Majorana准粒子与超导体-半导体异质纳米线

于春霖; 张浩

doi:10.7498/aps.69.20200177

摘要

Majorana准粒子是凝聚态物理版本的Majorana费米子. 由于Majorana准粒子间的交换操作服从非阿贝尔统计, 并基于此可构建更稳定的量子计算机, 近年来在凝聚态物理界引起广泛关注. 为帮助初学者快速理解Majorana准粒子的形成机理, 本文回顾了在一维超导体-半导体异质纳米线系统中Majorana准粒子模型的提出和理论演化过程, 介绍Kitaev链模型并分析了模型中各要素所起的作用. 还介绍了典型Majorana器件的构成和测量方法, 并结合最新的实验进展对探测到的零能电导峰进行了分析和述评. 最后对超越一维系统的超导体-半导体异质系统的实验前景进行了展望.

关键词:

Abstract

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.

Keywords:

作者及机构信息

于春霖¹,
张浩^2,3

1.
中国长城量子实验室, 长沙　410006

2.
清华大学物理系, 低维量子物理国家重点实验室, 北京　100084

3.
北京量子信息科学研究院, 北京　100193

通信作者: 张浩, hzquantum@mail.tsinghua.edu.cn

Authors and contacts

Yu Chun-Lin¹,
Zhang Hao^2,3

1.
China Greatwall Quantum Laboratory, Changsha 410006, China

2.
Department of Physics, Tsinghua University, Beijing 100084, China

3.
Beijing Academy of Quantum Information Sciences, Beijing 100193, China

Corresponding author: Zhang Hao, hzquantum@mail.tsinghua.edu.cn

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 Kitaev链模型示意图^[17]

Fig. 1. Schematic of Kitaevchain model^[17].

下载: 全尺寸图片幻灯片

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

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

下载: 全尺寸图片幻灯片

图 3 超导体-半导体异质纳米线体系在不同的∆-E_z-α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

Fig. 3. Energy dispersion of a superconductor-semiconductor hybrid nanowire at different ∆-E_z-α 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.

下载: 全尺寸图片幻灯片

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]

Fig. 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].

下载: 全尺寸图片幻灯片

map

[1]	Arute F, Arya K, Babbush R, Martinis JM 2019 Nature 574 505 Google Scholar
[2]	Kitaev A 2003 Ann. Phys. 303 2 Google Scholar
[3]	Wilczek F 1982 Phys. Rev. Lett. 49 957 Google Scholar
[4]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[5]	Majorana E 1937 Nuovo Cimento 14 171 Google Scholar
[6]	Moore G, Read N 1991 Nucl. Phys. 360 362 Google Scholar
[7]	Read N, Green D 2000 Phys. Rev. B 61 10267 Google Scholar
[8]	Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 Google Scholar
[9]	Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. 88 020407 Google Scholar
[10]	Sau JD, Tewari S, Lutchyn R M, Stanescu T D, Das Sarma S 2010 Phys. Rev. B 82 214509 Google Scholar
[11]	Alicea J 2010 Phys. Rev. B 81 125318 Google Scholar
[12]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[13]	Oreg Y, Refael G, Von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[14]	Dirac P A M 1931 Proc. R. Soc. London, Ser. A 133 60
[15]	Anderson C D 1933 Phys. Rev. 43 491 Google Scholar
[16]	Wilczek F 2009 Nat. Phys. 5 614 Google Scholar
[17]	Leijnse M, Flensberg K 2012 Semicond. Sci. Technol. 27 124003 Google Scholar
[18]	Kitaev A Y 2001 Phys.Usp. 44 131 Google 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 344 283 Google Scholar
[20]	Fasth C, Fuhrer A, Samuelson L, Golovach VN, Loss D 2007 Phys. Rev. Lett. 98 266801 Google 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 3151 Google Scholar
[22]	van Weperen I, Plissard S R, Bakkers E P A M, Frolov S M, Kouwenhoven L P 2013 Nano Lett. 13 387 Google Scholar
[23]	Nadj-Perge S, Frolov S M, Bakkers E P A M, Kouwenhoven L P 2010 Nature 468 1084 Google 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 309 272 Google 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 1003 Google Scholar
[27]	Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414 Google Scholar
[28]	Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887 Google 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 1557 Google Scholar
[30]	Rainis D, Trifunovic L, Klinovaja J, Loss D 2013 Phys. Rev. B 87 24515 Google Scholar
[31]	Stanescu T D, Lutchyn R M, Das Sarma S 2011 Phys. Rev. B 84 144522 Google 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 2690 Google Scholar
[33]	Zhang H, Gül Ö, Kouwenhoven L P, et al. 2017 Nat. Commun 8 16025 Google 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 3482 Google 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. 13 192 Google 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. 14 400 Google Scholar
[37]	Chang W, Albrecht S M, Jespersen T S, Kuemmeth F, Krogstrup P, Nygård J, Marcus C M 2015 Nat. Nanotechnol. 10 232 Google 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 548 434 Google 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 037703 Google 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 103049 Google 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 187702 Google Scholar
[46]	Woods B D, Stanescu T D, Das Sarma S 2018 Phys. Rev. B 98 035428 Google 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 100503 Google Scholar
[49]	Lee E J H, Jiang X, Aguado R, Katsaros G, Lieber C M, De Franceschi S 2012 Phys. Rev. Lett. 109 186802 Google Scholar
[50]	Liu C X, Sau J D, Stanescu T D, Das Sarma S 2017 Phys. Rev. B 96 075161 Google Scholar
[51]	Prada E, San-Jose P, Aguado R 2012 Phys. Rev. B 86 180503 Google Scholar
[52]	Reeg C, Dmytruk O, Chevallier D, Loss D, Klinovaja J 2018 Phys. Rev. B 98 245407 Google Scholar
[53]	Vuik A, Nijholt B, Akhmerov A, Wimmer M 2019 SciPost Phys. 7 061 Google Scholar
[54]	Cao Z, Zhang H, Lü H F, He W X, Lu H Z, Xie X C 2019 Phys. Rev. Lett. 122 147701 Google 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. 7 412 Google Scholar
[57]	Fu L 2010 Phys. Rev. Lett. 104 056402 Google Scholar
[58]	Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Marcus C M 2016 Nature 531 206 Google 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 4801 Google Scholar
[60]	Sherman D, Yodh J S, Albrecht S M, Nygård J, Krogstrup P, Marcus C M 2017 Nat. Nanotechnol. 12 212 Google Scholar
[61]	Liu D, Cao Z, Zhang H, Liu D E 2020 Phys. Rev. B 101 081406 Google Scholar
[62]	Chiu C K, Sau J D, Das Sarma S 2017 Phys. Rev. B 96 054504 Google Scholar
[63]	Takei S, Fregoso B M, Hui H Y, Lobos A M, Das Sarma S 2013 Phys. Rev. Lett. 110 186803 Google Scholar
[64]	Hyart T, Van Heck B, Fulga I C, Burrello M, Akhmerov A R, Beenakker C W J 2013 Phys. Rev. B 88 035121 Google 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 012001 Google 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 235305 Google Scholar
[68]	Vijay S, Fu L 2016 Phys. Rev. B 94 235446 Google Scholar
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Majorana准粒子与超导体-半导体异质纳米线