Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

doi:10.1088/1674-1056/ac9046

中国物理B ›› 2023, Vol. 32 ›› Issue (2): 20305-020305.doi: 10.1088/1674-1056/ac9046

Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

Junjie Wang(王俊杰)¹, Fude Li(李福德)¹, and Xuexi Yi(衣学喜)^1,2,†

1 Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China;
2 Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China

收稿日期:2022-03-08 修回日期:2022-08-17 接受日期:2022-09-08 出版日期:2023-01-10 发布日期:2023-01-31
通讯作者: Xuexi Yi E-mail:yixx@nenu.edu.cn
基金资助:
The authors acknowledge Hongzhi Shen and Weijun Cheng for helpful comments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12175033 and 12147206).

Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

Junjie Wang(王俊杰)¹, Fude Li(李福德)¹, and Xuexi Yi(衣学喜)^1,2,†

1 Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China;
2 Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China

Received:2022-03-08 Revised:2022-08-17 Accepted:2022-09-08 Online:2023-01-10 Published:2023-01-31
Contact: Xuexi Yi E-mail:yixx@nenu.edu.cn
Supported by:
The authors acknowledge Hongzhi Shen and Weijun Cheng for helpful comments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12175033 and 12147206).

摘要/Abstract

摘要： Two-band model works well for Hall effect in topological insulators. It turns out to be non-Hermitian when the system is subjected to environments, and its topology characterized by Chern numbers has received extensive studies in the past decades. However, how a non-Hermitian system responses to an electric field and what is the connection of the response to the Chern number defined via the non-Hermitian Hamiltonian remains barely explored. In this paper, focusing on a k-dependent decay rate, we address this issue by studying the response of such a non-Hermitian Chern insulator to an external electric field. To this aim, we first derive an effective non-Hermitian Hamiltonian to describe the system and give a specific form of k-dependent decay rate. Then we calculate the response of the non-Hermitian system to a constant electric field. We observe that the environment leads the Hall conductance to be a weighted integration of curvature of the ground band and hence the conductance is no longer quantized in general. And the environment induces a delay in the response of the system to the electric field. A discussion on the validity of the non-Hermitian model compared with the master equation description is also presented.

关键词: Hall conductance, non-Hermitian, topological insulators

Abstract: Two-band model works well for Hall effect in topological insulators. It turns out to be non-Hermitian when the system is subjected to environments, and its topology characterized by Chern numbers has received extensive studies in the past decades. However, how a non-Hermitian system responses to an electric field and what is the connection of the response to the Chern number defined via the non-Hermitian Hamiltonian remains barely explored. In this paper, focusing on a k-dependent decay rate, we address this issue by studying the response of such a non-Hermitian Chern insulator to an external electric field. To this aim, we first derive an effective non-Hermitian Hamiltonian to describe the system and give a specific form of k-dependent decay rate. Then we calculate the response of the non-Hermitian system to a constant electric field. We observe that the environment leads the Hall conductance to be a weighted integration of curvature of the ground band and hence the conductance is no longer quantized in general. And the environment induces a delay in the response of the system to the electric field. A discussion on the validity of the non-Hermitian model compared with the master equation description is also presented.

Key words: Hall conductance, non-Hermitian, topological insulators

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

03.65.Vf

Junjie Wang(王俊杰), Fude Li(李福德), and Xuexi Yi(衣学喜). Hall conductance of a non-Hermitian two-band system with k-dependent decay rates[J]. 中国物理B, 2023, 32(2): 20305-020305.

Junjie Wang(王俊杰), Fude Li(李福德), and Xuexi Yi(衣学喜). Hall conductance of a non-Hermitian two-band system with k-dependent decay rates[J]. Chin. Phys. B, 2023, 32(2): 20305-020305.

参考文献

[1] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[2] Yang Z, Chiu C K, Fang C and Hu J 2020 Phys. Rev. Lett. 124 186402
[3] Bernevig B A and Hughes T L 2013 Topological insulators and topeological superconductors (Princeton: Princeton University Press)
[4] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[5] Thouless D J, Kohmoto M, Nightingale M P and Nijs M den 1982 Phys. Rev. Lett. 49 405
[6] Klitzing K V, Dorda G and Pepper M 1980 Phys. Rev. Lett. 45 494
[7] Haldane F D M 1980 Phys. Rev. Lett. 45 494
[8] San-Jose P, Cayao J, Prada E and Aguado R 2016 Sci. Rep. 6 21427
[9] Leykam D, Bliokh K Y, Huang C, Chong Y D and Nori F 2017 Phys. Rev. Lett. 118 040401
[10] Rudner M S and Levitov L S 2009 Phys. Rev. Lett. 102 065703
[11] Shen H, Zhen B and Fu L 2018 Phys. Rev. Lett. 120 146402
[12] Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808
[13] Yao S Y and Wang Z 2018 Phys. Rev. Lett. 121 086803
[14] Yao S Y, Song F and Wang Z 2018 Phys. Rev. Lett. 121 136802
[15] Xiong Y 2018 J. Phys. Commun. 2 035043
[16] 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. 10 1038
[17] Yang Z S, Zhang K, Fang C and Hu J P 2020 Phys. Rev. Lett. 125 226402
[18] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801
[19] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401(R)
[20] Lee C H and Thomale R 2019 Phys. Rev. B 99 201103(R)
[21] Li L H, Lee C H and Gong J B 2020 Phys. Rev. Lett. 124 250402
[22] Hofmann T, Helbig T, Schindler F, Salgo N, Brzezińska M, Greiter M, Kiessling T, Wolf D, Vollhardt A, Kabaši A, Lee Ching Hua, Bilušić A, Thomale R and Neupert T 2020 Phys. Rev. Res. 2 023265
[23] Torres Luis E F Foa 2020 J. Phys. Mater. 3 014002
[24] Zhang K, Yang Z S and Fang C 2020 Phys. Rev. Lett. 125 126402
[25] Yi Y F and Yang Z S 2020 Phys. Rev. Lett. 125 186802
[26] Lee T E 2016 Phys. Rev. Lett. 116 133903
[27] Kawabata K, Shiozaki K and Ueda M 2018 Phys. Rev. B 98 165148
[28] Lieu S 2018 Phys. Rev. B 97 045106
[29] Lieu S 2018 Phys. Rev. B 98 115135
[30] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079
[31] Kawabata K, Higashikawa S, Gong Z, Ashida Y and Ueda M 2019 Nat. Commun. 10 297
[32] Liang S D and Huang G Y 2013 Phys. Rev. A 87 012118
[33] Wang J H, Tao Y L and Xu Y 2022 Chin. Phys. Lett. 39 010301
[34] Liu H F, Su Z X, Zhang Z Q and Jiang H 2020 Chin. Phys. B 29 050502
[35] Hirsbrunner M R, Philip T M and Gilbert M J 2019 Phys. Rev. B 100 081104(R)
[36] Chen Y and Zhai H 2018 Phys. Rev. B 98 245130
[37] Philip T M, Hirsbrunner M R and Gilbert M J 2018 Phys. Rev. B 98 155430
[38] Pan L, Chen X, Chen Y and Zhai H 2020 Nat. Phys. 16 767
[39] Schomerus H 2020 Phys. Rev. Res. 2 013058
[40] Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C and Xue P 2017 Nat. Phys. 13 1117
[41] Lee C H, Li L H, Thomale Ronny and Gong J B 2020 Phys. Rev. B 102 085151
[42] 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
[43] 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
[44] Rechtsman M C, Plotnik Y, Lumer Y, Nolte S, Rudner M S, Segev M and Szameit A 2015 Phys. Rev. Lett. 115 040402
[45] Zhao H, Miao P, Teimourpour M H, Malzard S, El-Ganainy R, Schomerus H and Feng L 2018 Nat. Commun. 9 981
[46] Pan M, Zhao H, Miao P, Longhi S and Feng L 2018 Nat. Commun. 9 1308
[47] Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C and Szameit A 2017 Nat. Mater. 16 433
[48] Rigolin G, Ortiz G and Ponce V H 2008 Phys. Rev. A 78 052508
[49] Bohm A, Mostafazadeh A, Koizumi H, Niu Q and Zwanziger J 2003 The geometric phase in quantum systems (Berlin: Springer)
[50] Ibáñez S and Muga J G 2014 Phys. Rev. A 89 033403
[51] Weng H W, Yu R, Hu X, Dai X and Fang Z 2015 Adv. Phys. 64 227
[52] Peierls R 1993 Z. Physik 80 763
[53] Zhang W Q, Shen H Z and Yi X X 2018 Sci. Rep. 8 1475
[54] Shen H Z, Zhang S S, Dai C M and Yi X X 2018 J. Phys. A: Math. Theor. 51 065302
[55] Orszag M 2000 Quantum Optics (Berlin: Springer)
[56] Breuer H P and Petruccione F 2007 The Theory of Open Quantum Systems (Oxford: Oxford University Press)
[57] Dürr S, Garcia-Ripoll J J, Syassen N, Bauer D M, Lettner M, Cirac J I and Rempe G 2009 Phys. Rev. A 79 023614
[58] Reiter F and Sorensen A S 2012 Phys. Rev. A 85 032111
[59] Reiter F, Kastoryano M J and Sorensen A S 2012 New J. Phys. 14 053022
[60] Lee T E and Chan C K 2014 Phys. Rev. X 4 041001
[61] Ashida Y, Furukawa S and Ueda M 2016 Phys. Rev. A 94 053615
[62] Ashida Y, Furukawa S and Ueda M 2017 Nat. Commun. 8 15791
[63] Yamamoto K, Nakagawa M, Adachi K, Takasan K, Ueda M and Kawakami N 2019 Phys. Rev. Lett. 123 123601
[64] Ziesche P 1987 J. Phys. A: Math. Gen. 20 2859
[65] Dattoli G and Torre A 1990 Phys. Rev. A 42 1467
[66] Li D X, Shen H Z, Liu H D and Yi X X Sci. Rep. 8 1475
[67] Shen H Z, Wang W and Yi X X 2014 Sci. Rep. 10 1038
[68] Qi L X, Wu Y S and Zhang S C 2006 Phys. Rev. B 74 085308
[69] Qiao Z, Yang S A, Feng W, Tse W K, Ding J, Yao Y, Wang J and Niu Q 2010 Phys. Rev. B 82 161414(R)

Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

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