C, Xu P, Guhne O, Goebel A, Chen Y A, Peng C Z, Chen Z B, Pan J W 2010 Nat. Phys. 6 331Google Scholar

    [90]

    Mair A, Vaziri A, Weihs G, Zeilinger A 2001 Nature 412 313Google Scholar

    [91]

    Prechtel J H, Kuhlmann A V, Houel J, Greuter L, Ludwig A, Reuter D, Wieck A D, Warburton R J 2013 Phys. Rev. X 3 041006

    [92]

    Jayakumar H, Predojevic A, Huber T, Kauten T, Solomon G S, Weihs G 2013 Phys. Rev. Lett. 110 135505Google Scholar

    [93]

    Crespi A, Osellame R, Ramponi R, Brod D J, Galvão E F, Spagnolo N, Vitelli C, Maiorino E, Mataloni P, Sciarrino F 2013 Nat. Photonics 7 545Google Scholar

    [94]

    Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G R 2012 Science 339 798

    [95]

    Tillmann M, Dakić B, Heilmann R, Nolte S, Szameit A, Walther P 2013 Nat. Photonics 7 540Google Scholar

    [96]

    Broome M A, Fedrizzi A, Rahimi-Keshari S, Dove J, Aaronson S, Ralph T C, White A G 2013 Science 339 794Google Scholar

    [97]

    Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P He Y M, Schneider C, Kamp M, Peng C Z, Hofling S, Lu C Y, Pan J W 2017 Nat. Photonics 11 361Google Scholar

    [98]

    Tang H, Lin X F, Feng Z, Chen J Y, Gao J, Sun K, Wang C Y, Lai P C, Xu X Y, Wang Y, Qiao L F, Yang A L, Jin X M 2018 Sci. Adv. 4 3174Google Scholar

    [99]

    Kashiwazaki T, Yamashima T, Takanashi N, Inoue A, Umeki T, Furusawa A 2021 Appl. Phys. Lett. 119 251104Google Scholar

    [100]

    Ashida Y, Zongping G, Masahito U 2020 Adv. Phys. 69 249

    [101]

    Zhao X M, Guo C X, Kou S P, Zhuang L, Liu W M 2021 Phys. Rev. B 104 205131Google Scholar

    [102]

    Zhao X M, Guo C X, Yang M L, Wang H, Liu W M, Kou S P 2021 Phys. Rev. B 104 214502Google Scholar

    [103]

    Jing D Y, Wang H Y, Liu W M 2022 J. Phys. Condens. Matter 34 195401Google Scholar

    [104]

    De Gennes P G 1999 Superconductivity of metals and alloys (Boca Raton: CRC Press)

    [105]

    Avron J E, Seiler R, Simon B 1983 Phys. Rev. Lett. 51 51Google Scholar

    [106]

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

    [107]

    Lahtinen V, Pachos J 2017 SciPost Phys. 3 021Google Scholar

    [108]

    Sarma S D, Freedman M, Nayak C 2015 NPJ Quantum Inf. 1 1

    [109]

    Read N, Green D 2000 Phys. Rev. B 61 10267Google Scholar

    [110]

    Fu L, Berg E 2010 Phys. Rev. Lett. 105 097001Google Scholar

    [111]

    Cho G Y, Bardarson J H, Lu Y M, Moore J E 2012 Phys. Rev. B 86 214514Google Scholar

    [112]

    Kobayashi S, Sato M 2015 Phys. Rev. Lett. 115 187001Google Scholar

    [113]

    Fu L, Kane C L 2008 Phys. Rev. Lett. 10 096407

    [114]

    Sato M, Takahashi Y, Fujimoto S 2009 Phys. Rev. Lett. 103 020401Google Scholar

    [115]

    Langbehn J, Peng Y, Trifunovic L, von Oppen F, Brouwer P W 2017 Phys. Rev. Lett. 119 246401Google Scholar

    [116]

    Song Z, Fang Z, Fang C 2017 Phys. Rev. Lett. 119 246402Google Scholar

    [117]

    Benalcazar W A, Bernevig B A, Hughes T L 2017 Phys. Rev. B 96 245115Google Scholar

    [118]

    Schindler F 2018 Sci. Adv. 4 0346

    [119]

    Zhu X 2019 Phys. Rev. Lett. 122 236401Google Scholar

    [120]

    Yan Z 2019 Phys. Rev. B 100 205406Google Scholar

    [121]

    Hsu C H, Stano P, Klinovaja J, Loss D 2018 Phys. Rev. Lett. 121 196801Google Scholar

    [122]

    Zhang P 2018 Science 360 182Google Scholar

    [123]

    Hassler F 2014 Majorana qubits arXiv: 1404.0897

    [124]

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

    [125]

    Yamakage A, Yada K, Sato M, Tanaka Y 2012 Phys. Rev. B 85 180509Google Scholar

    [126]

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

    [127]

    Wang Z, Qi X, Zhang S 2011 Phys. Rev. B 84 014527Google Scholar

    [128]

    Marra P, Citro R, Braggio A 2016 Phys. Rev. B 93 220507Google Scholar

    [129]

    Chung S B, Horowitz J, Qi X L 2013 Phys. Rev. B 88 214514Google Scholar

    [130]

    Yamakage A, Sato M, Yada K, Kashiwaya S, Tanaka Y 2013 Phys. Rev. B 87 100510Google Scholar

    [131]

    Sato M 2010 Phys. Rev. B 81 220504Google Scholar

    [132]

    Fu L, Berg E 2010 Phys. Rev. Lett. 105 097001

    [133]

    Berezinskii V L 1974 JETP Lett. 20 287

    [134]

    Asano Y, Tanaka Y 2013 Phys. Rev. B 87 104513Google Scholar

    [135]

    Hor Y S, Williams A J, Checkelsky J G, Roushan P, Seo J, Xu Q, Zandbergen H W, Yazdani A, Ong N P, Cava R J 2010 Phys. Rev. Lett. 104 057001Google Scholar

    [136]

    Wray L A, Xu S, Xia Y, Hor Y S, Qian D, Fedorov A V, Lin H, Bansil A, Cava R J, Hasan M Z 2010 Nat. Phys. 6 855Google Scholar

    [137]

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

    [138]

    Matano K, Kriener M, Segawa K, Ando Y, Zheng G 2016 Nat. Phys. 12 852Google Scholar

    [139]

    Yonezawa S, Tajiri K, Nakata S, Nagai Y, Wang Z, Segawa K, Ando Y, Maeno Y 2017 Nat. Phys. 13 123Google Scholar

    [140]

    Liu Z, Yao X, Shao J, Zuo M, Pi L, Tan S, Zhang C, Zhang Y 2015 J. Am. Chem. Soc. 137 10512Google Scholar

    [141]

    Asaba T, Lawson B J, Tinsman C, Chen L, Corbae P, Li G, Qiu Y, Hor Y S, Fu L, Li L 2017 Phys. Rev. X 7 011009

    [142]

    Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z, Wen J, Gu G D, Ding H, Shin S 2018 Science 360 182

    [143]

    Zhang P, Richard P, Xu N, Xu Y M, Ma J, Qian T, Fedorov A V, Denlinger J D, Gu G D, Ding H 2014 Appl. Phys. Lett. 105 172601Google Scholar

    [144]

    Wang Z, Zhang P, Xu G, Zeng L K, Miao H, Xu X, Qian T, Weng H, Richard P, Fedorov A V, Ding H, Dai X, Fang Z 2015 Phys. Rev. B 92 115119Google Scholar

    [145]

    Wu X, Qin S, Liang Y, Fan H, Hu J 2016 Phys. Rev. B 93 115129Google Scholar

    [146]

    Shi X, Han Z, Richard P, Wu X, Peng X, Qian T, Wang S, Hu J, Sun Y, Ding H 2017 Sci. Bull. 62 503Google Scholar

    [147]

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

    [148]

    Zhu S, Kong L, Cao L, Chen H, Papaj M, Du S, Xing Y, Liu W, Wang D, Shen C, Yang F, Schneeloch J, Zhong R, Gu G, Fu L, Zhang Y, Ding H, Gao H 2020 Science 367 189Google Scholar

    [149]

