-
Majorana fermions, particles that are their own antiparticles, have attracted significant attention in condensed matter physics due to their exotic properties and potential applications in fault-tolerant topological quantum computing. While nanowire-superconductor hybrid systems and topological insulator-superconductor heterostructures, are considered the most promising platforms for realizing Majorana fermions, recent experimental progress has been overshadowed by controversies, including the retraction of several high-profile papers claiming their observation. These controversies fundamentally originate from experimental data being selectively presented to conform to oversimplified theoretical models. Conventional phenomenological approaches, which model Majorana fermions through simplified effective Hamiltonians, neglect crucial experimental complexities such as quasiparticle excitations in superconductors and the effects of strong proximity tunneling and high magnetic fields. Consequently, they fail to predict the correct parameter regimes for Majorana fermion emergence in realistic devices, leading to false-positive signals in experiments. To overcome these challenges, we develop a comprehensive "dressed Majorana" theory that treats both the electrons in nanowire and superconducting quasiparticle excitations on equal footing. Our results reveal stringent conditions necessary for realization of Majorana fermions: precise alignment of chemical potentials (within ~1 meV in a 1 eV tuning range) and careful control of tunneling strength and magnetic field strengths. These findings explain the persistent absence of definitive signatures in experiments and provide quantitative guidelines for future studies. Notably, for alternative platforms like quantum dot-based "poor mans Majorana" syst ems, our analysis shows that the obtained Majorana wavefunctions are localized at both ends of the superconductor, demonstrating the superconducting components essential role in these configurations. In summary, our work not only clarifies the current controversies surrounding detection of Majorana fermions but also establishes a robust theoretical foundation guiding future experimental efforts toward unambiguous Majorana fermion observation.
-
Keywords:
- Majorana fermions (Zero modes) /
- Hybrid superconducting system /
- Topological superconducting phase
-
[1] Majorana E 1937 Nuovo Cimento 14 171
[2] Kitaev A Y 2001 Phys.-Uspekhi 44 131
[3] Kitaev A Yu 2003 Ann. Phys. 303 2
[4] Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083
[5] Yu C L, Zhang H 2020 Acta Phys. Sin. 69 077303（in Chinese）[于春霖, 张浩 2020 物理学报 69 077303]
[6] He Y P, Hong J S, Liu X J 2020 Acta Phys. Sin. 69 110302（in Chinese）[何映萍, 洪健松, 刘雄军 2020 物理学报 69 110302]
[7] Read N, Green D 2000 Phys. Rev. B 61 10267
[8] Alicea J 2012 Rep. Prog. Phys. 75 076501
