CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Bosonic Halperin (441) Fractional Quantum Hall Effect at Filling Factor $\nu=2/5$ |
Tian-Sheng Zeng1†*, Liangdong Hu2,3†, and W. Zhu4 |
1Department of Physics, School of Physical Science and Technology, Xiamen University, Xiamen 361005, China 2Zhejiang University, Hangzhou 310027, China 3School of Science, Westlake University, Hangzhou 310024, China 4Key Laboratory for Quantum Materials of Zhejiang Province, School of Science, Westlake University, Hangzhou 310024, China
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Cite this article: |
Tian-Sheng Zeng, Liangdong Hu, and W. Zhu 2022 Chin. Phys. Lett. 39 017301 |
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Abstract Quantum Hall effects with multicomponent internal degrees of freedom facilitate the playground of novel emergent topological orders. Here, we explore the correlated topological phases of two-component hardcore bosons at a total filling factor $\nu=2/5$ in topological lattice models under the interplay of intracomponent and intercomponent repulsions. We give the numerical demonstration of the emergence of Halperin (441) fractional quantum Hall effect based on exact diagonalization and density-matrix renormalization group methods. We elucidate its topological features including the degeneracy of the ground state, fractionally quantized topological Chern number matrix and chiral edge modes.
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Received: 06 October 2021
Editors' Suggestion
Published: 29 December 2021
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[1] | Wen X G and Zee A 1992 Phys. Rev. Lett. 69 1811 |
[2] | Moon K, Mori H, Yang K, Girvin S M, MacDonald A H, Zheng L, Yoshioka D, and Zhang S C 1995 Phys. Rev. B 51 5138 |
[3] | Yang K, Moon K, Belkhir L, Mori H, Girvin S M, MacDonald A H, Zheng L, and Yoshioka D 1996 Phys. Rev. B 54 11644 |
[4] | Yoshioka D, MacDonald A H, and Girvin S M 1988 Phys. Rev. B 38 3636(R) |
[5] | Yoshioka D, MacDonald A H, and Girvin S M 1989 Phys. Rev. B 39 1932 |
[6] | He S, Xie X C, Sarma S D, and Zhang F C 1991 Phys. Rev. B 43 9339(R) |
[7] | He S, Sarma S D, and Xie X C 1993 Phys. Rev. B 47 4394 |
[8] | Halperin B I 1983 Helv. Phys. Acta 56 75 |
[9] | Bolotin K I, Ghahari F, Shulman M D, Stormer H L, and Kim P 2009 Nature 462 196 |
[10] | Dean C, Young A, Cadden-Zimansky P, Wang L, Ren H, Watanabe K, Taniguchi T, Kim P, Hone J, and Shepard K 2011 Nat. Phys. 7 693 |
[11] | Liu X, Hao Z, Watanabe K, Taniguchi T, Halperin B I, and Kim P 2019 Nat. Phys. 15 893 |
[12] | Li J I A, Shi Q, Zeng Y, Watanabe K, Taniguchi T, Hone J, and Dean C R 2019 Nat. Phys. 15 898 |
[13] | Goerbig M O and Regnault N 2007 Phys. Rev. B 75 241405(R) |