    Kong L, Zhu S, Papaj M, Chen H, Cao L, Isobe H, Xing Y, Liu W, Wang D, Fan P, Sun Y, Du S, Schneeloch J, Zhong R, Gu G, Fu L, Gao H, Ding H 2019 Nat. Phys. 15 1181Google Scholar

    [150]

    Jiang D, Pan Y, Wang S, Lin Y, Holland C M, Kirtley J R, Chen X, Zhao J, Chen L, Yin S, Wang Y 2021 Sci. Bull. 66 425Google Scholar

    [151]

    Zhang P, Wang Z, Wu X, Yaji K, Ishida Y, Kohama Y, Dai G, Sun Y, Bareille C, Kuroda K, Kondo T, Okazaki K, Kindo K, Wang X, Jin C, Hu J, Thomale R, Sumida K, Wu S, Miyamoto K, Okuda T, Ding H, Gu G D, Tamegai T, Kawakami T, Sato M, Shin S 2019 Nat. Phys. 15 41Google Scholar

    [152]

    Liu Q, Chen C, Zhang T, Peng R, Yan Y, Wen C, Lou X, Huang Y, Tian J, Dong X, Wang G, Bao W, Wang Q, Yin Z, Zhao Z, Feng D 2018 Phys. Rev. X 8 041056

    [153]

    Chen C, Liu Q, Zhang T Z, Li D, Shen P P, Dong X L, Zhao Z X, Zhang T, Feng D L 2019 Chin. Phys. Lett. 36 057403Google Scholar

    [154]

    Zhang T, Bao W, Chen C, Li D, Lu Z, Hu Y, Yang W, Zhao D, Yan Y, Dong X, Wang Q, Zhang T, Feng D 2021 Phys. Rev. Lett. 126 127001Google Scholar

    [155]

    Novak M, Sasaki S, Kriener M, Segawa K, Ando Y 2013 Phys. Rev. B 88 140502Google Scholar

    [156]

    Sasaki S, Ren Z, Taskin A A, Segawa K, Fu L, Ando Y 2012 Phys. Rev. Lett. 109 217004Google Scholar

    [157]

    Sato T, Tanaka Y, Nakayama K, Souma S, Takahashi T, Sasaki S, Ren Z, Taskin A A, Segawa K, Ando Y 2013 Phys. Rev. Lett. 110 206804Google Scholar

    [158]

    Nie S, Xing L, Jin R, Xie W, Wang Z, Prinz F B 2018 Phys. Rev. B 98 125143Google Scholar

    [159]

    Chen C, Liang A, Liu S, Nie S, Huang J, Wang M, Li Y, Pei D, Yang H, Zheng H, Zhang Y, Lu D, Hashimoto M, Barinov A, Jozwiak C, Bostwick A, Rotenberg E, Kou X, Yang L, Guo Y, Wang Z, Yuan H, Liu Z, Chen Y 2020 Matter 3 2055Google Scholar

    [160]

    Liu S, Nie S, Qi Y, Guo Y, Yuan H, Yang L, Chen Y, Wang M, Liu Z 2021 Chin. Phys. Lett. 38 077302Google Scholar

    [161]

    Fang Y, Pan J, Zhang D, Wang D, Hirose H T, Terashima T, Uji S, Yuan Y, Li W, Tian Z, Xue J, Ma Y, Zhao W, Xue Q, Mu G, Zhang H, Huang F 2019 Adv. Mater. 31 1901942

    [162]

    Yuan Y, Pan J, Wang X, Fang Y, Song C, Wang L, He K, Ma X, Zhang H, Huang F, Li W, Xue Q 2019 Nat. Phys. 15 1046Google Scholar

    [163]

    Sato M, Fujimoto S 2009 Phys. Rev. B 79 094504Google Scholar

    [164]

    Yang X, Bao J, Lou Z, Li P, Jiang C, Wang J, Sun T, Liu Y, Guo W, Ramakrishnan S, Kotla S R, Tolkiehn M, Paulmann C, Cao G, Nie Y, Li, Yang Liu W, van Smaalen S, Lin X, Xu Z 2022 Adv. Mater. 34 2108550Google Scholar

    [165]

    Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I, Sanchez D S, Neupane M, Alidoust N, Liu C, Wang B, Lee C C, Jeng H T, Zhang C, Yuan Z, Jia S, Bansil A, Chou F, Lin H, Hasan M Z 2016 Nat. Commun. 7 10556Google Scholar

    [166]

    Guan S Y, Chen P J, Chu M W, Sankar R, Chou F, Jeng H T, Chang C S, Chuang T M 2016 Sci. Adv. 2 1600894Google Scholar

    [167]

    Le T, Sun Y, Jin H, Che L, Yin L, Li J, Pang G M, Xu C Q, Zhao L X, Kittaka S, Sakakibara T, Machida K, Sankar R, Yuan H Q, Chen G F, Xu X, Li S, Zhou Y, Lu X 2020 Sci. Bull. 65 1349Google Scholar

    [168]

    Sakano M, Okawa K, Kanou M, Sanjo H, Okuda T, Sasagawa T, Ishizaka K 2015 Nat. Commun. 6 8595Google Scholar

    [169]

    Lv Y F, Wang W L, Zhang Y M, Ding H, Li W, Wang L, He K, Song C L, Ma X C, Xue Q K 2017 Sci. Bull. 62 852Google Scholar

    [170]

    Guan J Y, Kong L, Zhou L Q, Zhong Y G, Li H, Liu H J, Tang C Y, Yan D Y, Yang F Z, Huang Y B, Shi Y G, Qian T, Weng H M, Sun Y J Ding H 2019 Sci. Bull. 64 1215Google Scholar

    [171]

    Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76Google Scholar

    [172]

    Wang Y, Liu E, Liu H, Pan Y, Zhang L, Zeng J, Fu Y, Wang M, Xu K, Huang Z, Wang Z, Lu H, Xing D, Wang B, Wan X, Miao F 2016 Nat. Commun. 7 13142Google Scholar

    [173]

    Peng L, Yuan Y, Li G, Yang X, Xian J, Yi C, Shi Y, Fu Y 2017 Nat. Commun. 8 659Google Scholar

    [174]

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

    [175]

    Sajadi E, Palomaki T, Fei Z, Zhao W, Bement P, Olsen C, Luescher S, Xu X, Folk J A, Cobden D H 2018 Science 362 922Google Scholar

    [176]

    Pan X, Chen X, Liu H, Feng Y, Wei Z, Zhou Y, Chi Z, Pi L, Yen F, Song F, Wan X, Yang Z, Wang B, Wang G, Zhang Y 2015 Nat. Commun. 6 7805Google Scholar

    [177]

    Kang D, Zhou Y, Yi W, Yang C, Guo J, Shi Y, Zhang S, Wang Z, Zhang C, Jiang S, Li A, Yang K, Wu Q, Zhang G, Sun L, Zhao Z 2015 Nat. Commun. 6 7804Google Scholar

    [178]

    Zhu L, Li Q Y, Lü Y Y, Li S, Zhu X Y, Jia Z Y, Chen Y B, Wen J, Li S C 2018 Nano Lett. 18 6585Google Scholar

    [179]

    Wang M X, Liu C, Xu J P, Yang F, Miao L, Yao M Y, Gao C L, Shen C, Ma X, Chen X, Xu Z A, Liu Y, Zhang S C, Qian D, Jia J F, Xue Q K 2012 Science 336 52Google Scholar

    [180]

    Xu J P, Liu C, Wang M X, Ge J, Liu Z L, Yang X, Chen Y, Liu Y, Xu Z A, Gao C L, Qian D, Zhang F C, Jia J F 2014 Phys. Rev. Lett. 112 217001Google Scholar

    [181]

    Xu J P, Wang M X, Liu Z L, Ge J F, Yang X, Liu C, Xu Z A, Guan D, Gao C L, Qian D, Liu Y, Wang Q H, Zhang F C, Xue Q K, Jia J F 2015 Phys. Rev. Lett. 114 017001Google Scholar

    [182]

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

    [183]

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

    [184]

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

    [185]

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

    [186]

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

    [187]

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

    [188]

    Gazibegovic S, Car D, Zhang H, Balk S C, Logan J A, de Moor M W A, Cassidy M C, 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, Lee J S, van Veldhoven P J, Koelling S, Verheijen M A, Kouwenhoven L P, Palmstrøm C J, Bakkers E P A M 2017 Nature 548 434Google Scholar

    [189]

    Pientka F, Keselman A, Berg E, Yacoby A, Stern A, Halperin B I 2017 Phys. Rev. X 7 021032

    [190]

    Ren H, Pientka F, Hart S, Pierce A T, Kosowsky M, Lunczer L, Schlereth R, Scharf B, Hankiewicz E M, Molenkamp L W, Halperin B I, Yacoby A 2019 Nature 569 93Google Scholar

    [191]

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

  • 图 1  经典比特(左)和量子比特(右)图示. 量子比特可以代表|0$\rangle $态和|1$\rangle $态的叠加态

    Fig. 1.  Classic bit (left) and qubit (right). Qubit presents the superposition of |0$\rangle $ and |1$\rangle $.