[9] Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407
[10] Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001
[11] Oreg Y, Refael G, Von Oppen F 2010 Phys. Rev. Lett. 105 177002
[12] Choy T P, Edge J M, Akhmerov A R, Beenakker C W J 2011 Phys. Rev. B 84 195442
[13] Nadj-Perge S, Drozdov I K, Bernevig B A, Yazdani A 2013 Phys. Rev. B 88 020407
[14] Sau J D, Sarma S D 2012 Nat. Commun. 3 964
[15] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003
[16] Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414
[17] Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887
[18] He Q L, Pan L, Stern A L, Burks E C, Che X, Yin G, Wang J, Lian B, Zhou Q, Choi E S, Murata K, Kou X, Chen Z, Nie T, Shao Q, Fan Y, Zhang S C, Liu K, Xia J, Wang K L 2017 Science 357 294
[19] Zhang H, Liu C X, Gazibegovic S, Xu D, Logan J A, Wang G, Van Loo N, Bommer J D S, De Moor M W A, Car D, Op Het Veld R L M, Van Veldhoven P J, Koelling S, Verheijen M A, Pendharkar M, Pennachio D J, Shojaei B, Lee J S, Palmstrøm C J, Bakkers E P A M, Sarma S D, Kouwenhoven L P 2018 Nature 556 74
[20] 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 548 434
[21] Vaitiekėnas S, Winkler G W, Van Heck B, Karzig T, Deng M T, Flensberg K, Glazman L I, Nayak C, Krogstrup P, Lutchyn R M, Marcus C M 2020 Science 367 eaav3392
[22] Frolov S 2021 Nature 592 350
[23] Kouwenhoven L 2025 Mod. Phys. Lett. B 39 2540002
[24] Qiao G J, Li S W, Sun C P 2022 Phys. Rev. B 106 104517
[25] Yue X, Qiao G J, Sun C P 2023 Phys. Rev. B 108 195405
[26] Reeg C, Loss D, Klinovaja J 2017 Phys. Rev. B 96 125426
[27] Reeg C, Loss D, Klinovaja J 2018 Phys. Rev. B 97 165425
[28] Legg H F, Loss D, Klinovaja J 2022 Phys. Rev. B 105 155413
[29] Qiao G J, Yue X, Sun C P 2024 Phys. Rev. Lett. 133 266605
[30] Dirac P A M 1928 Proc. R. Soc. Lond. A 117 610
[31] Dirac P A M 1931 Proc. R. Soc. Lond. A 133 60
[32] Jordan P, Wigner E 1928 Z Phys 47 631
[33] Li S W, Li Z Z, Cai C Y, Sun C P 2014 Phys. Rev. B 89 134505
[34] 乔国健 2025 博士学位论文（北京：中国工程物理研究院）
[35] Chiu C K, Teo J C Y, Schnyder A P, Ryu S 2016 Rev. Mod. Phys. 88 035005
[36] Sau J D, Lutchyn R M, Tewari S, Das Sarma S 2010 Phys. Rev. Lett. 104 040502
[37] Sau J D, Tewari S, Lutchyn R M, Stanescu T D, Das Sarma S 2010 Phys. Rev. B 82 214509
[38] Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61
[39] Qi X L, Hughes T L, Zhang S C 2010 Phys. Rev. B 82 184516
[40] Chung S B, Qi X L, Maciejko J, Zhang S C 2011 Phys. Rev. B 83 100512
[41] Wang J, Zhou Q, Lian B, Zhang S C 2015 Phys. Rev. B 92 064520
[42] Law K T, Lee P A, Ng T K 2009 Phys. Rev. Lett. 103 237001
[43] Flensberg K 2010 Phys. Rev. B 82 180516
[44] Liu J, Potter A C, Law K T, Lee P A 2012 Phys. Rev. Lett. 109 267002
[45] Bagrets D, Altland A 2012 Phys. Rev. Lett. 109 227005
[46] Lee E J H, Jiang X, Houzet M, Aguado R, Lieber C M, De Franceschi S 2014 Nat. Nanotechnol. 9 79
