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Majorana quasi-particles and superconductor-semiconductor hybrid nanowires

Yu Chun-Lin Zhang Hao

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Majorana quasi-particles and superconductor-semiconductor hybrid nanowires

Yu Chun-Lin, Zhang Hao
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  • Majorana fermions are known for being their own anti-particles. As the condensed matter version of Majorana fermions, Majorana quasiparticles have drawn extensive interests for being an ideal candidate for building a fault-tolerant quantum computer, due to their non-abelian statistics. This paper provides an introduction for beginners to the rapidly growing research field of Majorana quasiparticles focusing on one dimensional semiconductor nanowire-superconductor hybrid system. We aim to help readers to quickly understand Majorana quasiparticles and its formation mechanism and the latest experimental results. We first review the theoretical model of the Majorana quasiparticles with its historical background. We then discuss the Kitaev chain and analyze its key elements. We also introduce typical Majorana devices and their corresponding measurement methods. Furthermore, we discuss the observation of robust signatures of Majorana zero modes in recent experiments, with particular attention to tunneling conductance measurements. Finally, we give prospects on future experiments for advancing one dimensional semiconductor nanowire-superconductor hybrid system.
      Corresponding author: Zhang Hao, hzquantum@mail.tsinghua.edu.cn
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    Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407Google Scholar

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

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    Dirac P A M 1931 Proc. R. Soc. London, Ser. A 133 60

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  • 图 1  Kitaev链模型示意图[17]

    Figure 1.  Schematic of Kitaevchain model[17].

    图 2  一维超导体-半导体异质结构与Majorana准粒子态波函数示意图

    Figure 2.  Schematic sketch of a nanowire-superconductor hybrid structure and the wave function of the Majorana quasiparticle.

    图 3  超导体-半导体异质纳米线体系在不同的∆-Ez配置下的能量色散图谱(μ = 0). 其中, 蓝线和红线分别对应两个自旋分支(SOI方向投影), 实线对应粒子项分支, 虚线对应空穴项分支

    Figure 3.  Energy dispersion of a superconductor-semiconductor hybrid nanowire at different ∆-Ez configurations with μ = 0. Blue and red lines correspond to the two spin branch (along SOI direction), respectively, solid lines are particle branches, while dashed line are hole branches.

    图 4  超导体-半导体异质器件与探测到的零能电导峰 (a)−(c) NbTiN-InSb器件与零能电导峰[26]; (d)−(f) 全外延Al-InAs纳米线及纯净超导能隙中的零能电导峰[29]; (g), (h)全外延Al-InSb纳米线器件中量子化的零能电导峰[40]

    Figure 4.  Superconductor-semiconductor hybrid devices and the detected zero-energy conductance peaks: (a)−(c) NbTiN-InSb nanowire device and zero-energy conductance peak[26]; (d)−(f) Fully epitaxial Al-InAs nanowire and zero-energy conductance peak in hard gap[29]; (g), (h) Quantized zero-energy conductance peak in fully epitaxial Al-InSb nanowire devices[40].

  • [1]

    Arute F, Arya K, Babbush R, Martinis JM 2019 Nature 574 505Google Scholar

    [2]

    Kitaev A 2003 Ann. Phys. 303 2Google Scholar

    [3]

    Wilczek F 1982 Phys. Rev. Lett. 49 957Google Scholar

    [4]

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

    [5]

    Majorana E 1937 Nuovo Cimento 14 171Google Scholar

    [6]

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

    [7]

    Read N, Green D 2000 Phys. Rev. B 61 10267Google 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. 88 020407Google Scholar

    [10]

    Sau JD, Tewari S, Lutchyn R M, Stanescu T D, Das Sarma S 2010 Phys. Rev. B 82 214509Google Scholar

    [11]

    Alicea J 2010 Phys. Rev. B 81 125318Google Scholar

    [12]

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

    [13]

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

    [14]

    Dirac P A M 1931 Proc. R. Soc. London, Ser. A 133 60

    [15]

    Anderson C D 1933 Phys. Rev. 43 491Google Scholar

    [16]

    Wilczek F 2009 Nat. Phys. 5 614Google Scholar

    [17]

    Leijnse M, Flensberg K 2012 Semicond. Sci. Technol. 27 124003Google Scholar

    [18]

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

    [19]

    Hicks C W, Brodsky D O, Yelland E A, Gibbs A S, Bruin J A N, Barber M E, Edkins S D, Nishimura K, Yonezawa S, Maeno Y, Mackenzie A P 2014 Science 344 283Google Scholar

    [20]

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

    [21]

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

    [22]

    van Weperen I, Plissard S R, Bakkers E P A M, Frolov S M, Kouwenhoven L P 2013 Nano Lett. 13 387Google Scholar

    [23]

    Nadj-Perge S, Frolov S M, Bakkers E P A M, Kouwenhoven L P 2010 Nature 468 1084Google Scholar

    [24]

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

    [25]

    Nilsson H A, Samuelsson P, Caroff P, Xu H Q 2012 [Nano Lett. 12 26

    [26]

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

    [27]

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

    [28]

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

    [29]

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

    [30]

    Rainis D, Trifunovic L, Klinovaja J, Loss D 2013 Phys. Rev. B 87 24515Google Scholar

    [31]

    Stanescu T D, Lutchyn R M, Das Sarma S 2011 Phys. Rev. B 84 144522Google Scholar

    [32]

    Gül Ö, Zhang H, De Vries F K, Van Veen J, Zuo K, Mourik V, Conesa-Boj S, Nowak M P, Van Woerkom D J, Quintero-Pérez M, Cassidy M C, Geresdi A, Koelling S, Car D, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2017 Nano Lett. 17 2690Google Scholar

