Enhanced topological superconductivity in an asymmetrical planar Josephson junction

doi:10.1088/1674-1056/acaa29

Abstract As a platform for holding Majorana zero models (MZMs), the two-dimensional planar topological Josephson junction that can be used as carriers for topological quantum computing faces some challenges. One is a combination of mirror and time-reversal symmetries may make the system hold multiple pairs of MZMs. The other is that a soft gap dominated by a large momentum occurs in a clean system. To solve these problems, asymmetric junction can be introduced. Breaking this symmetry changes the symmetry class from class BDI to class D, and only a single pair of MZMs can be left at the boundary of the system. We numerically study four cases that create an asymmetric system and find out different superconducting pairing potential, different coupling coefficients between two-dimensional electron gases (2DEGs) and two superconducting bulks, different widths of two superconducting bulks make the gap of the system decrease at the optimal value, but make the gap at the minimum value increases. And the zigzag-shape quasi-one-dimensional junction eliminates the large momentum parallel to the junction and enhances the gap at the large momentum. However, the zigzag-shape junction cannot increase the gap at the region of multiple pairs of MZMs in a symmetric system. We show that by combining zigzag-shape junction with different coupling coefficients, the system can maintain a large gap (≈0.2 Δ) in a wide region of the parameter space.

Keywords: topological superconductivity planar Josephson junction Majorana zero modes

Received: 08 August 2022
Revised: 04 December 2022
Accepted manuscript online: 09 December 2022

PACS:	03.67.Lx	(Quantum computation architectures and implementations)
	74.78.-w	(Superconducting films and low-dimensional structures)
	74.45.+c	(Proximity effects; Andreev reflection; SN and SNS junctions)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11974271).

Corresponding Authors: Yu Zhang
E-mail: 646907259@qq.com

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Erhu Zhang(张二虎) and Yu Zhang(张钰) Enhanced topological superconductivity in an asymmetrical planar Josephson junction 2023 Chin. Phys. B 32 040307

[1] Kitaev A Y 2001 Phys. Usp. 44 131
[2] Kitaev A Y 2003 Ann. Phys. 303 2
[3] Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
[4] Alicea J 2012 Rep. Prog. Phys. 75 076501
[5] Elliott S R and Franz M 2015 Rev. Mod. Phys. 87 137
[6] Leijnse M and Flensberg K 2012 Semicond. Sci. Technol. 27 124003
[7] Das Sarma S, Freedman M and Nayak C 2015 NPJ Quantum Inform. 1 15001
[8] Beenakker C and Kouwenhoven L 2016 Nat. Phys. 12 618
[9] Aguado R 2017 Riv. Nuovo Cim. 40 523
[10] Chen W Q, Wang J C, Wu Y J, Qi J J, Liu J and Xie X C 2022 Phys. Rev. B 105 054507
[11] Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407
[12] Sau J D, Lutchyn R M, Tewari S and Das Sarma S 2010 Phys. Rev. Lett. 104 040502
[13] Fujimoto S 2008 Phys. Rev. B 77 220501
[14] Sato M, Takahashi Y and Fujimoto S 2010 Phys. Rev. B 82 134521
[15] Alicea J 2010 Phys. Rev. B 81 125318
[16] Lutchyn R M, Sau J D and Das Sarma S 2010 Phys. Lett. 105 077001
[17] Oreg Y, Refael G and Von Oppen F 2011 Phys. Rev. Lett. 105 177002
[18] Potter A C and Lee P A 2011 Phys. Rev. B 83 094525
[19] Klinovaja J, Stano P, Yazdani A and Loss D 2013 Phys. Rev. Lett. 111 186805
[20] Nadj-Perge S, Drozdov I K, Bernevig B A and Yazdani A 2013 Phys. Rev. B 88 020407
[21] Lutchyn R M, Bakkers E P A M, Kouwenhoven L P, Krogstrup P, Marcus C M and Oreg Y 2018 Nat. Rev. Mater. 3 52
[22] Chang W, Albrecht S M, Jespersen T S, Kuemmeth F, Krogstrup P, Nygård J and Marcus C M 2015 Nat. Nanotechnol. 10 232
[23] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M and Kouwenhoven L P 2012 Science 336 1003
[24] Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P and Xu H Q 2012 Nano Lett. 12 6414
[25] Das A, Ronen Y, Oreg Y, Heiblum M and Shtrikman H 2012 Nat. Phys. 8 887
[26] Fabrizio N, Asbjorn C C D, Alexander M W, Eoin C T O'Farrell, Henri J Suominen, Antonio F, Tian W, Gardner G C, Candice T, Anthony T Hatke, Krogstrup P, Manfra M J, Flensberg K and Marcus C M 2017 Phys. Rev. Lett. 119 136803
[27] Önder G, 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 and Kouwenhoven L P 2018 Nat. Nanotechnol. 13 192
[28] Zhang H, Liu C X, Gazibegovic S, Xu D, Logan J A, Wang G Z, Nick van Loo, Bommer J D S, de Moor M W A, Car D, Op het Veld R L M, Petrus J van Veldhoven, Koelling S, Verheijen M A, Pendharkar M, Pennachio D J, Shojaei B, Lee J S, Palmstrom C J, Bakkers E P A M, Das Sarma S and Kouwenhoven L P 2018 Nature 556 74
[29] Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygard J, Krogstrup P and Marcus C M 2016 Nature 531 206
[30] Nadj-perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, Allan H. MacDonald, Bernevig B A and Yazdani A 2014 Science 346 602
[31] Feldman B E, Randeria M T, Li J, Jeon S, Xie Y L, Wang Z J, Drozdov I K, Andrei Bernevig B and Yazdani A 2014 Nat. Phys. 13 286
[32] Bommer J D S, Zhang H, Gül Ö, Nijholt B, Wimmer M, Rybakov F N, Garaud J, Rodic D, Babaev E, Troyer M, Car D, Plissard S R, Bakkers E P A M, Watanabe K, Taniguchi T and Kouwenhoven L P 2019 Phys. Rev. Lett. 122 187702
[33] Sun H H, Zhang K W, Hu L H, Li C, Wang G Y, Ma H Y, Xu Z A, Gao C L, Guan D D, Li Y Y, Liu C, Qian D, Zhou Y, Fu L, Li S C, Zhang F C and Jia J F 2016 Phys. Rev. Lett. 116 257003
[34] Wang D F , Kong L Y, Fan P, Chen H, Zhu S Y, Liu W Y, Cao L, Sun Y J, Du S X, Schneeloch J, Zhong R D, Gu G D, Fu L, Ding H and Gao H J 2018 Science 362 333
[35] Qin L, Chen C, Tong Z, et al. 2018 Phys. Rev. X 8 041056
[36] Peng Z, Koichiro Y, Takahiro H, Yuichi O, Takeshi K, Kozo O, Wang Z J, W J S, Gu G D, Hong D and Shin S 2018 Science 360 182
[37] Farrell E C T O, Drachmann A C C, HelI M, Fornieri A, Whiticar A W, Hansen E B, Gronin S, Gardner G C, Thomas C, Manfra M J, Flensberg K, Marcus C M and Nichele F 2018 Phys. Rev. Lett. 121 256803
[38] Joon S L, Borzoyeh S, Mihir P, Anthony P M, Younghyun K, Henri J S, Morten K, Fabrizio N, Hao Z, Charles M M and Chris J P 2019 Nano Lett. 19 3083
[39] William M, William F S, Joseph Y, Mehdi H, Wendy L S, Stefan P S, Asher C, Leff T C, Kaushini S Wickramasinghe, Matthieu C Dartiailh, Igor Ž and Javad S 2020 ACS Appl. Electron. Mater. 2 2351
[40] Pankratova N, Lee H, Kuzmin R, Wickramasinghe K, Maye W Y J, Vavilov M G, Shabani J and Manucharyan V E 2020 Phys. Rev. X 10 031051
[41] Dartiailh M C, Mayer W, Yuan J, Wickramasinghe K S, Matos-Abiague A, Zutic I and Shabani J 2012 Phys. Rev. Lett. 126 036802
[42] Moehle C M, Ke C T, Wang Q Z, Thomas C, Di Xiao, Karwal S, Lodari M, Vincent van de Kerkhof, Termaat R, Gardner G C, Scappucci G, Manfra M J and Goswami S 2021 Nano Lett. 21 9990
[43] Fornieri A, Whiticar A M, Setiawan F, Portolés E, Drachmann A C C, Keselman A, Gronin S, Thomas C, Wang T, Kallaher R, Gardner G C, Berg E, Manfra M J, Stern A, Marcus C M and Nichele F 2019 Nature 569 89
[44] Ren H, Pientka F, Hart S, Pierce A, Kosowsky M, Lunczer L, Schlereth R, Scharf B, Hankiewicz E M, Molenkamp L W, Halperin B I and Yacoby A 2019 Nature 569 93
[45] Pientka F, Keselman A, Berg E, Yacob A, Stern A and Halperin B I 2017 Phys. Rev. X 7 021023
[46] Tom L, Bas N, Michael W and Anton R A 2020 Phys. Rev. Lett. 125 086802
[47] Setiawan F, Ady S and Erez B 2019 Phys. Rev. B 99 220506
[48] Haim A and Stern A 2019 Phys. Rev. Lett. 122 126801
[49] Hell M, Leijnse M and Flensberg K 2017 Phys. Rev. Lett. 118 107701
[50] Tewari S and Sau J D 2012 Phys. Rev. Lett. 109 150408
[51] Setiawan F, Wu C T and Levin K 2019 Phys. Rev. B 99 174511
[52] Zhang Y, Guo K and Liu J 2020 Phys. Rev. B 102 245403

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