[47] Sasaki S, De Franceschi S, Elzerman J M, Van Der Wiel W G, Eto M, Tarucha S, Kouwenhoven L P 2000 Nature 405 764
[48] Lee E J H, Jiang X, Aguado R, Katsaros G, Lieber C M, De Franceschi S 2012 Phys. Rev. Lett. 109 186802
[49] Lutchyn R M, Bakkers E P A M, Kouwenhoven L P, Krogstrup P, Marcus C M, Oreg Y 2018 Nat. Rev. Mater. 3 52
[50] Deng M T, Vaitiekėnas S, Hansen E B, Danon J, Leijnse M, Flensberg K, Nygård J, Krogstrup P, Marcus C M 2016 Science 354 1557
[51] Pan H, Sau J D, Das Sarma S 2021 Phys. Rev. B 103 014513
[52] Chang W, Albrecht S M, Jespersen T S, Kuemmeth F, Krogstrup P, Nygård J, Marcus C M 2015 Nat. Nanotechnol. 10 232
[53] Zhang H, De Moor M W A, Bommer J D S, Xu D, Wang G, Van Loo N, Liu C X, Gazibegovic S, Logan J A, Car D, Op Het Veld R L M, Van Veldhoven P J, Koelling S, Verheijen M A, Pendharkar M, Pennachio D J, Shojaei B, Lee J S, Palmstrøm C J, Bakkers E P A M, Sarma S D, Kouwenhoven L P 2021 Large zero-bias peaks in InSb-Al hybrid semiconductor-superconductor nanowire devices (arXiv)
[54] Wang Z, Song H, Pan D, Zhang Z, Miao W, Li R, Cao Z, Zhang G, Liu L, Wen L, Zhuo R, Liu D E, He K, Shang R, Zhao J, Zhang H 2022 Phys. Rev. Lett. 129 167702
[55] Zhang H, Gül Ö, Conesa-Boj S, Nowak M P, Wimmer M, De Vries F K, Van Veen J, De Moor M W A, Bommer J D S, Van Woerkom D J, Car D, Plissard S R, Bakkers E P A M, Quintero-Pérez M, Cassidy M C, Koelling S, Goswami S, Watanabe K, Taniguchi T, Kouwenhoven L P 2017 Nat. Commun. 8 16025
[56] Kayyalha M, Xiao D, Zhang R, Shin J, Jiang J, Wang F, Zhao Y F, Xiao R, Zhang L, Fijalkowski K M, Mandal P, Winnerlein M, Gould C, Li Q, Molenkamp L W, Chan M H W, Samarth N, Chang C Z 2020 Science 367 64
[57] Zhang P, Pan L, Yin G, He Q L, Wang K L 2019 A Note on Half-quantized Conductance Plateau of Chiral Majorana in Quantum Anomalous Hall Insulator and Superconductor Structures (arXiv)
[58] Huang Y, Fu Y, Zhang P, Wang K L, He Q L 2024 J. Phys. Condens. Matter 36 37LT01
[59] Uday A, Lippertz G, Bhujel B, Taskin A A, Ando Y 2025 Non-Majorana-origin of the half-integer conductance quantization elucidated by multi-terminal superconductor-quantum anomalous Hall insulator heterostructure (arXiv)
[60] Das Sarma S 2023 Nat. Phys. 19 165
[61] Leijnse M, Flensberg K 2012 Phys. Rev. B 86 134528
[62] Dvir T, Wang G, Van Loo N, Liu C X, Mazur G P, Bordin A, Ten Haaf S L D, Wang J Y, Van Driel D, Zatelli F, Li X, Malinowski F K, Gazibegovic S, Badawy G, Bakkers E P A M, Wimmer M, Kouwenhoven L P 2023 Nature 614 445
[63] Ten Haaf S L D, Wang Q, Bozkurt A M, Liu C X, Kulesh I, Kim P, Xiao D, Thomas C, Manfra M J, Dvir T, Wimmer M, Goswami S 2024 Nature 630 329
[64] Luethi M, Legg H F, Loss D, Klinovaja J 2024 Phys. Rev. B 110 245412
[65] Cao Z, Liu D E, He W X, Liu X, He K, Zhang H 2022 Phys. Rev. B 105 085424
[66] Jiang Y, Yang S, Li L, Song W, Miao W, Tong B, Geng Z, Gao Y, Li R, Chen F, Zhang Q, Meng F, Gu L, Zhu K, Zang Y, Shang R, Cao Z, Feng X, Xue Q K, Liu D E, Zhang H, He K 2022 Phys. Rev. Mater. 6 034205
[67] Wang Y, Chen F, Song W, Geng Z, Yu Z, Yang L, Gao Y, Li R, Yang S, Miao W, Xu W, Wang Z, Xia Z, Song H D, Feng X, Wang T, Zang Y, Li L, Shang R, Xue Q, He K, Zhang H 2023 Nano Lett. 23 11137
[68] Wang Y, Song W, Cao Z, Yu Z, Yang S, Li Z, Gao Y, Li R, Chen F, Geng Z, Yang L, Xu J, Wang Z, Zhang S, Feng X, Wang T, Zang Y, Li L, Shang R, Xue Q K, Liu D E, He K, Zhang H 2024 Proc. Natl. Acad. Sci. 121 e2406884121
[69] Gao Y, Song W, Yang S, Yu Z, Li R, Miao W, Wang Y, Chen F, Geng Z, Yang L, Xia Z, Feng X, Zang Y, Li L, Shang R, Xue Q K, He K, Zhang H 2024 Chin. Phys. Lett. 41 038502
[70] Li Z, Song W, Zhang S, Wang Y, Wang Z, Yu Z, Li R, Yan Z, Xu J, Gao Y, Yang S, Yang L, Feng X, Wang T, Zang Y, Li L, Shang R, Xue Q K, He K, Zhang H 2025 Phys. Rev. B 111 195416
[71] Zhang S, Song W, Li Z, Yu Z, Li R, Wang Y, Yan Z, Xu J, Wang Z, Gao Y, Yang S, Yang L, Feng X, Wang T, Zang Y, Li L, Shang R, Xue Q K, He K, Zhang H 2025 Robust zero modes in PbTe-Pb hybrid nanowires (arXiv)
[72] Aghaee M, Akkala A, Alam Z, Ali R, Alcaraz Ramirez A, Andrzejczuk M, Antipov A E, Aseev P, Astafev M, Bauer B, Becker J, Boddapati S, Boekhout F, Bommer J, Bosma T, Bourdet L, Boutin S, Caroff P, Casparis L, Cassidy M, Chatoor S, Christensen A W, Clay N, Cole W S, Corsetti F, Cui A, Dalampiras P, Dokania A, De Lange G, De Moor M, Estrada Saldaña J C, Fallahi S, Fathabad Z H, Gamble J, Gardner G, Govender D, Griggio F, Grigoryan R, Gronin S, Gukelberger J, Hansen E B, Heedt S, Herranz Zamorano J, Ho S, Holgaard U L, Ingerslev H, Johansson L, Jones J, Kallaher R, Karimi F, Karzig T, King E, Kloster M E, Knapp C, Kocon D, Koski J, Kostamo P, Krogstrup P, Kumar M, Laeven T, Larsen T, Li K, Lindemann T, Love J, Lutchyn R, Madsen M H, Manfra M, Markussen S, Martinez E, McNeil R, Memisevic E, Morgan T, Mullally A, Nayak C, Nielsen J, Nielsen W H P, Nijholt B, Nurmohamed A, O’Farrell E, Otani K, Pauka S, Petersson K, Petit L, Pikulin D I, Preiss F, Quintero-Perez M, Rajpalke M, Rasmussen K, Razmadze D, Reentila O, Reilly D, Rouse R, Sadovskyy I, Sainiemi L, Schreppler S, Sidorkin V, Singh A, Singh S, Sinha S, Sohr P, Stankevič T, Stek L, Suominen H, Suter J, Svidenko V, Teicher S, Temuerhan M, Thiyagarajah N, Tholapi R, Thomas M, Toomey E, Upadhyay S, Urban I, Vaitiekėnas S, Van Hoogdalem K, Van Woerkom D, Viazmitinov D V, Vogel D, Waddy S, Watson J, Weston J, Winkler G W, Yang C K, Yau S, Yi D, Yucelen E, Webster A, Zeisel R, Zhao R, Microsoft Quantum 2023 Phys. Rev. B 107 245423
