-
拓扑边界态因在带隙中的鲁棒性和无损耗的传输特性备受关注，但在复杂系统中实现其稳定激发仍是一个挑战。本文提出了一种利用亚对称性保护的边界态与长程非互易耦合系数，实现具有拓扑选择性的非厄密趋肤效应 (Non-Hermitian Skin Effect, NHSE) 的方法。该方法能够选择性地对平庸体态施加非厄密趋肤效应，同时保持拓扑边界态不受影响，从而实现拓扑模式与体态模式在空间上的有效分离，并在能带密集的系统中实现鲁棒的边界态激发。此外，我们将该模型扩展到二维体系，实现了角态与体态模式的有效分离。我们通过紧束缚模型进行理论预测，分析了该模型中非厄密效应对能谱和趋肤性质的调控机制，并利用有限元仿真在光学耦合环中验证了这一机制的可行性，研究了非厄密趋肤效应的本征态特性，并实现了拓扑态的鲁棒激发。该机制将非厄密物理与拓扑光子学相结合，为提升光子系统中信号的稳定性提供了新的思路与方向。Topologically protected waveguides have attracted growing interest due to their robustness against disorder and defects. In parallel, the advent of non-Hermitian physics—with its inherent gain-and-loss mechanisms—has introduced new tools for manipulating wave localization and transport. However, most attempts to combine non-Hermitian effects with topological systems impose the non-Hermitian skin effect (NHSE) uniformly on all modes, lacking selectivity for topological states.
In this work, we propose a scheme that realizes a topologically selective NHSE by combining sub-symmetry-protected boundary modes with long-range, non-reciprocal couplings. In a modified Su–Schrieffer–Heeger (SSH) chain, we analytically demonstrate that even in a spectrum densely populated with bulk states, a robust zero-energy edge mode can be preserved while the NHSE is selectively applied to the trivial bulk modes, achieving spatial separation between topological and bulk states. By tuning the long-range couplings, we observe a non-Hermitian phase transition in the complex energy spectrum: it evolves from a closed loop (circle), to an arc, and then to a loop with reversed winding direction. These transitions correspond to a leftward NHSE, the disappearance of the NHSE, and a rightward NHSE, respectively. Calculating the generalized Brillouin zone (GBZ), we confirm this transition by observing the GBZ crossing the unit circle, indicating a change in the NHSE direction.
We further extend our model to a two-dimensional higher-order SSH lattice, where selective non-Hermitian modulation enables clear spatial separation between topological corner states and bulk modes. To quantify this, we compute the local density of states (LDOS) in the complex energy plane for site 0 (a topologically localized corner) and site 288 (a region exhibiting NHSE). The LDOS comparison reveals that the topological states are primarily localized at site 0, while bulk states affected by NHSE accumulate at site 288.
To validate the theoretical predictions, we perform finite-element simulations of optical resonator arrays employing whispering-gallery modes. By tuning the coupling distances and incorporating gain/loss through refractive index engineering, we replicate the modified SSH model and confirm the selective localization of topological and bulk modes.
Our results demonstrate a robust method for the selective excitation and spatial control of topological states in non-Hermitian systems, providing a foundation for future low-crosstalk, high-stability topological photonic devices. -
[1] Su W P, Schrieffer J R, Heeger A J 1979 Physical Review Letters 421698
[2] Wang Z, Chong Y, Joannopoulos J D, Soljačić M 2009 Nature 461772
[3] Hafezi M, Demler E A, Lukin M D, Taylor J M 2011 Nature Physics 7907
[4] Fang K, Yu Z, Fan S 2012 Nature Photonics 6782
[5] Hafezi M, Mittal S, Fan J, Migdall A, Taylor J M 2013 Nature Photonics 71001
[6] Khanikaev A B, Hossein Mousavi S, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nature Materials 12233
[7] Wu L H, Hu X 2015 Physical Review Letters 114223901
