Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
Jiong-Hao Wang1 , Yu-Liang Tao1 , and Yong Xu1,2*
1 Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China2 Shanghai Qi Zhi Institute, Shanghai 200030, China
Abstract ：Non-Hermitian materials can exhibit not only exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is unclear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functions can only affect the Hall conductivity. However, we are surprised to find a non-Hermitian anomalous Berry connection induced anomalous linear longitudinal conductivity independent of the scattering time. We also show the emergence of a second-order nonlinear longitudinal conductivity induced by non-Hermitian anomalous Berry connection, violating a well-known fact of its absence in a Hermitian system with symmetric energy spectra. These anomalous phenomena are illustrated in a pseudo-Hermitian system with large non-Hermitian anomalous Berry connection. Finally, we propose a practical scheme to realize the anomalous oscillations in an optical system.
收稿日期: 2021-11-12
Express Letter
出版日期: 2021-12-16
:
03.65.Vf
(Phases: geometric; dynamic or topological)
72.90.+y
(Other topics in electronic transport in condensed matter)
[1] El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, and Christodoulides D N 2018 Nat. Phys. 14 11 [2] Xu Y 2019 Front. Phys. 14 43402 [3] Zhang D W, Zhu Y Q, Zhao Y X, Yan H, and Zhu S L 2019 Adv. Phys. 67 253 [4] Ashida Y, Gong Z, and Ueda M 2020 Adv. Phys. 69 249 [5] Bergholtz E J, Budich J C, and Kunst F K 2021 Rev. Mod. Phys. 93 015005 [6] 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 [7] Xu Y, Wang S T, and Duan L M 2017 Phys. Rev. Lett. 118 045701 [8] Cerjan A, Xiao M, Yuan L, and Fan S 2018 Phys. Rev. B 97 075128 [9] Zhou H Y, Peng C, Yoon Y, Hsu C W, Nelson K A, Fu L, Joannopoulos J D, Soljačić M, and Zhen B 2018 Science 359 1009 [10] Carlström J and Bergholtz E J 2018 Phys. Rev. A 98 042114 [11] Yang Z and Hu J 2019 Phys. Rev. B 99 041202(R) [12] Wang H Q, Ruan J W, and Zhang H J 2019 Phys. Rev. B 99 075130 [13] Özdemir S K, Rotter S, Nori F, and Yang L 2019 Nat. Mater. 18 783 [14] Cerjan A, Huang S, Wang M, Chen K P, Chong Y, and Rechtsman M C 2019 Nat. Photon. 13 623 [15] Kawabata K, Bessho T, and Sato M 2019 Phys. Rev. Lett. 123 066405 [16] Zhang X F, Ding K, Zhou X J, Xu J, and Jin D F 2019 Phys. Rev. Lett. 123 237202 [17] Hou J, Li Z, Luo X W, Gu Q, and Zhang C 2020 Phys. Rev. Lett. 124 073603 [18] Yang Z, Chiu C K, Fang C, and Hu J 2020 Phys. Rev. Lett. 124 186402 [19] Wang K K, Xiao L, Budich J C, Yi W, and Xue P 2021 Phys. Rev. Lett. 127 026404 [20] Kozii V and Fu L 2017 arXiv:1708.05841 [cond-mat.mes-hall] [21] Zyuzin A A and Zyuzin A Y 2018 Phys. Rev. B 97 041203(R) [22] Yoshida T, Peters R, and Kawakami N 2018 Phys. Rev. B 98 035141 [23] Zhao P L, Wang A M, and Liu G Z 2018 Phys. Rev. B 98 085150 [24] Yoshida T, Peters R, Kawakami N, and Hatsugai Y 2019 Phys. Rev. B 99 121101(R) [25] Nagai Y, Qi Y, Isobe H, Kozii V, and Fu L 2020 Phys. Rev. Lett. 125 227204 [26] Okuma N and Sato M 2021 Phys. Rev. Lett. 126 176601 [27] Tao Y L, Qin T, and Xu Y 2021 arXiv:2111.03348 [cond-mat.str-el] [28] Chang M C and Niu Q 1995 Phys. Rev. Lett. 75 1348 [29] Sundaram G and Niu Q 1999 Phys. Rev. B 59 14915 [30] Xiao D, Shi J, and Niu Q 2005 Phys. Rev. Lett. 95 137204 [31] Xiao D, Chang M C, and Niu Q 2010 Rev. Mod. Phys. 82 1959 [32] Gao Y, Yang S A, and Niu Q 2014 Phys. Rev. Lett. 112 166601 [33] Sodemann I and Fu L 2015 Phys. Rev. Lett. 115 216806 [34] Silberstein N, Behrends J, Goldstein M, and Ilan R 2020 Phys. Rev. B 102 245147 [35] See the Supplementary Material [36] Blohmann C 2003 Eur. Phys. J. C 30 435 [37] Zhu Y Q, Zheng W, Zhu S L, and Palumbo G 2021 Phys. Rev. B 104 205103 [38] Mostafazadeh A 2002 J. Math. Phys. 43 205 [39] Zhang K, Yang Z, and Fang C 2020 Phys. Rev. Lett. 125 126402 [40] Okuma N, Kawabata K, Shiozaki K, and Sato M 2020 Phys. Rev. Lett. 124 086801 [41] Borgnia D S, Kruchkov A J, and Slager R J 2020 Phys. Rev. Lett. 124 056802 [42] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803 [43] Xiong Y 2018 J. Phys. Commun. 2 035043 [44] Mao L, Deng T, and Zhang P 2021 Phys. Rev. B 104 125435 [45] Hafezi M, Demler E A, Lukin M D, and Taylor J M 2011 Nat. Phys. 7 907 [46] Yanik M F and Fan S 2004 Phys. Rev. Lett. 92 083901 [47] Longhi S, Gatti D, and Valle G D 2015 Sci. Rep. 5 13376
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
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[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2022, Vol. 39 
