Parity-dependent skin effects and topological properties in the multilayer nonreciprocal Su−Schrieffer−Heeger structures

doi:10.1007/s11467-023-1350-y

Frontiers of Physics

2024, Vol. 19

Issue (3): 33204 https://doi.org/10.1007/s11467-023-1350-y

本期目录

Parity-dependent skin effects and topological properties in the multilayer nonreciprocal Su−Schrieffer−Heeger structures

Jia-Rui Li¹, Cui Jiang², Han Su¹, Di Qi¹, Lian-Lian Zhang¹, Wei-Jiang Gong¹(

)

¹. College of Sciences, Northeastern University, Shenyang 110819, China
². Basic Department, Shenyang Institute of Engineering, Shenyang 110136, China

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Abstract：

We concentrate on the skin effects and topological properties in the multilayer non-Hermitian Su−Schrieffer−Heeger (SSH) structure, by taking into account the nonreciprocal couplings between the different sublattices in the unit cells. Following the detailed demonstration of the theoretical method, we find that in this system, the skin effects and topological phase transitions induced by nonreciprocal couplings display the apparent parity effect, following the increase of the layer number of this SSH structure. On the one hand, the skin effect is determined by the parity of the layer number of this SSH system, as well as the parity of the band index of the bulk states. On the other hand, for the topological edge modes, such an interesting parity effect can also be observed clearly. Next, when the parameter disorders are taken into account, the zero-energy edge modes in the odd-layer structures tend to be more robust, whereas the other edge modes are easy to be destroyed. In view of these results, it can be ascertained that the findings in this work promote to understand the influences of nonreciprocal couplings on the skin effects and topological properties in the multilayer SSH lattices.

Key words： multilayer SSH lattice nonreciprocal couplings band structure skin effect

收稿日期: 2023-05-10 出版日期: 2023-11-10

Corresponding Author(s): Wei-Jiang Gong

引用本文:

. [J]. Frontiers of Physics, 2024, 19(3): 33204.
Jia-Rui Li, Cui Jiang, Han Su, Di Qi, Lian-Lian Zhang, Wei-Jiang Gong. Parity-dependent skin effects and topological properties in the multilayer nonreciprocal Su−Schrieffer−Heeger structures. Front. Phys. , 2024, 19(3): 33204.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-023-1350-y
https://academic.hep.com.cn/fop/CN/Y2024/V19/I3/33204