    图 2  约瑟夫森结示意图.

    Fig. 2.  The schematic of Josephson Junction.

    图 3  (a) 量子中继协议中的纠缠连接示意图[86]; (b) 量子中继模块之间的纠缠连接的实验系统示意图[86]

    Fig. 3.  (a) A sketch of entanglement connection (swapping) in the quantum repeater protocol[86]; (b) the whole experimental set-up[86]

    图 4  多光子玻色采样实验装置图[97]

    Fig. 4.  Experimental set-up for multiphoton boson-sampling[97].

    图 5  (a), (b), (c)展示了在x方向为有限边界而y方向为周期性边界时的能级结构, 从(a)到(c)缓慢增加磁场h的大小, 当满足$ {\psi }_{s}^{2}+ϵ{\left(\mathrm{0, 0}\right)}^{2} < {h}^{2} < {\psi }_{s}^{2}+ϵ{\left(0, \mathrm{\pi }\right)}^{2} $时, 即(c), 边界涌现了两个无能隙的边界模, 表明发生了拓扑相变[114]

    Fig. 5.  (a), (b), and (c) The band energy of the lattice Hamiltonian with edges at x direction. The magnetic field increases from Figure (a) to Figure (c). The red thin line indicates a gapless chiral edge mode localized on the one side and green thick line a gapless chiral edge mode on the other side. They appear for$ {\psi }_{s}^{2}+ϵ{\left(\mathrm{0, 0}\right)}^{2} < {h}^{2} < {\psi }_{s}^{2}+ϵ{\left(0, \mathrm{\pi }\right)}^{2} $ at Figure (c), which indicates the occurrence of topological phase transition[114].

    图 6  三维拓扑超导体测量量子热霍尔效应的实验示意图[127]

    Fig. 6.  Illustration of the experimental setting for the measurement of quantum thermal Hall effect in the 3D topological superconductor[127].

    图 7  (a) 纳米线在普通金属/超导体结 (NS) 上示意图[134]; (b) 纳米线在超导体/普通金属/超导体约瑟夫森结 (SNS) 上示意图[134]

    Fig. 7.  Schematic pictures of NS (a) and SNS (b) junctions[134]

    图 8  微分电导GNS随偏置电压eV的变化曲线 (a) 不具有拓扑性的纳米线的曲线[134]; (b) 具有拓扑性的纳米线的曲线[134]

    Fig. 8.  The differential conductance of NS nanowires is plotted as a function of the bias voltage for nontopological nanowire in (a) and for the topological nanowire in (b)[134].

    图 9  拓扑纳米线的SNS结的电流-相位关系, 作为对比, 黑色实线是非拓扑纳米线的电流-相位关系[134]

    Fig. 9.  Current-phase relationship in SNS junctions of topological wire. For comparison, the results for nontopological wire is plotted with a solid line[134].

    图 10  在CuxBi2Se3中发现了Tc = 3.8 K的超导电性[135]

    Fig. 10.  Superconductivity at 3.8 K in CuxBi2Se3[135].

    图 11  Fe1+ySexTe1–x上马约拉纳零能模的近量子化电导平台特征 (a) 扫描隧道显微镜示意图[148]; (b) 小图中涡旋的线界面图[148]; (c) 微分电导谱[148]; (d) 三维微分电导谱[148]; (e) 图(c)的彩色图[148]; (f), 图(e)在零偏置是的水平切线[148]; (g) 图(e)在高偏置是的水平切线[148]

    Fig. 11.  Zero-bias conductance plateau observed on Fe1+ySexTe1–x: (a) Schematic of variable tunnel coupling STM/S method[148]; (b) a line-cut intensity plot along the dashed white arrow in the inset[148]; (c) an overlapping plot of dI/dV spectra[148]; (d) 3D plot of tunnel coupling dependent measurement, dI/dV (E, GN) [148]; (e) color-scale plot of Figure (c) [148]; (f) horizontal line-cut at the zero-bias from Figure (e)[148]; (g) horizaontal line-cuts at high-bias from Figure (e)[148].

    图 12  超导抗磁性在Fe1+ySexTe1–x薄片中的分布 (a) 样品光学显微镜照片[150]; (b), (c) 样品的抗磁和磁化强度sSQUID扫描图[150]; (d)—(g) 随温度变化的抗磁sSQUID扫描图[150]; (h) 图(d)中r箭头指向的不同温度抗磁曲线[150]; (i) 根据图(h)做出的彩图[150]; (j) 在图(d)中1和2两点处提取的随温度变化的超流密度[150]

    Fig. 12.  Distinctive edge features in susceptometry of Fe1+ySexTe1–x flake: (a) Optical image of the sample[150]; (b), (c) the susceptometry and magnetometry images of the sample, respectively[150]; (d)–(g) susceptometry images of the sample at various T[150]; (h) line cuts of the susceptometry images at various T along the vector direction (r) as labeled by the arrow in Figure (d) [150]; (i) interpolated image from the line cuts in Figure (h) [150]; (j) superfluid densities as a function of T extracted from point 1 and 2 in Figure (d)[151]

    图 13  Li(Fe, Co)As的电子结构 (a) Li(Fe, Co)As的晶体结构[151]; (b) LiFeAs随ΓMΓZ的能带色散[151]; (c), (b) Cut D处的面内能带结构[151]; (d) LiFeAs (001)面的表面谱[151]; (e) 15 K时LiFe1–xCoxAs (x = 3%)的ARPES谱[151]; (f) 10 K时LiFe1–xCoxAs (x = 9%)的ARPES谱[151]

    Fig. 13.  Electronic structure of Li(Fe, Co)As: (a) Crystal structure of Li(Fe, Co)As[151]; (b) zoomed-in view of the LiFeAs band dispersion along ΓM and ΓZ[151]; (c) in-plane band structure at Cut D in Figure(b) [151]; (d) (001) surface spectrum of LiFeAs[151]; (e) ARPES intensity plot of LiFe1–xCoxAs (x = 3%) at 15  K[151]; (f) ARPES intensity plot of LiFe1–xCoxAs (x = 9%) at 10  K[151].

    图 14  (Li, Fe)OHFeSe中量子化的零偏置电导峰[153]

    Fig. 14.  Quantized zero-bias conductance peak in (Li, Fe) OHFeSe[153].

    图 15  Sn1–xInxTe的零偏置电导峰 (a) 固定磁场改变温度[156]; (b) 固定温度改变磁场[156]

    Fig. 15.  Zero-bias conductance peak in Sn1–xInxTe: (a) Different temperatures at B = 0 T[156]; (b) different magnetic fields at T = 0.37 K[156].

    图 16  TaSe3的电子结构[159]

    Fig. 16.  Electronic structure of TaSe3[159].

    图 17  2M-WS2的拓扑表面态 [161]

    Fig. 17.  Topological surface states of 2M-WS2[161].

    图 18  PbTaSe2中有两个拓扑表面态[165]

    Fig. 18.  Two topological surface states in PbTaSe2[165].

    图 19  分子束外延β-Bi2Pd薄膜的拓扑超导电性和马约拉纳零能模 (a) 扫描隧道显微镜的扫描图[169]; (b) β-Bi2Pd 的微分电导谱[169]; (c) 归一化的零偏置电导峰分布图[169]; (d) 隧穿电导谱[169]; (e) 涡旋核心附近的归一化微分电导谱[169]

    Fig. 19.  Topological superconductivity and MZM in β-Bi2Pd film grown by MBE: (a) STM topography[169]; (b) Differential conductance dI/dV spectrum[169]; (c) normalized zero-bias conductance map[169]; (d) tunneling conductance dI/dV spectrum[169]; (e) normalized dI/dV spectra measured at location with radial distance r from the vortex center[169].