[8] Ma T, Shvets G 2016 New Journal of Physics 18025012
[9] Wang Z Y, Chen F J, Xi X, Gao Z, Yang Y H 2024 Acta Physica Sinica 73064201(in Chinese) [王子尧, 陈福家, 郗翔, 高振, 杨怡豪2024物理学报73064201]
[10] Wang H F, Xie B Y, Zhan P, Lu M H, Chen Y F 2019 Acta Physica Sinica 68224206(in Chinese) [王洪飞, 解碧野, 詹鹏, 卢明辉, 陈延峰2019物理学报68, 224206]
[11] Xiao-Chen S, Cheng H, Ming-Hui L, Yan-Feng C 2017 Acta Physica Sinica 66224203(in Chinese) [孙晓晨, 何程, 卢明辉, 陈延峰2017物理学报66224203]
[12] Xie B, Wang H X, Zhang X, Zhan P, Jiang J H, Lu M, Chen Y 2021 Nature Reviews Physics 3520
[13] Benalcazar W A, Noh J, Wang M, Huang S, Chen K P, Rechtsman M C 2022 Physical Review B 105195129
[14] Wang Q, Xue H, Zhang B, Chong Y 2020 Physical Review Letters 124243602
[15] Hu J R, Kong P, Bi R G, Deng K, Zhao H P 2022 Acta Physica Sinica 71054301(in Chinese) [胡军容, 孔鹏, 毕仁贵, 邓科, 赵鹤平2022物理学报71054301]
[16] Yan Z B 2019 Acta Physica Sinica 68226101(in Chinese) [严忠波2019物理学报68226101]
[17] Wang Z, Wang X, Hu Z, Bongiovanni D, Jukić D, Tang L, Song D, Morandotti R, Chen Z, Buljan H 2023 Nature Physics 1
[18] Bender C M, Boettcher S 1998 Physical Review Letters 805243
[19] Bender C M 2007 Reports on Progress in Physics 70947
[20] Bender C, Boettcher S, Meisinger P 1999 Journal of Mathematical Physics 402201
[21] Yao S, Wang Z 2018 Physical Review Letters 121086803
[22] Lee T E 2016 Physical Review Letters 116133903
[23] Okuma N, Kawabata K, Shiozaki K, Sato M 2020 Physical Review Letters 124086801
[24] Song W, Sun W, Chen C, Song Q, Xiao S, Zhu S, Li T 2019 Physical Review Letters 123165701
[25] Li Y, Liang C, Wang C, Lu C, Liu Y C 2022 Physical Review Letters 128223903
[26] Wang W, Wang X, Ma G 2022 Nature 60850
[27] Zhu W, Gong J 2022 Physical Review B 106035425
[28] Liu G G, Mandal S, Zhou P, Xi X, Banerjee R, Hu Y H, Wei M, Wang M, Wang Q, Gao Z, Chen H, Yang Y, Chong Y, Zhang B 2024 Physical Review Letters 132113802
[29] Song W, Lin Z, Ji J, Sun J, Chen C, Wu S, Huang C, Yuan L, Zhu S, Li T 2024 Physical Review Letters 132143801
[30] Chen J, Shi A, Peng Y, Peng P, Liu J 2024 Chin. Phys. Lett. 41
[31] Martinez Alvarez V M, Barrios Vargas J E, Foa Torres L E F 2018 Physical Review B 97121401
[32] Pan M, Zhao H, Miao P, Longhi S, Feng L 2018 Nature Communications 91308
[33] Huang Q K L, Liu Y K, Cao P C, Zhu X F, Li Y 2023 Chinese Physics Letters 40106601
[34] Leykam D, Bliokh K Y, Huang C, Chong Y, Nori F 2017 Physical Review Letters 118040401
[35] Liu X, Lin Z, Song W, Sun J, Huang C, Wu S, Xiao X, Xin H, Zhu S, Li T 2024 Physical Review Letters 132016601
[36] Jackiw R, Rebbi C 1976 Physical Review D 133398
[37] Qi X L, Wu Y S, Zhang S C 2006 Physical Review B 74045125
[38] Zhang K, Yang Z, Fang C 2020 Physical Review Letters 125126402
[39] Yang Z, Zhang K, Fang C, Hu J 2020 Physical Review Letters 125226402
[40] Wang Z, Wang X, Li A, Zhang K, Ji Y, Zhong M 2023 Chinese Physics B 32064207
[41] Chen Y T, Wang J W, Chen W J, Xu J 2020 Acta Physica Sinica 69154206(in Chinese) [陈云天, 王经纬, 陈伟锦, 徐竞2020物理学报69154206]
[42] Ozawa T, Price H M, Amo A, Goldman N, Hafezi M, Lu L, Rechtsman M C, Schuster D, Simon J, Zilberberg O, Carusotto I 2019 Reviews of Modern Physics 91015006
[43] Yan Q C, Ma R, Hu X Y, Gong Q H 2023 Chinese Physics B 33010301
[44] Xu Y X, Tang W J, Jiang L W, Wu D X, Wang H, Xu B C, Chen L 2024 Chinese Physics B 33060306
[45] Wu D, Chen J, Su W, Wang R, Wang B, Xing D Y 2023 Communications Physics 61
[46] Xu X W, Li Y Z, Liu Z F, Chen A X 2020 Physical Review A 101063839
计量
- 文章访问数: 10
- PDF下载量: 0
- 被引次数: 0
下载:
