-
本文研究了一维Fibonacci准晶势调制下的p波超导体下的拓扑相变和局域化性质.在Fibonacci准晶势调制下,通过计算Z2拓扑不变量确定了系统的拓扑相图.分析相图,指出在Fibonacci准晶势调制下,系统可以由拓扑平庸超导相进入拓扑安德森超导相.进一步分析,发现在某些参数下,系统会发生多次拓扑安德森超导相转变并伴随着零能态的出现.此外,还研究了系统的局域化性质,通过分析分形维度,平均逆参与率序参量,发现Fibonacci准晶势诱导的拓扑安德森超导相,其体态的波函数则表现出多重分形行为,这与随机无序诱导出来的传统拓扑安德森超导相完全不同.该研究结果为一维p波超导体中拓扑相变和局域化转变的研究提供了一些新的理解和参考.This paper investigates the topological phase transitions and localization properties in a 1D p-wave superconductor under Fibonacci quasi-periodic potential modulation. By calculating the Z2 topological invariant, we numerically determine the topological phase diagram of the system. We find that, under Fibonacci quasi-periodic modulation, the system can transition from a topologically trivial phase to a topological Anderson superconductor phase. Moreover, under certain parameters, the system undergoes multiple topological Anderson superconductor phases transitions, accompanied by the emergence of zero-energy modes. However, in the case of strong disorder, the topological Anderson superconductor phase is destroyed, indicating that the topological Anderson superconductor phase can only be induced within a finite range of parameters. Furthermore, by calculating and analyzing the fractal dimension and the mean inverse participation ratio (MIPR) order parameter, we analyze the localization properties of the system. The results show that regardless of the increase in disorder strength, the fractal dimension values of most eigenstates always remain within the range (0;1). Subsequently, the variations in the fractal dimensions of all eigenstates for different system sizes were studied. The results show that the fractal dimension values of most eigenstates are away from 0 and 1. These results indicate that the wavefunction in the bulk of the topological Anderson superconductor phase induced by Fibonacci quasi-periodic potential are critical state wavefunction, with the system overall being in a critical phase. The stability of the critical phase is confirmed by scale behavior of MIPR, as shown in Fig.(a).
It differs from the traditional topological Anderson superconductor phase induced by random disorder or AA-type quasi-periodic disorder. The results provide new insights and references for the study of topological phase transitions and localization transitions in 1D p-wave superconductors. -
[1] Nakajima S, Takei N, Sakuma K, Kuno Y, Marra P, Takahashi Y, 2021 Nat. Phys. 17844
[2] Thouless D J, Kohmoto M, Nightingale M P, den Nijs M, 1982 Phys. Rev. Lett. 49405
[3] Hasan M X and Kane C L, 2010 Rev. Mod. Phys. 823045
[4] Qi X L and Zhang S C, 2011 Rev. Mod. Phys. 831057
[5] Bansil A, Lin H, T. Das, 2016 Rev. Mod. Phys. 88021004
[6] Xiao T, Xie D, Dong Z, Chen T, Yi W, Yan B, 2021 Sci. Bull. 662175
[7] Szameit A and Rechtsman M C, 2024 Nat. Phys. 20905
[8] König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L, Qi X L, Zhang S C, 2007 Science 318766
[9] Zhang H J, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C, 2009 Nat. Phys. 5438
[10] Zhang Y Y, Chu R L, Zhang F C, Shen S Q, 2012 Phys. Rev. B 85035107
[11] Jiang H, Wang L, Sun Q f, Xie X C, 2009 Phys. Rev. B 80165316
[12] Li X Q, Zhang H H, Xu H, San H D, Wang X N, Qi S F, Qiao Z H, 2024 Phys. Rev. B 109155427
[13] Su W P, Schrieffer J R, Heeger A J, 1979 Phys. Rev. Lett. 421698
[14] Song F, Yao S, Wang Z, 2019 Phys. Rev. Lett. 123246801
[15] Velury S, Bradlyn B, Hughes T L, 2021 Phys. Rev. B 103024205
[16] Xu L, Li P L, Lü Z Z, Shen J, Qu F M, Liu G T, Lü L 2023 Acta Phys. Sin. 72177401(in Chinese)[徐磊, 李沛岭, 吕昭征, 沈洁, 屈凡明, 刘广同, 吕力2023 72177401]
[17] Guan X, Chen G 2023 Acta Phys. Sin. 72140301(in Chinese) [关欣, 陈刚2023 72140301]
[18] Gu Y, Lu Z P 2024 Chin. Phys.B 33090202