    图 20  单个晶胞厚的WTe2通过门电压调控出超导电性[174]

    Fig. 20.  Gate-tuned superconductivity in monolayer WTe2[174]

    图 21  Bi2Te3/NbSe2上的零偏置电导峰劈裂 (a) 电导曲线[181]; (b) 通过图(a)做出的彩色图[181]; (c)—(g) 2—6层的电导彩色图[181]; (h) 劈裂点随层数变化曲线[181]

    Fig. 21.  (a) A series of dI/dV curves[181]; (b) the color image of Figure (a) [181]; (c)–(g) the experimental results for 2-6QL samples, following the similar data process of Figure (b) [181]; (h) summary of the start points of the peak split [181].

    图 22  分子束外延生长的Al/InAs结构中测得的量子化零偏置电导峰 (a) B-Vsd扫描谱[187]; (b) 从图(a)中提取的不同磁场下的微分电导曲线[187]

    Fig. 22.  Quantum zero-bias conductance peak in Al/InAs grown by MBE: (a) B-Vsd sweep[187]; (b) differential conductance line-cut plots taken from Figure (a) at various B values[187].

    图 23  不同磁场下隧穿电导峰[190]

    Fig. 23.  The differential conductance curves as a function of the bias voltage at different magnetic fields[190].

  • [1]

    Park J 1970 Found. Phys. 1 23Google Scholar

    [2]

    Wootters W, Zurek W 1982 Nature 299 802Google Scholar

    [3]

    Bennett C 1973 IBM J. Res. Dev. 17 525Google Scholar

    [4]

    Benioff P 1980 J. Stat. Phys. 22 563Google Scholar

    [5]

    Manin Y I 1980 Sov. Radio 13

    [6]

    Deutsch D, Jozsa R 1992 Proc. R. Soc. London, Ser. A 439 553Google Scholar

    [7]

    Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895Google Scholar

    [8]

    Shor P W 1994 Proceedings 35th Annual Symposium on Foundations of Computer Science Santa Fe, NM, USA, November 20–22, 1994 pp124–134

    [9]

    Monroe C, Meekhof D M, King B E, Itano W M, Wineland D J 1995 Phys. Rev. Lett. 75 4714Google Scholar

    [10]

    Divincenzo D P 1997 Mesoscopic Electron Transport NATO ASI Series p345 (Dordrecht: Springer)

    [11]

    Grover L K 1996 In Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, Association for Computing Machinery New York, NY, USA, May 22–24, 1996 p212

    [12]

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

    [13]

    Chuang I L, Gershenfeld N, Kubinec M 1998 Phys. Rev. Lett. 80 3408Google Scholar

    [14]

    Pati A K, Braunstein S L 2000 Nature 404 164

    [15]

    Knill E, Laflamme R, Milburn G J 2001 Nature 409 46Google Scholar

    [16]

    Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188Google Scholar

    [17]

    Pittman T B, Fitch M J, Jacobs B C, Franson J D 2003 Phys. Rev. A 68 032316Google Scholar

    [18]

    O'Brien J L, Pryde G J, White A G, Ralph T C, Branning D 2003 Nature 426 264Google Scholar

    [19]

    Riebe M, Häffner H, Roos C F, Hänsel W, Benhelm J, Lancaster G P T, Körber T W, Becher C, Schmidt-Kaler F, James D F V, Blatt R 2004 Nature 429 734Google Scholar

    [20]

    Chanelière T, Matsukevich D N, Jenkins S D, Lan S Y, Kennedy T A B, Kuzmich A 2005 Nature 438 833Google Scholar

    [21]

    Hijlkema M, Weber B, Specht H P, Webster S C, Kuhn A, Rempe G 2007 Nat. Phys. 3 253Google Scholar

    [22]

    Menicucci N C, Flammia S T, Pfister O 2008 Phys. Rev. Lett. 101 130501Google Scholar

    [23]

    Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502Google Scholar

    [24]

    DiCarlo L, Chow J M, Gambetta J M, Bishop L S, Johnson B R, Schuster D I, Majer J, Blais A, Frunzio L, Girvin S M, Schoelkopf R J 2009 Nature 460 240Google Scholar

    [25]

    Politi A, Matthews J C F, O'Brien J L 2009 Science 325 1221Google Scholar

    [26]

    Devitt S J, Fowler A G, Stephens A M, Greentree A D, Hollenberg L C L, Munro W J, Nemoto K 2009 New J. Phys. 11 1221

    [27]

    Schneider C, Enderlein M, Huber T, Schaetz T 2010 Nat. Photonics 4 772Google Scholar

    [28]

    Monz T, Schindler P, Barreiro J T, Chwalla M, Nigg D, Coish W A, Harlander M, Hänsel W, Hennrich M, Blatt R 2011 Phys. Rev. Lett. 106 130506Google Scholar

    [29]

    Aaronson S, Arkhipov A 2011 The Computational Complexity of Linear Optics (New York: ACM Press) p333

    [30]

    Saeedi K, Simmons S, Salvail J Z, Dluhy P, Riemann H, Abrosimov N V, Becker P, Pohl H, Lorton J J L, Thewalt M W 2013 Science 342 830Google Scholar

    [31]

    Devitt S, Stephens A M, Munro W J, Nemoto K 2013 Nat. Commun. 4 2524Google Scholar

    [32]

    Nemoto K, Trupke M, Devitt S J, Stephens A M, Scharfenberger M, Buczak K, Nöbauer T, Everitt M S, Schmiedmayer J, Munro W J 2014 Phys. Rev. X 4 031022

    [33]

    Pfaff W, Jensen B H, Bernien H, Van Dam S B, Blok M S, Taminiau T H, Tiggelman M J, Schouten R N, Markham M, Twitchen D J, Hanson R 2014 Science 345 532Google Scholar

    [34]

    Monz T, Nigg D, Martinez E A, Brandl M F, Schindler P, Rines R, Wang S X, Chuang I L, Blatt R 2016 Science 351 1068Google Scholar

    [35]

    Devitt S J 2016 Phys. Rev. A 94 032329Google Scholar

    [36]

    O'Malley P J J 2016 Phys. Rev. X 6 031007

    [37]

    Kues M, Reimer C, Roztocki P, Cortés L R, Sciara S, Wetzel B, Zhang Y, Cino A, Chu S T, Little B E, Moss D J, Caspani L, Azaña J, Morandotti R 2017 Nature 546 622Google Scholar

    [38]

    Cao Y, Li Y, Cao Z, Yin J, Chen Y, Yin H, Chen T, Ma X, Peng C, Pan J 2017 Proc. Natl. Acad. Sci. U.S.A. 114 4920Google Scholar

    [39]

    Liang Q Y, Venkatramani A V, Cantu S H, Nicholson T L, Hullans M J, Gorshkov A V, Thompson J D, Chin C, Lukin M D, Vuletic V 2018 Science 359 783Google Scholar

    [40]

    Watson T F, Philips S G J, Kawakami E, Ward D R, Scarlino P, Veldhorst M, Savage D E, Lagally M G, Friesen M, Coppersmith S N, Eriksson M A, Vandersypen L M K 2018 Nature 555 633Google Scholar

    [41]

    Lenzini F, Janousek J, Thearle O, Villa M, Haylock B, Kasture S, Cui L, Phan H P, Dao D V, Yonezawa H, Lam P K, Huntington E H, Lobino M 2018 Sci. Adv. 4 eaat9331Google Scholar

    [42]

    Kokail C, Maier C, van Bijnen R, Brydges T, Joshi M K, Jurcevic P, Muschik C A, Silvi P, Blatt R, Roos C F, Zoller P 2019 Nature 569 355Google Scholar

    [43]

    Wang H, Qin J, Ding X, Chen M, Chen S, You X, He Y, Jiang X, You L, Wang Z, Schneider C, Renema J J, Höfling S, Lu C, Pan J 2019 Phys. Rev. Lett. 123 250503Google Scholar

    [44]

    Mukai H, Sakata K, Devitt S J, Wang R, Zhou Y, Nakajima Y, Tsai J S 2020 New J. Phys. 22 043013Google Scholar

    [45]

    Bienfait A, Zhong Y P, Chang H S, Chou M H, Conner C R, Dumur E, Grebel J, Peairs G A, Povey R G, Satzinger K J, Cleland A N 2020 Phys. Rev. X 10 021055

    [46]

    Google AI Quantum Collaborators, Arute F, Arya K, Babbush R, Bacon D, Bardin J C, Barends R, Boixo S, Broughton M, Buckley B B, Buell D A, Burkett B, Bushnell N, Chen Y, Chen Z, Chiaro B, Collins R, Courtney W, Demura S, Dunsworth A, Eppens D, Farhi E, Fowler A, Foxen B, Gidney C, Giustina M, Graff R, Habegger S, Harrigan M P, Ho A, Hong S, Huang T, Huggins W J, Ioffe L, Isakov S V, Jeffrey E, Jiang Z, Jones C, Kafri D, Kechedzhi K, Kelly J, Kim S, Klimov P V, Korotkov A, Kostritsa F, Landhuis D, Laptev P, Lindmark M, Lucero E, Martin E, Martinis J M, McClean J R, McEwen M, Megrant A, Mi X, Mohseni M, Mruczkiewicz W, Mutus J, Naaman O, Neeley M, Neill C, Neven H, Niu M, O'Brien T E, Ostby E, Petukhov A, Putterman H, Quintana C, Roushan P, Rubin N C, Sank D, Satzinger K J, Smelyanskiy V, Strain D, Sung K J, Szalay M, Takeshita T Y, Vainsencher A, White T, Wiebe N, Yao Z, Yeh P, Zalcman A 2020 Science 369 1084Google Scholar

    [47]

    Joshi S K, Aktas D, Wengerowsky S, Loncaric M, Neumann S P, Liu B, Scheidl T, Lorenzo G C, Samec Z, Kling L, Qiu A, Razavi M, Stipcevic M, Rarity J, Ursin R 2020 Sci. Adv. 6 eaba0959Google Scholar

    [48]

    Zhong H, Wang H, Deng Y, Chen M, Peng L, Luo Y, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X, Zhang W, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N, Lu C, Pan J 2020 Science 370 1460Google Scholar

    [49]

    Chen Y, Zhang Q, Chen T, Cai W, Liao S, Zhang J, Chen K, Yin J, Ren J, Chen Z, Han S, Yu Q, Liang K, Zhou F, Yuan X, Zhao M, Wang T, Jiang X, Zhang L, Liu W, Li Y, Shen Q, Cao Y, Lu C, Shu R, Wang J, Li L, Liu N, Xu F, Wang X, Peng C, Pan J 2021 Nature 589 214Google Scholar

    [50]

    Liu H, Tian X, Gu C, Fan P, Ni X, Yang R, Zhang J, Hu M, Guo J, Cao X, Hu X, Zhao G, Lu Y, Gong Y, Xie Z, Zhu S 2021 Phys. Rev. Lett. 126 020503Google Scholar

    [51]

    Daiss S, Langenfeld S, Welte S, Distante E, Thomas P, Hartung L, Morin O, Rempe G 2021 Science 371 614Google Scholar

    [52]

    Pogorelov I, Feldker T, Marciniak C D, Postler L, Jacob G, Krieglsteiner O, Podlesnic V, Meth M, Negnevitsky V, Stadler M, Höfer B, Wächter C, Lakhmanskiy K, Blatt R, Schindler P, Monz T 2021 PRX Quantum 2 020343Google Scholar

    [53]

    Ebadi S, Wang T T, Levine H, Keesling A, Semeghini G, Omran A, Bluvstein D, Samajdar R, Pichler H, Ho W, Choi S, Sachdev S, Greiner M, Vuletić V, Lukin M D 2021 Nature 595 227Google Scholar

    [54]

    Scholl P, Schuler M, Williams H J, Eberharter A A, Barredo D, Schymik K, Lienhard V, Henry L, Lang T C, Lahaye T, Läuchli A M, Browaeys A 2021 Nature 595 233Google Scholar

    [55]

    Atas Y Y, Zhang J, Lewis R, Jahanpour A, Haase J F, Muschik C A 2021 Nat. Commun. 12 6499Google Scholar

    [56]

    Schrödinger E 1936 Proc. Cambridge Philos. Soc. 32 446Google Scholar

    [57]

    Kwiat P G, Mattle K, Weinfurter H, Zeilinger A, Sergienko A V, Shih Y 1995 Phys. Rev. Lett. 75 4337Google Scholar

    [58]

    Aharonovich I, Englund D, Toth M 2016 Nat. Photonics 10 631Google Scholar

    [59]

    Bouwmeester D, Pan J, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575Google Scholar

    [60]

    Takeda S, Mizuta T, Fuwa M, van Loock P, Furusawa A 2013 Nature 500 315Google Scholar

    [61]

    王吉林, 刘建设, 陈培毅 2009 微纳电子技术 46 321Google Scholar

    Wang J, Liu J, Chen P 2009 Micronanoelectron. Technol. 46 321Google Scholar

    [62]

    Nakamura Y, Pashkin Y A, Tsai J S 1999 Nature 398 786Google Scholar

    [63]

    Arute F, Arya K, Babbush R, Bacon D, Bardin J C, Barends R, Biswas R, Boixo S, Fernando G. S. L. Brandao F G S L, Buell D A, Burkett B, Chen Y, Chen Z, Chiaro B, Collins R, Courtney W, Dunsworth A, Farhi E, Foxen B, Fowler A, Gidney C, Giustina M, Graff R, Guerin K, Habegger S, Harrigan M P, Hartmann M J, Ho A, Hoffmann M, Huang T, Humble T S, Isakov S V, Jeffrey E, Jiang Z, Kafri D, Kechedzhi K, Kelly J, Klimov P V, Knysh S, Korotkov A, Kostritsa F, Landhuis D, Lindmark M, Lucero E, Lyakh D, Mandrà S, McClean J R, McEwen M, Megrant A, Mi X, Michielsen K, Mohseni M, Mutus J, Naaman O, Neeley M, Neill C, Niu M, Ostby E, Petukhov A, Platt J C, Quintana C, Rieffel E G, Roushan P, Rubin N C, Sank D, Satzinger K J, Smelyanskiy V, Sung K J, Trevithick M D, Vainsencher A, Villalonga B, White T, Yao Z, Yeh P, Zalcman A, Neven H, Martinis J M 2019 Nature 574 505Google Scholar

    [64]

    Gong M, Wang S, Zha C, Chen M C, Huang H L, Wu Y, Zhu Q, Zhao Y, Li S, Guo S, Qian H, Ye Y, Chen F, Ying C, Yu J, Fan D, Wu D, Su H, Deng H, Rong H, Zhang K, Cao S, Lin J, Xu Y, Sun L, Guo C, Li N, Liang F, Bastidas V M, Nemoto K, Munro W J, Huo Y H, Lu C Y, Peng C Z, Zhu X, Pan J W 2021 Science 372 948Google Scholar

    [65]

    Guo Q, Cheng C, Li H, Xu S, Zhang P, Wang Z, Song C, Liu W, Ren W, Dong H, Mondaini R, Wang H 2021 Phys. Rev. Lett. 127 240502Google Scholar

    [66]

    Zhang X, Li H, Cao G, Xiao M, Guo G C, Guo G P National Sci. Rev. 6 32

    [67]

    Petta J R, Johnson A C, Taylor J M, Laird E A, Yacoby A, Lukin M D, Marcus C M, Hanson M P, Gossard A C 2005 Science 309 2180Google Scholar

    [68]

    Wang Z 2010 Topological Quantum Computation (Rhode Island: American Mathematical Soc) p112

    [69]

    Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324Google Scholar

    [70]

    Hile S J, Fricke L, House M G, Peretz E, Chen C Y, Wang Y, Broome M, Gorman S K, Keizer J G, Rahman R, Simmons M Y 2018 Sci. adv. 4 1459

    [71]

    Morello A, Pla J J, Zwanenburg F A, Chan K W, Tan K Y, Huebl H, Möttönen M, Nugroho C D, Yang C, van Donkelaar J A, Alves A D C, Jamieson D N, Escott C C, Hollenberg L C L, Clark R G, Dzurak A S 2010 Nature 467 687Google Scholar

    [72]

    Harvey-Collard P, D’Anjou B, Rudolph M, Jacobson N T, Dominguez J, Eyck G A T, Wendt J R, Pluym T, Lilly M P, Coish W A, Pioro-Ladrière M, Carroll M S 2018 Phys. Rev. X 8 021046

    [73]

    Yoneda J, Takeda K, Otsuka T, Nakajima T, Delbecq M R, Allison G, Honda T, Kodera T, Oda S, Hoshi Y, Usami N, Itoh K M, Tarucha S 2018 Nat. Nanotechnol. 13 102Google Scholar

    [74]

    Muhonen J T, Dehollain J P, Laucht A, Hudson F E, Kalra R, Sekiguchi T, Itoh K M, Jamieson D N, McCallum J C, Dzurak A S, Morello A 2014 Nat. Nanotechnol. 9 986Google Scholar

    [75]

    Huang W, Yang C H, Chan K W, Tanttu T, Hensen B, Leon R C C, Fogarty M A, Hwang J C C, Hudson F E, Itoh K M, Morello A, Laucht A, Dzurak A S 2019 Nature 569 532Google Scholar

    [76]

    Blume-Kohout R, Gamble J K, Nielsen E, Rudinger K, Mizrahi J, Fortier K, Maunz P 2017 Nat. Commun. 8 1Google Scholar

    [77]

    Mądzik M T, Asaad S, Youssry A, Joecker B, Rudinger K M, Nielsen E, Young K C, Proctor T J, Baczewski A D, Laucht A, Schmitt V, Hudson F E, Itoh K M, Jakob A M, Johnson B C, Jamieson D N, Dzurak A S, Ferrie C, Blume-Kohout R, Morello A 2022 Nature 601 348Google Scholar

    [78]

    Noiri A, Takeda K, Nakajima T, Kobayashi T, Sammak A, Scappucci G, Tarucha S 2022 Nature 601 338Google Scholar

    [79]

    Xue X, Russ M, Samkharadze N, Undseth B, Sammak A, Scappucci G, Vandersypen L M K 2022 Nature 601 343Google Scholar

    [80]

    Monz T, Kim K, Villar A S, Schindler P, Chwalla M, Riebe M. Roos C F, Haffner H, Hansel W, Hennrich M, Blatt R 2009 Phys. Rev. Lett. 103 200503Google Scholar

    [81]

    Wilk T, Webster S C, Kuhn A, Rempe G 2007 Science 317 488Google Scholar

    [82]

    DeMille D 2002 Phys. Rev. Lett. 88 067901Google Scholar

    [83]

    Jaksch D, Bruder C, Cirac J I, Gardiner C W, Zoller P 1998 Phys. Rev. Lett. 81 3108Google Scholar

    [84]

    Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 415 39Google Scholar

    [85]

    Cirac J I, Zoller P 2004 Phys. Today 57 38

    [86]

    Pu Y F, Zhang S, Wu Y K, Jiang N, Chang W, Li C, Duan L M 2021 Nat. Photonics 15 374Google Scholar

    [87]

    Hartke T, Oreg B, Jia N, Zwierlein M 2022 Nature 601 537Google Scholar

    [88]

    Singh K, Anand S, Pocklington A, Kemp J T, Bernien H 2022 Phys. Rev. X 12 011040

    [89]

    Gao W B, Lu C Y, Yao X C, Xu P, Guhne O, Goebel A, Chen Y A, Peng C Z, Chen Z B, Pan J W 2010 Nat. Phys. 6 331Google Scholar

    [90]

    Mair A, Vaziri A, Weihs G, Zeilinger A 2001 Nature 412 313Google Scholar

    [91]

    Prechtel J H, Kuhlmann A V, Houel J, Greuter L, Ludwig A, Reuter D, Wieck A D, Warburton R J 2013 Phys. Rev. X 3 041006

    [92]

    Jayakumar H, Predojevic A, Huber T, Kauten T, Solomon G S, Weihs G 2013 Phys. Rev. Lett. 110 135505Google Scholar

    [93]

    Crespi A, Osellame R, Ramponi R, Brod D J, Galvão E F, Spagnolo N, Vitelli C, Maiorino E, Mataloni P, Sciarrino F 2013 Nat. Photonics 7 545Google Scholar

    [94]

    Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G R 2012 Science 339 798

    [95]

    Tillmann M, Dakić B, Heilmann R, Nolte S, Szameit A, Walther P 2013 Nat. Photonics 7 540Google Scholar

    [96]

    Broome M A, Fedrizzi A, Rahimi-Keshari S, Dove J, Aaronson S, Ralph T C, White A G 2013 Science 339 794Google Scholar

    [97]

    Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P He Y M, Schneider C, Kamp M, Peng C Z, Hofling S, Lu C Y, Pan J W 2017 Nat. Photonics 11 361Google Scholar

    [98]

    Tang H, Lin X F, Feng Z, Chen J Y, Gao J, Sun K, Wang C Y, Lai P C, Xu X Y, Wang Y, Qiao L F, Yang A L, Jin X M 2018 Sci. Adv. 4 3174Google Scholar

    [99]

    Kashiwazaki T, Yamashima T, Takanashi N, Inoue A, Umeki T, Furusawa A 2021 Appl. Phys. Lett. 119 251104Google Scholar

    [100]

    Ashida Y, Zongping G, Masahito U 2020 Adv. Phys. 69 249

    [101]

    Zhao X M, Guo C X, Kou S P, Zhuang L, Liu W M 2021 Phys. Rev. B 104 205131Google Scholar

    [102]

    Zhao X M, Guo C X, Yang M L, Wang H, Liu W M, Kou S P 2021 Phys. Rev. B 104 214502Google Scholar

    [103]

    Jing D Y, Wang H Y, Liu W M 2022 J. Phys. Condens. Matter 34 195401Google Scholar

    [104]

    De Gennes P G 1999 Superconductivity of metals and alloys (Boca Raton: CRC Press)

    [105]

    Avron J E, Seiler R, Simon B 1983 Phys. Rev. Lett. 51 51Google Scholar

    [106]

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

    [107]

    Lahtinen V, Pachos J 2017 SciPost Phys. 3 021Google Scholar

    [108]

    Sarma S D, Freedman M, Nayak C 2015 NPJ Quantum Inf. 1 1

    [109]

    Read N, Green D 2000 Phys. Rev. B 61 10267Google Scholar

    [110]

    Fu L, Berg E 2010 Phys. Rev. Lett. 105 097001Google Scholar

    [111]

    Cho G Y, Bardarson J H, Lu Y M, Moore J E 2012 Phys. Rev. B 86 214514Google Scholar

    [112]

    Kobayashi S, Sato M 2015 Phys. Rev. Lett. 115 187001Google Scholar

    [113]

    Fu L, Kane C L 2008 Phys. Rev. Lett. 10 096407

    [114]

    Sato M, Takahashi Y, Fujimoto S 2009 Phys. Rev. Lett. 103 020401Google Scholar

    [115]

    Langbehn J, Peng Y, Trifunovic L, von Oppen F, Brouwer P W 2017 Phys. Rev. Lett. 119 246401Google Scholar

    [116]

    Song Z, Fang Z, Fang C 2017 Phys. Rev. Lett. 119 246402Google Scholar

    [117]

    Benalcazar W A, Bernevig B A, Hughes T L 2017 Phys. Rev. B 96 245115Google Scholar

    [118]

    Schindler F 2018 Sci. Adv. 4 0346

    [119]

    Zhu X 2019 Phys. Rev. Lett. 122 236401Google Scholar

    [120]

    Yan Z 2019 Phys. Rev. B 100 205406Google Scholar

    [121]

    Hsu C H, Stano P, Klinovaja J, Loss D 2018 Phys. Rev. Lett. 121 196801Google Scholar

    [122]

    Zhang P 2018 Science 360 182Google Scholar

    [123]

    Hassler F 2014 Majorana qubits arXiv: 1404.0897

    [124]

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

    [125]

    Yamakage A, Yada K, Sato M, Tanaka Y 2012 Phys. Rev. B 85 180509Google Scholar

    [126]

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

    [127]

    Wang Z, Qi X, Zhang S 2011 Phys. Rev. B 84 014527Google Scholar

    [128]

    Marra P, Citro R, Braggio A 2016 Phys. Rev. B 93 220507Google Scholar

    [129]

    Chung S B, Horowitz J, Qi X L 2013 Phys. Rev. B 88 214514Google Scholar

    [130]

    Yamakage A, Sato M, Yada K, Kashiwaya S, Tanaka Y 2013 Phys. Rev. B 87 100510Google Scholar

    [131]

    Sato M 2010 Phys. Rev. B 81 220504Google Scholar

    [132]

    Fu L, Berg E 2010 Phys. Rev. Lett. 105 097001

    [133]

    Berezinskii V L 1974 JETP Lett. 20 287

    [134]

    Asano Y, Tanaka Y 2013 Phys. Rev. B 87 104513Google Scholar

    [135]

    Hor Y S, Williams A J, Checkelsky J G, Roushan P, Seo J, Xu Q, Zandbergen H W, Yazdani A, Ong N P, Cava R J 2010 Phys. Rev. Lett. 104 057001Google Scholar

    [136]

    Wray L A, Xu S, Xia Y, Hor Y S, Qian D, Fedorov A V, Lin H, Bansil A, Cava R J, Hasan M Z 2010 Nat. Phys. 6 855Google Scholar

    [137]

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

    [138]

    Matano K, Kriener M, Segawa K, Ando Y, Zheng G 2016 Nat. Phys. 12 852Google Scholar

    [139]

    Yonezawa S, Tajiri K, Nakata S, Nagai Y, Wang Z, Segawa K, Ando Y, Maeno Y 2017 Nat. Phys. 13 123Google Scholar

    [140]

    Liu Z, Yao X, Shao J, Zuo M, Pi L, Tan S, Zhang C, Zhang Y 2015 J. Am. Chem. Soc. 137 10512Google Scholar

    [141]

    Asaba T, Lawson B J, Tinsman C, Chen L, Corbae P, Li G, Qiu Y, Hor Y S, Fu L, Li L 2017 Phys. Rev. X 7 011009

    [142]

    Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z, Wen J, Gu G D, Ding H, Shin S 2018 Science 360 182

    [143]

    Zhang P, Richard P, Xu N, Xu Y M, Ma J, Qian T, Fedorov A V, Denlinger J D, Gu G D, Ding H 2014 Appl. Phys. Lett. 105 172601Google Scholar

    [144]

    Wang Z, Zhang P, Xu G, Zeng L K, Miao H, Xu X, Qian T, Weng H, Richard P, Fedorov A V, Ding H, Dai X, Fang Z 2015 Phys. Rev. B 92 115119Google Scholar

    [145]

    Wu X, Qin S, Liang Y, Fan H, Hu J 2016 Phys. Rev. B 93 115129Google Scholar

    [146]

    Shi X, Han Z, Richard P, Wu X, Peng X, Qian T, Wang S, Hu J, Sun Y, Ding H 2017 Sci. Bull. 62 503Google Scholar

    [147]

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

    [148]

    Zhu S, Kong L, Cao L, Chen H, Papaj M, Du S, Xing Y, Liu W, Wang D, Shen C, Yang F, Schneeloch J, Zhong R, Gu G, Fu L, Zhang Y, Ding H, Gao H 2020 Science 367 189Google Scholar

    [149]

    Kong L, Zhu S, Papaj M, Chen H, Cao L, Isobe H, Xing Y, Liu W, Wang D, Fan P, Sun Y, Du S, Schneeloch J, Zhong R, Gu G, Fu L, Gao H, Ding H 2019 Nat. Phys. 15 1181Google Scholar

    [150]

    Jiang D, Pan Y, Wang S, Lin Y, Holland C M, Kirtley J R, Chen X, Zhao J, Chen L, Yin S, Wang Y 2021 Sci. Bull. 66 425Google Scholar

    [151]

    Zhang P, Wang Z, Wu X, Yaji K, Ishida Y, Kohama Y, Dai G, Sun Y, Bareille C, Kuroda K, Kondo T, Okazaki K, Kindo K, Wang X, Jin C, Hu J, Thomale R, Sumida K, Wu S, Miyamoto K, Okuda T, Ding H, Gu G D, Tamegai T, Kawakami T, Sato M, Shin S 2019 Nat. Phys. 15 41Google Scholar

    [152]

    Liu Q, Chen C, Zhang T, Peng R, Yan Y, Wen C, Lou X, Huang Y, Tian J, Dong X, Wang G, Bao W, Wang Q, Yin Z, Zhao Z, Feng D 2018 Phys. Rev. X 8 041056

    [153]

    Chen C, Liu Q, Zhang T Z, Li D, Shen P P, Dong X L, Zhao Z X, Zhang T, Feng D L 2019 Chin. Phys. Lett. 36 057403Google Scholar

    [154]

    Zhang T, Bao W, Chen C, Li D, Lu Z, Hu Y, Yang W, Zhao D, Yan Y, Dong X, Wang Q, Zhang T, Feng D 2021 Phys. Rev. Lett. 126 127001Google Scholar

    [155]

    Novak M, Sasaki S, Kriener M, Segawa K, Ando Y 2013 Phys. Rev. B 88 140502Google Scholar

    [156]

    Sasaki S, Ren Z, Taskin A A, Segawa K, Fu L, Ando Y 2012 Phys. Rev. Lett. 109 217004Google Scholar

    [157]

    Sato T, Tanaka Y, Nakayama K, Souma S, Takahashi T, Sasaki S, Ren Z, Taskin A A, Segawa K, Ando Y 2013 Phys. Rev. Lett. 110 206804Google Scholar

    [158]

    Nie S, Xing L, Jin R, Xie W, Wang Z, Prinz F B 2018 Phys. Rev. B 98 125143Google Scholar

    [159]

    Chen C, Liang A, Liu S, Nie S, Huang J, Wang M, Li Y, Pei D, Yang H, Zheng H, Zhang Y, Lu D, Hashimoto M, Barinov A, Jozwiak C, Bostwick A, Rotenberg E, Kou X, Yang L, Guo Y, Wang Z, Yuan H, Liu Z, Chen Y 2020 Matter 3 2055Google Scholar

    [160]

    Liu S, Nie S, Qi Y, Guo Y, Yuan H, Yang L, Chen Y, Wang M, Liu Z 2021 Chin. Phys. Lett. 38 077302Google Scholar

    [161]

    Fang Y, Pan J, Zhang D, Wang D, Hirose H T, Terashima T, Uji S, Yuan Y, Li W, Tian Z, Xue J, Ma Y, Zhao W, Xue Q, Mu G, Zhang H, Huang F 2019 Adv. Mater. 31 1901942

    [162]

    Yuan Y, Pan J, Wang X, Fang Y, Song C, Wang L, He K, Ma X, Zhang H, Huang F, Li W, Xue Q 2019 Nat. Phys. 15 1046Google Scholar

    [163]

    Sato M, Fujimoto S 2009 Phys. Rev. B 79 094504Google Scholar

    [164]

    Yang X, Bao J, Lou Z, Li P, Jiang C, Wang J, Sun T, Liu Y, Guo W, Ramakrishnan S, Kotla S R, Tolkiehn M, Paulmann C, Cao G, Nie Y, Li, Yang Liu W, van Smaalen S, Lin X, Xu Z 2022 Adv. Mater. 34 2108550Google Scholar

    [165]

    Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I, Sanchez D S, Neupane M, Alidoust N, Liu C, Wang B, Lee C C, Jeng H T, Zhang C, Yuan Z, Jia S, Bansil A, Chou F, Lin H, Hasan M Z 2016 Nat. Commun. 7 10556Google Scholar

    [166]

    Guan S Y, Chen P J, Chu M W, Sankar R, Chou F, Jeng H T, Chang C S, Chuang T M 2016 Sci. Adv. 2 1600894Google Scholar

    [167]

    Le T, Sun Y, Jin H, Che L, Yin L, Li J, Pang G M, Xu C Q, Zhao L X, Kittaka S, Sakakibara T, Machida K, Sankar R, Yuan H Q, Chen G F, Xu X, Li S, Zhou Y, Lu X 2020 Sci. Bull. 65 1349Google Scholar

    [168]

    Sakano M, Okawa K, Kanou M, Sanjo H, Okuda T, Sasagawa T, Ishizaka K 2015 Nat. Commun. 6 8595Google Scholar

    [169]

    Lv Y F, Wang W L, Zhang Y M, Ding H, Li W, Wang L, He K, Song C L, Ma X C, Xue Q K 2017 Sci. Bull. 62 852Google Scholar

    [170]

    Guan J Y, Kong L, Zhou L Q, Zhong Y G, Li H, Liu H J, Tang C Y, Yan D Y, Yang F Z, Huang Y B, Shi Y G, Qian T, Weng H M, Sun Y J Ding H 2019 Sci. Bull. 64 1215Google Scholar

    [171]

    Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76Google Scholar

    [172]

    Wang Y, Liu E, Liu H, Pan Y, Zhang L, Zeng J, Fu Y, Wang M, Xu K, Huang Z, Wang Z, Lu H, Xing D, Wang B, Wan X, Miao F 2016 Nat. Commun. 7 13142Google Scholar

    [173]

    Peng L, Yuan Y, Li G, Yang X, Xian J, Yi C, Shi Y, Fu Y 2017 Nat. Commun. 8 659Google Scholar

    [174]

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

    [175]

    Sajadi E, Palomaki T, Fei Z, Zhao W, Bement P, Olsen C, Luescher S, Xu X, Folk J A, Cobden D H 2018 Science 362 922Google Scholar

    [176]

    Pan X, Chen X, Liu H, Feng Y, Wei Z, Zhou Y, Chi Z, Pi L, Yen F, Song F, Wan X, Yang Z, Wang B, Wang G, Zhang Y 2015 Nat. Commun. 6 7805Google Scholar

    [177]

    Kang D, Zhou Y, Yi W, Yang C, Guo J, Shi Y, Zhang S, Wang Z, Zhang C, Jiang S, Li A, Yang K, Wu Q, Zhang G, Sun L, Zhao Z 2015 Nat. Commun. 6 7804Google Scholar

    [178]

    Zhu L, Li Q Y, Lü Y Y, Li S, Zhu X Y, Jia Z Y, Chen Y B, Wen J, Li S C 2018 Nano Lett. 18 6585Google Scholar

    [179]

    Wang M X, Liu C, Xu J P, Yang F, Miao L, Yao M Y, Gao C L, Shen C, Ma X, Chen X, Xu Z A, Liu Y, Zhang S C, Qian D, Jia J F, Xue Q K 2012 Science 336 52Google Scholar

    [180]

    Xu J P, Liu C, Wang M X, Ge J, Liu Z L, Yang X, Chen Y, Liu Y, Xu Z A, Gao C L, Qian D, Zhang F C, Jia J F 2014 Phys. Rev. Lett. 112 217001Google Scholar

    [181]

    Xu J P, Wang M X, Liu Z L, Ge J F, Yang X, Liu C, Xu Z A, Guan D, Gao C L, Qian D, Liu Y, Wang Q H, Zhang F C, Xue Q K, Jia J F 2015 Phys. Rev. Lett. 114 017001Google Scholar

    [182]

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

    [183]

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

    [184]

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

    [185]

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

    [186]

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

    [187]

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

    [188]

    Gazibegovic S, Car D, Zhang H, Balk S C, Logan J A, de Moor M W A, Cassidy M C, 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, Lee J S, van Veldhoven P J, Koelling S, Verheijen M A, Kouwenhoven L P, Palmstrøm C J, Bakkers E P A M 2017 Nature 548 434Google Scholar

    [189]

    Pientka F, Keselman A, Berg E, Yacoby A, Stern A, Halperin B I 2017 Phys. Rev. X 7 021032

    [190]

    Ren H, Pientka F, Hart S, Pierce A T, Kosowsky M, Lunczer L, Schlereth R, Scharf B, Hankiewicz E M, Molenkamp L W, Halperin B I, Yacoby A 2019 Nature 569 93Google Scholar

    [191]

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

  • [1] 杨晓堃, 李维, 黄永畅. 量子博弈—“PQ”问题. 物理学报, 2024, 73(3): 030301. doi: 10.7498/aps.73.20230592
    [2] 吴海滨, 刘迎娣, 刘彦军, 李金花, 刘建军. 量子点耦合强度对手性Majorana费米子共振交换的调制. 物理学报, 2024, 73(13): 130502. doi: 10.7498/aps.73.20240739
    [3] 王美红, 郝树宏, 秦忠忠, 苏晓龙. 连续变量量子计算和量子纠错研究进展. 物理学报, 2022, 71(16): 160305. doi: 10.7498/aps.71.20220635
    [4] 王晨旭, 贺冉, 李睿睿, 陈炎, 房鼎, 崔金明, 黄运锋, 李传锋, 郭光灿. 量子计算与量子模拟中离子阱结构研究进展. 物理学报, 2022, 71(13): 133701. doi: 10.7498/aps.71.20220224
    [5] 周宗权. 量子存储式量子计算机与无噪声光子回波. 物理学报, 2022, 71(7): 070305. doi: 10.7498/aps.71.20212245
    [6] 宿非凡, 杨钊华, 赵寿宽, 严海生, 田野, 赵士平. 铌基超导量子比特及辅助器件的制备. 物理学报, 2022, 71(5): 050303. doi: 10.7498/aps.71.20211865
    [7] 王宁, 王保传, 郭国平. 硅基半导体量子计算研究进展. 物理学报, 2022, 71(23): 230301. doi: 10.7498/aps.71.20221900
    [8] 张结印, 高飞, 张建军. 硅和锗量子计算材料研究进展. 物理学报, 2021, 70(21): 217802. doi: 10.7498/aps.70.20211492
    [9] 张诗豪, 张向东, 李绿周. 基于测量的量子计算研究进展. 物理学报, 2021, 70(21): 210301. doi: 10.7498/aps.70.20210923
    [10] 文炼均, 潘东, 赵建华. 从高质量半导体/超导体纳米线到马约拉纳零能模. 物理学报, 2021, 70(5): 058101. doi: 10.7498/aps.70.20201750
    [11] 陈晨, 刘琴, 张童, 封东来. 电子型FeSe基高温超导体的磁通束缚态与Majorana零能模. 物理学报, 2021, 70(1): 017401. doi: 10.7498/aps.70.20201673
    [12] 梁奇锋, 王志, 川上拓人, 胡晓. 拓扑超导Majorana束缚态的探索. 物理学报, 2020, 69(11): 117102. doi: 10.7498/aps.69.20190959
    [13] 李牮. 基于Yu-Shiba-Rusinov态的拓扑超导理论. 物理学报, 2020, 69(11): 117401. doi: 10.7498/aps.69.20200831
    [14] 梁超, 张洁, 赵可, 羊新胜, 赵勇. 拓扑超导体FeSexTe1–x单晶超导性能与磁通钉扎. 物理学报, 2020, 69(23): 237401. doi: 10.7498/aps.69.20201125
    [15] 何映萍, 洪健松, 刘雄军. 马约拉纳零能模的非阿贝尔统计及其在拓扑量子计算的应用. 物理学报, 2020, 69(11): 110302. doi: 10.7498/aps.69.20200812
    [16] 范桁. 量子计算与量子模拟. 物理学报, 2018, 67(12): 120301. doi: 10.7498/aps.67.20180710
    [17] 赵士平, 刘玉玺, 郑东宁. 新型超导量子比特及量子物理问题的研究. 物理学报, 2018, 67(22): 228501. doi: 10.7498/aps.67.20180845
    [18] 赵娜, 刘建设, 李铁夫, 陈炜. 超导量子比特的耦合研究进展. 物理学报, 2013, 62(1): 010301. doi: 10.7498/aps.62.010301
    [19] 叶 宾, 须文波, 顾斌杰. 量子Harper模型的量子计算鲁棒性与耗散退相干. 物理学报, 2008, 57(2): 689-695. doi: 10.7498/aps.57.689
    [20] 叶 宾, 谷瑞军, 须文波. 周期驱动的Harper模型的量子计算鲁棒性与量子混沌. 物理学报, 2007, 56(7): 3709-3718. doi: 10.7498/aps.56.3709
计量
  • 文章访问数:  8938
  • PDF下载量:  435
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-03-31
  • 修回日期:  2022-04-26
  • 上网日期:  2022-08-07
  • 刊出日期:  2022-08-20

/

返回文章
返回