    [33]

    Zhang H, Gül Ö, Kouwenhoven L P, et al. 2017 Nat. Commun 8 16025Google Scholar

    [34]

    Kammhuber J, Cassidy M C, Zhang H, Gül Ö, Pei F, de Moor M W A, Nijholt B, Watanabe K, Taniguchi T, Car D, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2016 Nano Lett. 16 3482Google Scholar

    [35]

    Gül Ö, Zhang H, Bommer J D S, De Moor M W A, Car D, Plissard S R, Bakkers E P A M, Geresdi A, Watanabe K, Taniguchi T, Kouwenhoven LP 2018 Nat. Nanotechnol. 13 192Google Scholar

    [36]

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

    [37]

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

    [38]

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

    [39]

    Gazibegovic S, Zhang H, Bakkers E P A M, et al. 2017 Nature 548 434Google Scholar

    [40]

    Zhang H, Liu C X, Gazibegovic S, et al. 2017 arxiv 1710.10701

    [41]

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

    [42]

    Antipov A E, Bargerbos A, Winkler G W, Bauer B, Rossi E, Lutchyn R M 2018 Phys. Rev. X 8 031041

    [43]

    Mikkelsen A E G, Kotetes P, Krogstrup P, Flensberg K 2018 Phys. Rev. X 8 031040

    [44]

    De Moor M W A, Bommer J D S, Zhang H, et al. 2018 New J. Phys 20 103049Google Scholar

    [45]

    Bommer J D S, Zhang H, Gül Ö, Nijholt B, Wimmer M, Rybakov FN, Garaud J, Rodic D, Babaev E, Troyer M, Car D, Plissard S R, Bakkers E P A M, Watanabe K, Taniguchi T, Kouwenhoven L P 2019 Phys. Rev. Lett. 122 187702Google Scholar

    [46]

    Woods B D, Stanescu T D, Das Sarma S 2018 Phys. Rev. B 98 035428Google Scholar

    [47]

    Moore C, Zeng C, Stanescu T D, Tewari S 2018 Phys. Rev. B 94 155314

    [48]

    Kells G, Meidan D, Brouwer PW 2012 Phys. Rev. B 86 100503Google Scholar

    [49]

    Lee E J H, Jiang X, Aguado R, Katsaros G, Lieber C M, De Franceschi S 2012 Phys. Rev. Lett. 109 186802Google Scholar

    [50]

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

    [51]

    Prada E, San-Jose P, Aguado R 2012 Phys. Rev. B 86 180503Google Scholar

    [52]

    Reeg C, Dmytruk O, Chevallier D, Loss D, Klinovaja J 2018 Phys. Rev. B 98 245407Google Scholar

    [53]

    Vuik A, Nijholt B, Akhmerov A, Wimmer M 2019 SciPost Phys. 7 061Google Scholar

    [54]

    Cao Z, Zhang H, Lü H F, He W X, Lu H Z, Xie X C 2019 Phys. Rev. Lett. 122 147701Google Scholar

    [55]

    Car D, Conesa-Boj S, Zhang H, Op het Veld R L M, de Moor M W A, Fadaly E M T, Gül Ö, Kölling S, Plissard S R, Toresen V, Wimmer M T, Watanabe K, Taniguchi T, Kouwenhoven L P, Bakkers E P A M 2017 Nano Lett. 17 7

    [56]

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

    [57]

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

    [58]

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

    [59]

    Shen J, Heedt S, Borsoi F, van Heck B, Gazibegovic S, Op Het Veld R L M, Car D, Logan J A, Pendharkar M, Ramakers S J J, Wang G, Xu D, Bouman D, Geresdi A, Palmstrøm C J, Bakkers E P A M, Kouwenhoven LP 2018 Nat. Commun. 9 4801Google Scholar

    [60]

    Sherman D, Yodh J S, Albrecht S M, Nygård J, Krogstrup P, Marcus C M 2017 Nat. Nanotechnol. 12 212Google Scholar

    [61]

    Liu D, Cao Z, Zhang H, Liu D E 2020 Phys. Rev. B 101 081406Google Scholar

    [62]

    Chiu C K, Sau J D, Das Sarma S 2017 Phys. Rev. B 96 054504Google Scholar

    [63]

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

    [64]

    Hyart T, Van Heck B, Fulga I C, Burrello M, Akhmerov A R, Beenakker C W J 2013 Phys. Rev. B 88 035121Google Scholar

    [65]

    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 031016

    [66]

    Plugge S, Rasmussen A, Egger R, Flensberg K 2017 New J. Phys. 19 012001Google Scholar

    [67]

    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

    [68]

    Vijay S, Fu L 2016 Phys. Rev. B 94 235446Google Scholar

    [69]

    Fadaly E M T, Zhang H, Conesa-Boj S, Car D, Gül Ö, Plissard S R, Op het Veld R L M, Kölling S, Kouwenhoven L P, Bakkers E P A M 2017 Nano Lett. 17 6511Google Scholar

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    Vaitiekenas S, Whiticar AM, Deng M T, Krizek F, Sestoft J E, Palmstrøm CJ, Marti-Sanchez S, ArbiolJ, Krogstrup P, Casparis L, Marcus C M 2018 Phys. Rev. Lett. 121 147701Google Scholar

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Metrics
  • Abstract views:  9794
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Publishing process
  • Received Date:  04 February 2020
  • Accepted Date:  23 February 2020
  • Published Online:  05 April 2020

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