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1	M. Bender C., C. Brody D., F. Jones H.. Complex extension of quantum mechanics. Phys. Rev. Lett., 2002, 89: 270401
2	V. Konotop V., Yang J., A. Zezyulin D.. Non-linear waves in PT-symmetric systems. Rev. Mod. Phys., 2016, 88: 035002
3	Ashida Y., Gong Z., Ueda M.. Non-Hermitian physics. Adv. Phys., 2020, 69: 249
4	K. Özdemir S., Rotter S., Nori F., Yang L.. Parity−time symmetry and exceptional points in photonics. Nat. Mater., 2019, 18: 783
5	Wu C., Liu N., Chen G., Jia S.. Non-Hermiticity-induced topological transitions in long-range Su−Schrieffer−Heeger models. Phys. Rev. A, 2022, 106: 012211
6	Fan A., D. Liang S.. Complex energy plane and topological invariant in non-Hermitian systems. Front. Phys., 2022, 17: 33501
7	C. Budich J., J. Bergholtz E.. Non-Hermitian topological sensors. Phys. Rev. Lett., 2020, 125: 180403
8	Koch F., C. Budich J.. Quantum non-Hermitian topological sensors. Phys. Rev. Research, 2022, 4: 013113
9	McDonald A., A. Clerk A.. Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics. Nat. Commun., 2020, 11: 5382
10	Parto M., Wittek S., Hodaei H., Harari G.. et al.. Edge-mode lasing in 1D topological active arrays. Phys. Rev. Lett., 2018, 120: 113901
11	Weidemann S., Kremer M., Helbig T., Hofmann T.. et al.. Topological funneling of light. Science, 2020, 368: 311
12	Garmon S., Noba K.. Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su−Schrieffer−Heeger model. Phys. Rev. A, 2021, 104: 062215
13	Li J.-R., Zhang L.-L., Cui W.-B., Gong W.-J.. Topological properties in non-Hermitian tetratomic Su−Schrieffer−Heeger lattices. Phys. Rev. Research, 2022, 4: 023009
14	Yoshida A., Otaki Y., Otaki R., Fukui T.. Edge states, corner states, and flat bands in a two-dimensional PT-symmetric system. Phys. Rev. B, 2019, 100: 125125
15	F. Tzortzakakis A., Katsaris A., E. Palaiodi-mopoulos N., A. Kalozoumis P.. et al.. Topological edge states of the PT-symmetric Su−Schrieffer−Heeger model: An effective two-state description. Phys. Rev. A, 2022, 106: 023513
16	Zhu X., Wang H., K. Gupta S., Zhang H., Xie B., Lu M., Chen Y.. Photonic non-Hermitian skin effect and non-Bloch bulk−boundary correspondence. Phys. Rev. Research, 2020, 2: 013280
17	Xu K., Zhang X., Luo K., Yu R., Li D., Zhang H.. Coexistence of topological edge states and skin effects in the non-Hermitian Su−Schrieffer−Heeger model with long-range nonreciprocal hopping in topoelectric realizations. Phys. Rev. B, 2021, 103: 125411
18	M. Rafi-Ul-Islam S., S. Zhuo B., Haydar S., H. Lee C., B. A. Jalil M.. Critical hybridization of skin modes in coupled non-Hermitian chains. Phys. Rev. Research, 2022, 4: 013243
19	Lin R., Tai T., Li L., H. Lee C.. Topological non-Hermitian skin effect. Front. Phys., 2023, 18: 53605
20	M. Bender C., Boettcher S.. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 1998, 80: 5243
21	M. Bender C.. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys., 2007, 70: 947
22	Longhi S.. Convective and absolute PT-symmetry breaking in tight-binding lattices. Phys. Rev. A, 2013, 88: 052102
23	K. Kunst F., Edvardsson E., C. Budich J., J. Bergholtz E.. Biorthogonal bulk−boundary correspondence in non-Hermitian systems. Phys. Rev. Lett., 2018, 121: 026808
24	Jin L., Wang P., Song Z.. Su−Schrieffer−Heeger chain with one pair of PT-symmetric defects. Sci. Rep., 2017, 7: 5903
25	Xing Y., Qi L., Cao J., Y. Wang D., H. Bai C., F. Wang H., D. Zhu A., Zhang S.. Spontaneous PT-symmetry breaking in non-Hermitian coupled-cavity array. Phys. Rev. A, 2017, 96: 043810
26	S. Li X., Z. Li Z., L. Zhang L., J. Gong W.. PT symmetry of the Su−Schrieffer−Heeger model with imaginary boundary potentials and next-nearest-neighboring coupling. J. Phys. Condens. Matter, 2020, 32: 165401