[14] | Cooper N R 2020 Fractional Quantum Hall States of Bosons: Properties and Prospects for Experimental Realization in Fractional Quantum Hall Effects: New Developments edited by Halperin B I and Jain J K (Singapore: World Scientific) chap 10 |
[15] | Ardonne E and Schoutens K 1999 Phys. Rev. Lett. 82 5096 |
[16] | Reijnders J W, van Lankvelt F J M, Schoutens K, and Read N 2002 Phys. Rev. Lett. 89 120401 |
[17] | Ardonne E, Kedem R, and Stone M 2005 J. Phys. A 38 617 |
[18] | Grosfeld E and Schoutens K 2009 Phys. Rev. Lett. 103 076803 |
[19] | Ardonne E and Regnault N and 2011 Phys. Rev. B 84 205134 |
[20] | Davenport S C and Simon S H 2012 Phys. Rev. B 85 075430 |
[21] | Hormozi L, Möller G, and Simon S H 2012 Phys. Rev. Lett. 108 256809 |
[22] | Chen X, Gu Z C, Liu Z X, and Wen X G 2013 Phys. Rev. B 87 155114 |
[23] | Senthil T and Levin M 2013 Phys. Rev. Lett. 110 046801 |
[24] | Lu Y M and Vishwanath A 2012 Phys. Rev. B 86 125119 |
[25] | Juliá Díaz T G B, Barberán N, and Lewenstein M 2012 Phys. Rev. A 86 021603(R) |
[26] | Furukawa S and Ueda M 2012 Phys. Rev. A 86 031604(R) |
[27] | Wu Y H and Jain J K 2013 Phys. Rev. B 87 245123 |
[28] | Furukawa S and Ueda M 2013 Phys. Rev. Lett. 111 090401 |
[29] | Regnault N and Senthil T 2013 Phys. Rev. B 88 161106(R) |
[30] | Raventós T G D, Lewenstein M, and Juliá Díaz B 2014 Phys. Rev. B 89 045114 |
[31] | Furukawa S and Ueda M 2017 Phys. Rev. A 96 053626 |
[32] | Möller G and Cooper N R 2009 Phys. Rev. Lett. 103 105303 |
[33] | Sterdyniak A, Cooper N R, and Regnault N 2015 Phys. Rev. Lett. 115 116802 |
[34] | Möller G and Cooper N R 2015 Phys. Rev. Lett. 115 126401 |
[35] | Zhu W, Gong S S, Sheng D N, Sheng L 2015 Phys. Rev. B 91 245126 |
[36] | Liu Z, Vaezi A, Repellin C, and Regnault N 2016 Phys. Rev. B 93 085115 |
[37] | Wen X G 2016 Natl. Sci. Rev. 3 68 |
[38] | Sørensen A S, Demler E, and Lukin M D 2005 Phys. Rev. Lett. 94 086803 |
[39] | Hafezi M, Sørensen A S, Demler E, and Lukin M D 2007 Phys. Rev. A 76 023613 |
[40] | Palmer R N and Jaksch D 2006 Phys. Rev. Lett. 96 180407 |
[41] | Palmer R N, Klein A, and Jaksch D 2008 Phys. Rev. A 78 013609 |
[42] | Kapit E and Mueller E 2010 Phys. Rev. Lett. 105 215303 |
[43] | Haldane F D M 1988 Phys. Rev. Lett. 61 2015 |
[44] | Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B, and Bloch I 2013 Phys. Rev. Lett. 111 185301 |
[45] | Miyake H, Siviloglou G A, Kennedy C J, Burton W C, and Ketterle W 2013 Phys. Rev. Lett. 111 185302 |
[46] | Mancini M, Pagano G, Cappellini G, Livi L, Rider M, Catani J, Sias C, Zoller P, Inguscio M, Dalmonte M, and Fallani L 2015 Science 349 1510 |
[47] | Stuhl B K, Lu H I, Aycock L M, Genkina D, and Spielman I B 2015 Science 349 1514 |
[48] | Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, and Esslinger T 2014 Nature 515 237 |
[49] | Wolf T M R, Lado J L, Blatter G, and Zilberberg O 2019 Phys. Rev. Lett. 123 096802 |
[50] | Chittari B L, Chen G, Zhang Y, Wang F, and Jung J 2019 Phys. Rev. Lett. 122 016401 |
[51] | Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T et al. 2020 Nature 579 56 |
[52] | Kang M, Fang S, Ye L, Po H C, Denlinger J, Jozwiak C, Bostwick A, Rotenberg E, Kaxiras E, Checkelsky J G et al. 2020 Nat. Commun. 11 4004 |
[53] | Sun K, Gu Z, Katsura H, and Sarma S D 2011 Phys. Rev. Lett. 106 236803 |
[54] | Sheng D N, Gu Z, Sun K, and Sheng L 2011 Nat. Commun. 2 389 |
[55] | Neupert T, Santos L, Chamon C, and Mudry C 2011 Phys. Rev. Lett. 106 236804 |
[56] | Tang E, Mei J W, and Wen X G 2011 Phys. Rev. Lett. 106 236802 |
[57] | Wang Y F, Gu Z C, Gong C D, and Sheng D N 2011 Phys. Rev. Lett. 107 146803 |
[58] | Regnault N and Bernevig B A 2011 Phys. Rev. X 1 021014 |
[59] | Wen X G and Zee A 1992 Phys. Rev. B 46 2290 |
[60] | Wen X G and Zee A 1992 Phys. Rev. Lett. 69 953 |
[61] | Blok B and Wen X G 1990 Phys. Rev. B 42 8133 |
[62] | Blok B and Wen X G 1990 Phys. Rev. B 42 8145 |
[63] | Blok B and Wen X G 1991 Phys. Rev. B 43 8337 |
[64] | Liu Z, Bergholtz E J, Fan H, and Läuchli A M 2012 Phys. Rev. Lett. 109 186805 |
[65] | Wang Y F, Yao H, Gong C D, and Sheng D N 2012 Phys. Rev. B 86 201101(R) |
[66] | Yang S, Gu Z C, Sun K, and Sarma S D 2012 Phys. Rev. B 86 241112(R) |
[67] | Sterdyniak A, Repellin C, Bernevig B A, and Regnault N 2013 Phys. Rev. B 87 205137 |
[68] | Wang D, Liu Z, Cao J, and Fan H 2013 Phys. Rev. Lett. 111 186804 |
[69] | Wu Y L, Regnault N, and Bernevig B A 2013 Phys. Rev. Lett. 110 106802 |
[70] | Wu Y L, Regnault N, and Bernevig B A 2014 Phys. Rev. B 89 155113 |
[71] | Wu Y H, Jain J K, and Sun K 2015 Phys. Rev. B 91 041119(R) |
[72] | Zeng T S, Zhu W, and Sheng D N 2017 Phys. Rev. B 95 125134 |
[73] | Zeng T S and Sheng D N 2018 Phys. Rev. B 97 035151 |
[74] | Zeng T S, Sheng D N, and Zhu W 2019 Phys. Rev. B 100 075106 |
[75] | Zeng T S 2021 Phys. Rev. B 103 L201118 |
[76] | Wang Y F, Yao H, Gu Z C, Gong C D, and Sheng D N 2012 Phys. Rev. Lett. 108 126805 |
[77] | Sheng D N, Balents L, and Wang Z 2003 Phys. Rev. Lett. 91 116802 |
[78] | Sheng D N, Weng Z Y, Sheng L, and Haldane F D M 2006 Phys. Rev. Lett. 97 036808 |
[79] | Niu Q, Thouless D J, and Wu Y S 1985 Phys. Rev. B 31 3372 |
[80] | Gong S S, Zhu W, and Sheng D N 2014 Sci. Rep. 4 6317 |
[81] | Wen X G 1995 Adv. Phys. 44 405 |
[82] | Wen X G 1992 Int. J. Mod. Phys. B 6 1711 |
[83] | Li H and Haldane F D M 2008 Phys. Rev. Lett. 101 010504 |
[84] | Qi X L, Katsura H, and Ludwig A W W 2012 Phys. Rev. Lett. 108 196402 |
[85] | He Y C, Bhattacharjee S, Moessner R, and Pollmann F 2015 Phys. Rev. Lett. 115 116803 |
[86] | Zeng T S, Sheng D N, and Zhu W 2020 Phys. Rev. B 101 195310 |
[87] | Cooper N R, Dalibard J, and Spielman I B 2019 Rev. Mod. Phys. 91 015005 |
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