[73] Microsoft Azure Quantum, Aghaee M, Alcaraz Ramirez A, Alam Z, Ali R, Andrzejczuk M, Antipov A, Astafev M, Barzegar A, Bauer B, Becker J, Bhaskar U K, Bocharov A, Boddapati S, Bohn D, Bommer J, Bourdet L, Bousquet A, Boutin S, Casparis L, Chapman B J, Chatoor S, Christensen A W, Chua C, Codd P, Cole W, Cooper P, Corsetti F, Cui A, Dalpasso P, Dehollain J P, De Lange G, De Moor M, Ekefjärd A, El Dandachi T, Estrada Saldaña J C, Fallahi S, Galletti L, Gardner G, Govender D, Griggio F, Grigoryan R, Grijalva S, Gronin S, Gukelberger J, Hamdast M, Hamze F, Hansen E B, Heedt S, Heidarnia Z, Herranz Zamorano J, Ho S, Holgaard L, Hornibrook J, Indrapiromkul J, Ingerslev H, Ivancevic L, Jensen T, Jhoja J, Jones J, Kalashnikov K V, Kallaher R, Kalra R, Karimi F, Karzig T, King E, Kloster M E, Knapp C, Kocon D, Koski J V, Kostamo P, Kumar M, Laeven T, Larsen T, Lee J, Lee K, Leum G, Li K, Lindemann T, Looij M, Love J, Lucas M, Lutchyn R, Madsen M H, Madulid N, Malmros A, Manfra M, Mantri D, Markussen S B, Martinez E, Mattila M, McNeil R, Mei A B, Mishmash R V, Mohandas G, Mollgaard C, Morgan T, Moussa G, Nayak C, Nielsen J H, Nielsen J M, Nielsen W H P, Nijholt B, Nystrom M, O’Farrell E, Ohki T, Otani K, Paquelet Wütz B, Pauka S, Petersson K, Petit L, Pikulin D, Prawiroatmodjo G, Preiss F, Puchol Morejon E, Rajpalke M, Ranta C, Rasmussen K, Razmadze D, Reentila O, Reilly D J, Ren Y, Reneris K, Rouse R, Sadovskyy I, Sainiemi L, Sanlorenzo I, Schmidgall E, Sfiligoj C, Shah M B, Simoes K, Singh S, Sinha S, Soerensen T, Sohr P, Stankevic T, Stek L, Stuppard E, Suominen H, Suter J, Teicher S, Thiyagarajah N, Tholapi R, Thomas M, Toomey E, Tracy J, Turley M, Upadhyay S, Urban I, Van Hoogdalem K, Van Woerkom D J, Viazmitinov D V, Vogel D, Watson J, Webster A, Weston J, Winkler G W, Xu D, Yang C K, Yucelen E, Zeisel R, Zheng G, Zilke J 2025 Nature 638 651
[74] Legg H F 2025 Comment on “InAs-Al hybrid devices passing the topological gap protocol”, Microsoft Quantum, Phys. Rev. B 107, 245423 (2023) (arXiv)
[75] Legg H F 2025 Comment on “Interferometric single-shot parity measurement in InAs-Al hybrid devices”, Microsoft Quantum, Nature 638, 651-655 (2025) (arXiv)
[76] Stanescu T D, Lutchyn R M, Das Sarma S 2011 Phys. Rev. B 84 144522
[77] Stanescu T D, Das Sarma S 2017 Phys. Rev. B 96 014510
[78] Wen L J, Pan D, Zhao J H 2021 Acta Phys. Sin. 70 058101（in Chinese）[文炼均, 潘东, 赵建华 2021 物理学报 70 058101]
[79] Cole W S, Sau J D, Das Sarma S 2016 Phys. Rev. B 94 140505
[80] Woods B D, Stanescu T D, Das Sarma S 2018 Phys. Rev. B 98 035428
[81] Mikkelsen A E G, Kotetes P, Krogstrup P, Flensberg K 2018 Phys. Rev. X 8 031040
[82] Antipov A E, Bargerbos A, Winkler G W, Bauer B, Rossi E, Lutchyn R M 2018 Phys. Rev. X 8 031041
[83] Winkler G W, Antipov A E, Van Heck B, Soluyanov A A, Glazman L I, Wimmer M, Lutchyn R M 2019 Phys. Rev. B 99 245408
[84] Zhang Z L, Qiao G J, Sun C P 2025 Poor Man’s Majoranon in Two Quantum Dots Dressed by Superconducting Quasi-Excitations (arXiv)
Metrics
- Abstract views: 68
- PDF Downloads: 6
- Cited By: 0
下载:
