Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

doi:10.1088/1674-1056/ac3738

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 10308-010308.doi: 10.1088/1674-1056/ac3738

所属专题： SPECIAL TOPIC — Non-Hermitian physics

Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

Xiaosen Yang(杨孝森)^†, Yang Cao(曹阳), and Yunjia Zhai(翟云佳)

Department of physics, Jiangsu University, Zhenjiang 212013, China

收稿日期:2021-08-23 修回日期:2021-11-04 接受日期:2021-11-06 出版日期:2021-12-03 发布日期:2021-12-23
通讯作者: Xiaosen Yang E-mail:yangxs@ujs.edu.cn
基金资助:
We would like to thank Zhong Wang for fruitful discussion. Project supported by the National Natural Science Foundation of China (Grants No. 11504143).

Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

Xiaosen Yang(杨孝森)^†, Yang Cao(曹阳), and Yunjia Zhai(翟云佳)

Department of physics, Jiangsu University, Zhenjiang 212013, China

Received:2021-08-23 Revised:2021-11-04 Accepted:2021-11-06 Online:2021-12-03 Published:2021-12-23
Contact: Xiaosen Yang E-mail:yangxs@ujs.edu.cn
Supported by:
We would like to thank Zhong Wang for fruitful discussion. Project supported by the National Natural Science Foundation of China (Grants No. 11504143).

摘要/Abstract

摘要： We investigate novel features of three-dimensional non-Hermitian Weyl semimetals, paying special attention to the unconventional bulk-boundary correspondence. We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram, which is also confirmed by the energy spectra from our numerical results. It is shown that, in sharp contrast to Hermitian systems, the conventional (Bloch) bulk-boundary correspondence breaks down in non-Hermitian topological semimetals, which is caused by the non-Hermitian skin effect. We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals: the topological edge modes are determined by the non-Bloch Chern number of the bulk bands. Moreover, these topological edge modes can manifest as the unidirectional edge motion, and their signatures are consistent with the non-Bloch bulk-boundary correspondence. Our work establishes the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.

关键词: non-Hermitian skin effect, Weyl semimental, bulk-boundary correspondence

Abstract: We investigate novel features of three-dimensional non-Hermitian Weyl semimetals, paying special attention to the unconventional bulk-boundary correspondence. We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram, which is also confirmed by the energy spectra from our numerical results. It is shown that, in sharp contrast to Hermitian systems, the conventional (Bloch) bulk-boundary correspondence breaks down in non-Hermitian topological semimetals, which is caused by the non-Hermitian skin effect. We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals: the topological edge modes are determined by the non-Bloch Chern number of the bulk bands. Moreover, these topological edge modes can manifest as the unidirectional edge motion, and their signatures are consistent with the non-Bloch bulk-boundary correspondence. Our work establishes the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.

Key words: non-Hermitian skin effect, Weyl semimental, bulk-boundary correspondence

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

73.43.Nq (Quantum phase transitions) 73.20.At (Surface states, band structure, electron density of states)

Xiaosen Yang(杨孝森), Yang Cao(曹阳), and Yunjia Zhai(翟云佳). Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence[J]. 中国物理B, 2022, 31(1): 10308-010308.

Xiaosen Yang(杨孝森), Yang Cao(曹阳), and Yunjia Zhai(翟云佳). Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence[J]. Chin. Phys. B, 2022, 31(1): 10308-010308.

参考文献

[1] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
[2] Bernevig B A, Hughes T L and Zhang S C 2006 Science 314 1757
[3] Moore J E and Balents L 2007 Phys. Rev. B 75 121306
[4] Fu L, Kane C L and Mele E J 2007 Phys. Rev. Lett. 98 106803
[5] Qi X L, Hughes T L and Zhang S C 2008 Phys. Rev. B 78 195424
[6] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[7] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[8] Dzero M, Sun K, Galitski V and Coleman P 2010 Phys. Rev. Lett. 104 106408
[9] Fu L 2011 Phys. Rev. Lett. 106 106802
[10] Wang Z and Zhang S C 2012 Phys. Rev. X 2 031008
[11] Qi X L, Hughes T L, Raghu S and Zhang S C 2009 Phys. Rev. Lett. 102 187001
[12] Hor Y S, Williams A J, Checkelsky J G, Roushan P, Seo J, Xu Q, Zandbergen H W, Yazdani A, Ong N P and Cava R J 2010 Phys. Rev. Lett. 104 057001
[13] Sasaki S, Kriener M, Segawa K, Yada K, Tanaka Y, Sato M and Ando Y 2011 Phys. Rev. Lett. 107 217001
[14] Nakosai S, Tanaka Y and Nagaosa N 2012 Phys. Rev. Lett. 108 147003
[15] Xu C and Balents L 2018 Phys. Rev. Lett. 121 087001
[16] Zhang F, Kane C L and Mele E J 2013 Phys. Rev. Lett. 111 056403
[17] Zhang W and Yi W 2013 Nat. Commu. 4 2711
[18] Qu C, Zheng Z, Gong M, Xu Y, Mao L, Zou X, Guo G and Zhang C 2013 Nat. Commun. 4 2710
[19] Wan X, Turner A M, Vishwanath A and Savrasov S Y 2011 Phys. Rev. B 83 205101
[20] Burkov A A and Balents L 2011 Phys. Rev. Lett. 107 127205
[21] Xu G, Weng H, Wang Z, Dai X and Fang Z 2011 Phys. Rev. Lett. 107 186806
[22] Xu S Y, Belopolski I, Alidoust N, Neupane M, Bian G, Zhang C, Sankar R, Chang G, Yuan Z, Lee C C, Huang S M, Zheng H, Ma J, Sanchez D S, Wang B, Bansil A, Chou F, Shibayev P P, Lin H, Jia S, and Hasan M Z 2015 Science 349 613
[23] Lv B Q, Weng H M, Fu B B, Wang X P, Miao H, Ma J, Richard P, Huang X C, Zhao L X, Chen G F, Fang Z, Dai X, Qian T and Ding H 2015 Phys. Rev. X 5 031013
[24] Weng H, Fang C, Fang Z, Bernevig B A and Dai X 2015 Phys. Rev. X 5 011029
[25] Young S M and Kane C L 2015 Phys. Rev. Lett. 115 126803
[26] Sun X Q, Zhang S C and Wang Z 2015 Phys. Rev. Lett. 115 076802
[27] Yan Z and Wang Z 2016 Phys. Rev. Lett. 117 087402
[28] Bansil A, Lin H and Das T 2016 Rev. Mod. Phys. 88 021004
[29] Armitage N P, Mele E J and Vishwanath A 2018 Rev. Mod. Phys. 90 015001
[30] Chen Y, Xie Y, Gao Y, Chang P Y, Zhang S and Vanderbilt D 2018 Phys. Rev. Materials 2 044205
[31] Gong C, Xie Y, Chen Y, Kim H S and Vanderbilt D 2018 Phys. Rev. Lett. 120 106403
[32] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[33] Diehl S, Rico E, Baranov M A and Zoller P 2011 Nat. Phys. 7 971
[34] Choi Y, Kang S, Lim S, Kim W, Kim J R, Lee J H and An K 2010 Phys. Rev. Lett. 104 153601
[35] Malzard S, Poli C and Schomerus H 2015 Phys. Rev. Lett. 115 200402
[36] Zhen B, Hsu C W, Igarashi Y, Lu L, Kaminer I, Pick A, Chua S L, Joannopoulos J D and Soljačić M 2015 Nature 525 354
[37] Cao H and Wiersig J 2015 Rev. Mod. Phys. 87 61
[38] Lee T E and Chan C K 2014 Phys. Rev. X 4 041001
[39] Zhu B, Lü R, and Chen S 2014 Phys. Rev. A 89 062102
[40] Xu Y, Wang S T and Duan L M 2017 Phys. Rev. Lett. 118 045701
[41] Cai J Q, Xue Z Y, Gong M, Guo G C and Hu Y 2018 arXiv: 1812.02610
[42] Yoshida T, Peters R and Kawakami N 2018 Phys. Rev. B 98 035141)
[43] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079
[44] Lee C H, Li G, Liu Y, Tai T, Thomale R and Zhang X 2018 arXiv:1812.02011
[45] Chen Y and Zhai H 2018 Phys. Rev. B 98 245130
[46] Zhu W, Fang X, Li D, Sun Y, Li Y, Jing Y and Chen H 2018 Phys. Rev. Lett. 121 124501
[47] Carlström J, Stålhammar M, Budich J C and Bergholtz E J 2019 Phys. Rev. B 99 161115
[48] Cerjan A, Xiao M, Yuan L and Fan S 2018 Phys. Rev. B 97 075128
[49] Parto M, Wittek S, Hodaei H, Harari G, Bandres M A, Ren J, Rechtsman M C, Segev M, Christodoulides D N and Khajavikhan M 2018 Phys. Rev. Lett. 120 113901
[50] Yin C, Jiang H, Li L, Lü R and Chen S 2018 Phys. Rev. A 97 052115
[51] Zhang S Y, Gong M, Guo G C and Zhou Z W 2020 Phys. Rev. B 101 155150
[52] Liu T, Zhang Y R, Ai Q, Gong Z, Kawabata K, Ueda M and Nori F 2019 Phys. Rev. Lett. 122 076801
[53] Kawabata K, Higashikawa S, Gong Z, Ashida Y and Ueda M 2019 Nat. Commun. 10 297
[54] Yang Z and Hu J 2019 Phys. Rev. B 99 081102
[55] Mu S, Lee C H, Li L and Gong J 2020 Phys. Rev. B 102 081115
[56] Lee C H, Li L, Thomale R and Gong J 2020 Phys. Rev. B 102 085151
[57] Mc Clarty P A and Rau J G 2019 Phys. Rev. B 100 100405
[58] Ghatak A and Das T 2019 J. Phys.: Condens. Matter 31 263001
[59] Liu J, Han Y and Liu C 2019 Chin. Phys. B 28 100304
[60] Jiang X P, Qiao Y and Cao J 2021 Chin. Phys. B 30 077101
[61] Makris K G, El-Ganainy R, Christodoulides D N and Musslimani Z H 2008 Phys. Rev. Lett. 100 103904
[62] Klaiman S, U Günther and Moiseyev N 2008 Phys. Rev. Lett. 101 080402
[63] Longhi S 2009 Phys. Rev. Lett. 103 123601
[64] Rüter C E, Makris K, El-Ganainy G R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192
[65] Liertzer M, Ge L, Cerjan A, Stone A D, Türeci H E and Rotter S 2012 Phys. Rev. Lett. 108 173901
[66] Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N and Peschel U 2012 Nature 488 167
[67] Peng B, Özdemir S K, Rotter S, Yilmaz H, Liertzer M, Monifi F, Bender C M, Nori F and Yang L 2014 Science 346 328
[68] Lu L, Joannopoulos J D and Soljačić M 2014 Nat. Photon. 8 821
[69] Fleury R, Sounas D and Alù A 2015 Nat. Commu. 6 5905
[70] Jiang X, Qiao Y and Cao J 2021 Chin. Phys. B 30 077101
[71] Kozii V and Fu L 2017 arXiv:1708.05841
[72] Zhou H, Peng C, Yoon Y, Hsu C W, Nelson K A, Fu L, Joannopoulos J D, Soljačić M and Zhen B 2018 Science 359 1009
[73] Zyuzin A A and Zyuzin A Y 2018 Phys. Rev. B 97 041203
[74] Papaj M, Isobe H and Fu L 2019 Rev. B 99 201107
[75] Zyuzin A A and Simon P 2019 Phys. Rev. B 99 165145
[76] Moors K, Zyuzin A A, Zyuzin A Y, Tiwari R P and Schmidt T L 2019 Phys. Rev. B 99 041116
[77] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[78] Yao S, Song F and Wang Z 2018 Phys. Rev. Lett. 121 136802
[79] Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 170401
[80] Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 246801
[81] Lee C H and Thomale R 2019 Phys. Rev. B 99 201103
[82] Martinez Alvarez V M, Barrios Vargas J E, Berdakin M and Foa Torres L E F 2018 EPJ-Special Topics 227 1295
[83] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401