[19] Li G Q, Wang B H, Tang J Y, Peng P, Dong L W 2023 Chin. Phys. B 32077102
[20] Huang A H, Ke S S, Guan J H, Li J, Lou W K 2024 Chin. Phys. Lett. 41097302
[21] Chang Z W, Hao W C, Bustamante M, Liu X 2024 Chin. Phys. Lett. 41037302
[22] Xu Z, Zhang R, Chen S, Fu L, Zhang Y, 2020 Phys. Rev. A 101013635
[23] Prodan E, Hughes T L, Bernevig B A, 2010 Phys. Rev. Lett. 105115501
[24] Cai X, Lang L J, Chen S, Wang Y, 2013 Phys. Rev. Lett. 110176403
[25] Liu J, Potter A C, Law K T, Lee P A, 2012 Phys. Rev. Lett. 109267002
[26] Li J, Chu R L, Jain J K, Shen S Q, 2009 Phys. Rev. Lett. 102136806
[27] Groth C W, Wimmer M, Akhmerov A R, Tworzydlo J, Beenakker C W J, 2009 Phys. Rev. Lett. 103196805
[28] Meier E J, An F A, Dauphin A, Maffei M, Massignan P, Hughes T L, Gadway B, 2018 Science 362929
[29] Stützer S, Plotnik Y, Lumer Y, Titum P, Lindner N H, Segev M, Rechtsman M C, Szameit A, 2018 Nature (London) 560461
[30] Borchmann J, Farrell A, Pereg-Barnea T, 2016 Phys. Rev. B 93125133
[31] Kitaev A Y, 2001 Phys. Usp. 44131
[32] Ivanov D A 2001 Phys. Rev. Lett. 86268
[33] Zhu S L, Shao L B, Wang Z D, Duan L M 2011 Phys. Rev. Lett. 106100404
[34] Lindner N H, Berg E, Refael G, Stern A 2012 Phys. Rev. X 2041002
[35] Nayak C, Simon S H, Stern A, Freedman M, Sarma S D 2008 Rev. Mod. Phys. 801083
[36] Lang L J, Chen S 2012 Phys. Rev. B. 86205135
[37] Cai X M, Lang L J, Chen S, Wang Y P 2013 Phys. Rev. Lett. 110176403
[38] Hua C B, Chen R, Xu D H, Zhou B, 2019 Phys. Rev. B 100205302
[39] Hegde S S, Vishveshwara S 2016 Phys. Rev. Lett. 94115166
[40] DeGottardi W, Thakurathi M, Vishveshwara S, Sen D 2013 Phys. Rev. B 88165111
[41] Wakatsuki R, Ezawa M, Tanaka Y, Nagaosa N, 2014 Phys. Rev. B 90014505
[42] Jagannathan A, 2021 Rev. Mod. Phys. 93045001
[43] Aubry S, André G 1980 Ann. Isr. Phys. Soc. 318
[44] Merlin R, Bajema K, Clarke R, Juang F Y, Bhattacharya P K, 1985 Phys. Rev. Lett. 551768
[45] Longhi S 2019 Phys. Rev. Lett. 122237601
[46] Kobiałka A, Awoga O A, Leijnse M, Domański T, Holmvall P, Black-Schaffer A M, 2024 Phys. Rev. B 110134508
[47] Hu Y C, Kane C L, 2018 Phys. Rev. Lett. 120066801
[48] Tong L, Cheng S J, Guo H, Gao X L, 2021 Phys. Rev. B 103104203
[49] Zhu J X 2016 Bogoliubov-de Gennes Method and Its Applications (Lecture Notes in Physics 924)
[50] Lieb E, Schultz T, Mattis D 1961 Ann. Phys. 16407
[51] P. Zhang and F. Nori, 2016 New J. Phys. 18043033
[52] Akhmerov A R, Dahlhaus J P, Hassler F, Wimmer M, Beenakker C W J 2011 Phys. Rev. Lett. 106057001
[53] Fulga I C, Hassler F, Akhmerov A R, Beenakker C W J 2011 Phys. Rev. B 83155429
[54] Roy S, Mishra T, Tanatar B, Basu S 2021 Phys. Rev. Lett. 126106803
[55] Li X, Sarma S D 2020 Phys. Rev. B 101064203
[56] Wang Y, Zhang L, Niu S, Yu D, Liu X J, 2020 Phys. Rev. Lett. 125073204
[57] Longhi S, 2020 Opt. Lett. 454036
[58] Lang L J, Cai X M, Chen S, 2012 Phys. Rev. Lett. 108220401
[59] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P, 2012 Science 3361003
[60] Law K T, Lee P A, Ng T K, 2009 Phys. Rev. Lett. 103237001
[61] Lin C H, Sau J D, Das Sarma S, 2012 Phys. Rev. B 86224511
[62] Prada E, San Jose P, Aguado R, 2012 Phys. Rev. B 86180503
[63] Nichele F, Drachmann A C C, Whiticar A M, OFarrell E C T, Suominen H J, Fornieri A, Wang T, Gardner G C, Thomas C, Hatke A T, Krogstrup P, Manfra M J, Flensberg K, Marcus C M, 2017 Phys. Rev. Lett. 119136803
[64] Kells G, Meidan D, Brouwer P W, 2012 Phys. Rev. B 85060507
[65] Chen J, Woods B D, Yu P, Hocevar M, Car D, Plissard S R, Bakkers E P A M, Stanescu T D, Frolov S M, 2019 Phys. Rev. Lett. 123107703
[66] Yu P, Chen J, Gomanko M, Badawy G, Bakkers E P A M, Zuo K, Mourik V, Frolov S M, 2021 Nat. Phys. 17482
计量
- 文章访问数: 59
- PDF下载量: 0
- 被引次数: 0
下载:
