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Random-Gate-Voltage Induced Al'tshuler–Aronov–Spivak Effect in Topological Edge States |
| Kun Luo1, Wei Chen1,2*, Li Sheng1,2, and D. Y. Xing1,2 |
1National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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| Cite this article: |
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Kun Luo, Wei Chen, Li Sheng et al 2021 Chin. Phys. Lett. 38 110302 |
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Abstract Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the random-gate-voltage induced $\varPhi_0/2$-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the $\varPhi_0/2$-period Al'tshuler–Aronov–Spivak oscillation proportional to $\sin^2(2\pi\varPhi/\varPhi_0)$ by quenching the $\varPhi_0$-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced $\pi$ Berry phase is key to such weak antilocalization behavior with zero return probability at $\varPhi=0$. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at $\varPhi=0$. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.
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Received: 09 August 2021
Editors' Suggestion
Published: 28 October 2021
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| PACS: |
03.65.Vf
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(Phases: geometric; dynamic or topological)
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73.20.-r
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(Electron states at surfaces and interfaces)
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75.47.-m
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(Magnetotransport phenomena; materials for magnetotransport)
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| Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 12074172, 11674160, and 11974168), the Startup Grant at Nanjing University, the State Key Program for Basic Researches of China (Grant No. 2017YFA0303203), and the Excellent Programme at Nanjing University. |
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| [1] | Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057 |
| [2] | Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045 |
| [3] | Huang H, Xu Y, Wang J, and Duan W 2017 WIREs: Comput. Mol. Sci. 7 e1296 |
| [4] | Wang Z, Jin K H, and Liu F 2017 WIREs: Comput. Mol. Sci. 7 e1304 |
| [5] | Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801 |
| [6] | Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106802 |
| [7] | Bernevig B A, Hughes T L, and Zhang S C 2006 Science 314 1757 |
| [8] | Liu C, Hughes T L, Qi X L, Wang K, and Zhang S C 2008 Phys. Rev. Lett. 100 236601 |
| [9] | König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, and Zhang S C 2007 Science 318 766 |
| [10] | Knez I, Du R R, and Sullivan G 2011 Phys. Rev. Lett. 107 136603 |
| [11] | Knez I, Rettner C T, Yang S H, Parkin S S P, Du L, Du R R, and Sullivan G 2014 Phys. Rev. Lett. 112 026602 |
| [12] | Du L, Knez I, Sullivan G, and Du R R 2015 Phys. Rev. Lett. 114 096802 |
| [13] | Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407 |
| [14] | Fu L and Kane C L 2009 Phys. Rev. B 79 161408 |
| [15] | Kitaev A Y 2001 Phys.-Usp. 44 131 |
| [16] | Nguyen B M, Kiselev A A, Noah R, Yi W, Qu F, Beukman A J A, de Vries F K, van Veen J, Nadj-Perge S, Kouwenhoven L P, Kjaergaard M, Suominen H J, Nichele F, Marcus C M, Manfra M J, and Sokolich M 2016 Phys. Rev. Lett. 117 077701 |
| [17] | Nichele F, Suominen H J, Kjaergaard M, Marcus C M, Sajadi E, Folk J A, Qu F, Beukman A J A, de Vries F K, van Veen J, Nadj-Perge S, Kouwenhoven L P, Nguyen B M, Kiselev A A, Yi W, Sokolich M, Manfra M J, Spanton E M, and Moler K A 2016 New J. Phys. 18 083005 |
| [18] | Mueller S, Mittag C, Tschirky T, Charpentier C, Wegscheider W, Ensslin K, and Ihn T 2017 Phys. Rev. B 96 075406 |
| [19] | Sazgari V, Sullivan G, and Kaya İ 2019 Phys. Rev. B 100 041404 |
| [20] | de Vries F K, Timmerman T, Ostroukh V P, van Veen J, Beukman A J A, Qu F, Wimmer M, Nguyen B M, Kiselev A A, Yi W, Sokolich M, Manfra M J, Marcus C M, and Kouwenhoven L P 2018 Phys. Rev. Lett. 120 047702 |
| [21] | de Vries F K, Sol M L, Gazibegovic S, Veld R L M O H, Balk S C, Car D, Bakkers E P A M, Kouwenhoven L P, and Shen J 2019 Phys. Rev. Res. 1 032031 |
| [22] | Hou C Y, Kim E A, and Chamon C 2009 Phys. Rev. Lett. 102 076602 |
| [23] | Schmidt T L 2011 Phys. Rev. Lett. 107 096602 |
| [24] | Das S and Rao S 2011 Phys. Rev. Lett. 106 236403 |
| [25] | Soori A, Das S, and Rao S 2012 Phys. Rev. B 86 125312 |
| [26] | Edge J M, Li J, Delplace P, and Büttiker M 2013 Phys. Rev. Lett. 110 246601 |
| [27] | Romeo F and Citro R 2014 Phys. Rev. B 90 155408 |
| [28] | Chen W, Deng W Y, Hou J M, Shi D N, Sheng L, and Xing D Y 2016 Phys. Rev. Lett. 117 076802 |
| [29] | Al'tshuler B, Aronov A, and Spivak B 1981 JETP Lett. 33 94 |
| [30] | Al'tshuler B, Aronov A, Spivak B, Sharvin D Y, and Sharvin Y V 1982 JETP Lett. 35 588 |
| [31] | Strunz J, Wiedenmann J, Fleckenstein C, Lunczer L, Beugeling W, Müller V L, Shekhar P, Ziani N T, Shamim S, Kleinlein J et al. 2020 Nat. Phys. 16 83 |
| [32] | Rothe D, Reinthaler R, Liu C, Molenkamp L, Zhang S, and Hankiewicz E 2010 New J. Phys. 12 065012 |
| [33] | Ström A, Johannesson H, and Japaridze G 2010 Phys. Rev. Lett. 104 256804 |
| [34] | Väyrynen J I and Ojanen T 2011 Phys. Rev. Lett. 106 076803 |
| [35] | Bardarson J H and Moore J E 2013 Rep. Prog. Phys. 76 056501 |
| [36] | Groth C W, Wimmer M, Akhmerov A R, and Waintal X 2014 New J. Phys. 16 063065 |
| [37] | Haidekker G T, Hoffman S, Recher P, Klinovaja J, and Loss D 2020 Phys. Rev. Lett. 125 157701 |
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