[84] Xiao L, Deng T, Wang K, Zhu G, Wang Z, Yi W and Xue P 2020 Nat. Phys. 16 761
[85] Helbig T, Hofmann T, Imhof S, Abdelghany M, Kiessling T, Molenkamp L W, Lee C H, Szameit A, Greiter M and Thomale R 2020 Nat. Phys. 16 747
[86] Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 170401
[87] Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402
[88] Luo K, Feng J, Zhao Y X and Yu R 2018 arXiv: 181009231
[89] Carlström J and Bergholtz E J 2018 Phys. Rev. A 98 042114
[90] Sokolov A V, Andrianov A A and Cannata F 2006 J. Phys. A Math. Gen. 39 10207
[91] Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808
[92] Qiu X, Deng T S, Hu Y, Xue P and Yi W 2019 iScience 20 392
[93] Edvardsson E, Kunst F K and Bergholtz E J 2019 Phys. Rev. B 99 081302
[94] Lee T E 2016 Phys. Rev. Lett. 116 133903
[95] Xiong Y 2018 J. Phys. Commun. 2 035043
[96] Shen H and Fu L 2018 Phys. Rev. Lett. 121 026403
[97] Wang B X and Zhao C Y 2018 Phys. Rev. B 98 165435
[98] Wang H, Ruan J and Zhang H 2019 Phys. Rev. B 99 075130
[99] Lee C H, Li L and Gong J 2019 Phys. Rev. Lett. 123 016805
[100] Jiang H, Lang L J, Yang C, Zhu S L and Chen S 2019 Phys. Rev. B 100 054301
[101] Ezawa M 2019 Phys. Rev. B 100 045407
[102] Borgnia D S, Jura Kruchkov A and Slager R J 2020 Phys. Rev. Lett. 124 056802
[103] Luo X W and Zhang C 2019 Phys. Rev. Lett. 123 073601
[104] Deng T S and Yi W 2019 Phys. Rev. B 100 035102
[105] Ghatak A and Das T 2019 J. Phys.s: Condens. Matter 31 263001
[106] Yokomizo K and Murakami S 2019 Phys. Rev. Lett. 123 066404
[107] Li L, Lee C H, Mu S and Gong J 2020 Nat. Commun. 11 5491
[108] Jin L and Song Z 2019 Phys. Rev. B 99 081103
[109] Kawabata K, Shiozaki K and Ueda M 2018 Phys. Rev. B 98 165148
[110] Zyuzin A A and Zyuzin A Y 2018 Phys. Rev. B 97 041203
[111] Carlström J and Bergholtz E J ¨ 2018 Phys. Rev. A 98 042114
[112] Cerjan A, Huang S, Chen K P, Chong Y and Rechts-man M C 2019 Nature Photonics 13 623
[113] Budich J C, Carlström J, Kunst F K, and Bergholtz E J 2019 Phys. Rev. B 99 041406
[114] Carlström J, Stålhammar M, Budich J C and Bergholtz E J 2019 Phys. Rev. B 99 161115
[115] Moors K, Zyuzin A A, Zyuzin A Y, Tiwari R P and Schmidt T L 2019 Phys. Rev. B 99 041116
[116] Bergholtz E J and Budich J C 2019 Phys. Rev. Research 1 012003
[117] Yoshida T, Peters R, Kawakami N and Hatsugai Y 2019 Phys. Rev. B 99 121101
[118] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401
[119] Morimoto T and Furusaki A 2014 Phys. Rev. B 89 235127

Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

Metrics

本文评价

推荐阅读 0

[1]	Boxue Zhang(张博学), Qingya Li(李青铔), Xiao Zhang(张笑), and Ching Hua Lee(李庆华). Real non-Hermitian energy spectra without any symmetry[J]. 中国物理B, 2022, 31(7): 70308-070308.
[2]	Hui Jiang and Ching Hua Lee. Filling up complex spectral regions through non-Hermitian disordered chains[J]. 中国物理B, 2022, 31(5): 50307-050307.
[3]	Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎). Topological properties of non-Hermitian Creutz ladders[J]. 中国物理B, 2022, 31(1): 10310-010310.
[4]	刘建森, 韩炎桢, 刘承师. A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect[J]. 中国物理B, 2020, 29(1): 10302-010302.