27	Kawabata K., Ashida Y., Katsura H., Ueda M.. Parity−time-symmetric topological superconductor. Phys. Rev. B, 2018, 98: 085116
28	Klett M., Cartarius H., Dast D., Main J., Wunner G.. Relation between PT-symmetry breaking and topologically nontrivial phases in the Su−Schrieffer−Heeger and Kitaev models. Phys. Rev. A, 2017, 95: 053626
29	Jin L.. Topological phases and edge states in a non-Hermitian trimerized optical lattice. Phys. Rev. A, 2017, 96: 032103
30	L. Zhang L., R. Li J., Zhang D., T. Xu T., B. Cui W., J. Gong W.. PT-symmetric non-Hermitian zigzag-edged ribbon of bilayer photonic graphene. Results in Physics, 2022, 34: 105274
31	M. Zhao X., X. Guo C., P. Kou S., Zhuang L., M. Liu W.. Defective Majorana zero modes in a non-Hermitian Kitaev chain. Phys. Rev. B, 2021, 104: 205131
32	Yuce C., Ramezani H.. Topological states in a non-Hermitian two-dimensional Su−Schrieffer−Heeger model. Phys. Rev. A, 2019, 100: 032102
33	Feng L., El-Ganainy R., Ge L.. Non-Hermitian photonics based on parity−time symmetry. Nature Photon., 2017, 11: 752
34	Regensburger A., Bersch C., A. Miri M., On-ishchukov G., N. Christodoulides D., Peschel U.. Parity−time synthetic photonic lattices. Nature, 2012, 488: 167
35	Wu Y., Zhu B., F. Hu S.. et al.. Floquet control of the gain and loss in a PT-symmetric optical coupler. Front. Phys., 2017, 12: 121102
36	Chen C., Liu Y., Zhao L.. et al.. Asymmetric nonlinear-mode-conversion in an optical waveguide with PT symmetry. Front. Phys., 2022, 17: 52504
37	Stegmaier A., Imhof S., Helbig T., Hofmann T., H. Lee C., Kremer M., Fritzsche A.. et al.. Topological defect engineering and PT symmetry in non-Hermitian electrical circuits. Phys. Rev. Lett., 2021, 126: 215302
38	Lin Z., Schindler J., M. Ellis F., Kottos T.. Experimental observation of the dual behavior of PT-symmetric scattering. Phys. Rev. A, 2012, 85: 050101(R)
39	Lu L., D. Joannopoulos J., Soljăcić M.. Topological photonics. Nature Photon., 2014, 8: 821
40	G. Silveirinha M.. Topological theory of non-Hermitian photonic systems. Phys. Rev. B, 2019, 99: 125155
41	Ozawa T., M. Price H., Amo A., Goldman N., Hafezi M., Lu L., C. Rechtsman M., Schuster D., Simon J., Zilberberg O., Carusotto I.. Topological photonics. Rev. Mod. Phys., 2019, 91: 015006
42	Q. Liang G., D. Chong Y.. Optical resonator analog of a two-dimensional topological insulator. Phys. Rev. Lett., 2013, 110: 203904
43	Hodaei H., A. Miri M., U. Hassan A., E. Hayenga W., Heinrich M., N. Christodoulides D.. et al.. Single mode lasing in transversely multi-moded PT-symmetric microring resonators. Laser Photonics Rev., 2016, 10: 494
44	Y. Fu Y., Fei Y., X. Dong D.. et al.. Photonic spin Hall effect in PT symmetric metamaterials. Front. Phys., 2019, 14: 62601
45	Kang M., Liu F., Li J.. Effective spontaneous PT-symmetry breaking in hybridized metamaterials. Phys. Rev. A, 2013, 87: 053824
46	Sun Y., Tan W., Q. Li H., Li J., Chen H.. Experimental demonstration of a coherent perfect absorber with PT phase transition. Phys. Rev. Lett., 2014, 112: 143903
47	Jing H., K. Ozdemir S., Y. Lü X., Zhang J., Yang L., Nori F.. PT-symmetric phonon laser. Phys. Rev. Lett., 2014, 113: 053604
48	D. Chong Y., Ge L., D. Stone A.. PT-symmetry breaking and laser-absorber modes in optical scattering systems. Phys. Rev. Lett., 2011, 106: 093902
49	Yao S., Wang Z.. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett., 2018, 121: 086803
50	Yao S., Song F., Wang Z.. Non-Hermitian Chern bands. Phys. Rev. Lett., 2018, 121: 136802
51	M. Martinez Alvarez V., E. Barrios Vargas J., E. F. Foa Torres L.. Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points. Phys. Rev. B, 2018, 97: 121401(R)
52	H. Lee C., Thomale R.. Anatomy of skin modes and topology in non-Hermitian systems. Phys. Rev. B, 2019, 99: 201103
53	Weidemann S., Kremer M., Helbig T., Hofmann T., Stegmaier A., Greiter M., Thomale R., Szameit A.. Topological funneling of light. Science, 2020, 19: 311
54	Xiong Y.. Why does bulk boundary correspondence fail in some non-Hermitian topological models. J. Phys. Commun., 2018, 2: 035043
55	S. Deng T., Yi W.. Non-Bloch topological invariants in a non-Hermitian domain wall system. Phys. Rev. B, 2019, 100: 035102
56	Song F., Yao S., Wang Z.. Non-Hermitian topological invariants in real space. Phys. Rev. Lett., 2019, 123: 246801
57	Yokomizo K., Murakami S.. Non-Bloch band theory of non-Hermitian systems. Phys. Rev. Lett., 2019, 123: 066404
58	Xiao L., S. Deng T., K. Wang K., Y. Zhu G., Wang Z., Yi W., Xue P.. Observation of non-Hermitian bulk−boundary correspondence in quantum dynamics. Nat. Phys., 2020, 16: 761
59	C. Cao P., G. Peng Y., Li Y., F. Zhu X.. Phase-locking diffusive skin effect. Chin. Phys. Lett., 2022, 39: 057801
60	Ghatak A., Brandenbourger M., van Wezel J., Coulais C.. Observation of non-Hermitian topology and its bulk−edge correspondence in an active mechanical metamaterial. Proc. Natl. Acad. Sci., 2020, 117: 29561
61	J. Bergholtz E., C. Budich J., K. Kunst F.. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys., 2021, 93: 015005
62	Helbig T., Hofmann T., Imhof S., Abdelghany M., Kiessling T., W. Molenkamp L., H. Lee C., Szameit A., Greiter M., Thomale R.. Chiral voltage propagation and calibration in a topolectrical Chern circuit. Nat. Phys., 2020, 16: 747
63	Xie L., Jin L., Song Zhi. Antihelical edge states in two-dimensional photonic topological metals. Sci. Bull., 2023, 68: 255
64	Kawabata K., Shiozaki K., Ueda M., Sato M.. Symmetry and topology in non-Hermitian physics. Phys. Rev. X, 2019, 9: 041015
65	P. Gong Z., Ashida Y., Kawabata K., Takasan K., Higashikawa S., Ueda M.. Topological phases of non-Hermitian systems. Phys. Rev. X, 2018, 8: 031079
66	Takata K., Notomi M.. Photonic topological insulating phase induced solely by gain and loss. Phy. Rev. Lett., 2018, 121: 213902
67	C. Wu H., Jin L., Song Z.. Topology of an anti-parity−time symmetric non-Hermitian Su−Schrieffer−Heeger model. Phys. Rev. B, 2021, 103: 235110
68	S. Deng T., Yi W.. Non-Bloch topological invariants in a non-Hermitian domain wall system. Phys. Rev. B, 2019, 100: 035102
69	X. Guo C., H. Liu C., M. Zhao X., Liu Y., Chen S.. Exact solution of non-Hermitian systems with generalized boundary conditions: Size-dependent boundary effect and fragility of the skin effect. Phys. Rev. Lett., 2021, 127: 116801
70	R. Li J., Luo C., L. Zhang L., F. Zhang S., P. Zhu P., J. Gong W.. Band structures and skin effects of coupled nonreciprocal Su−Schrieffer−Heeger lattices. Phys. Rev. A, 2023, 107: 022222
71	X. Liu Y., C. Wang Y., J. Liu X., Zhou Q., Chen S.. Exact mobility edges, PT-symmetry breaking, and skin effect in one-dimensional non-Hermitian quasicrystals. Phys. Rev. B, 2021, 103: 014203
72	J. Zhai L., Y. Huang G., Yin S.. Cascade of the delocalization transition in a non-Hermitian interpolating Aubry−André−Fibonacci chain. Phys. Rev. B, 2021, 104: 014202
73	Mejia-Cortes C., I. Molina M.. Interplay of disorder and PT symmetry in one-dimensional optical lattices. Phys. Rev. A, 2015, 91: 033815
74	Jin L., Song Z.. Bulk−boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry. Phys. Rev. B, 2019, 99: 081103(R)
75	Evers F., D. Mirlin A.. Fluctuations of the inverse participation ratio at the Anderson transition. Phys. Rev. Lett., 2000, 84: 3690
76	M. M. Alvarez V., D. Coutinho-Filho M.. Edge states in trimer lattices. Phys. Rev. A, 2019, 99: 013833
77	E. Lee T.. Anomalous edge state in a non-Hermitian lattice. Phys. Rev. Lett., 2016, 116: 133903

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